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2 vol .LIFRARY
I Mtchngan State 9
University
._ _J
This is to certify that the
thesis entitled

IMPLICATIONS OF CLAW MORPHOLOGY FOR POSSIBLE
AQUATIC LOCOMOTION IN PTERANODON

presented by

AMY C SMITH

has been accepted towards fulfillment
of the requirements for the

MS. degree in Geological Sciences

 

 

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2/05 c:/ClRC/DateDue.lndd-p.15

IMPLICATIONS OF CLAW MORPHOLOGY FOR POSSIBLE AQUATIC
LOCOMOTION IN PTERANODON

By

Amy C. Smith

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Geological Sciences

2007

ABSTRACT

IMPLICATIONS OF CLAW MORPHOLOGY FOR POSSIBLE AQUATIC
LOCOMOTION IN PTERANODON

By
Amy C Smith

Previous studies (Bennett 2001 , Bramwell and Whitfield 1974) have suggested
that Pteranodon may have been capable of aquatic locomotion in the epicontinental
seaway that covered Kansas during the Cretaceous. Quantitative morphometrics were
employed here to examine pteranodont pes claw morphology to ascertain how the
morphologies of the claws of this genus relate morphometrically to the claws found on
the pedes of various birds and crocodylians, which served as extant phylogenetic
bracketing taxa for pterosaurs. These taxa included four species of swimming birds, one
wading bird, one terrestrial/perching bird, two species of crocodile, and one species of
alligator, along with one species of Pteranodon.

Homologous landmarks were placed on digital photographs of avian, crocodylian,
and pteranodont claws. Once these landmarks were transformed into Bookstein
coordinates, morphometric data were derived for all specimens. These data were then
analyzed through the use of the programs SYSTAT and Excel in search of statistically
significant differences between homologous claws at significance level a = 0.05.

ANOVA calculations indicated that pteranodont claws are most statistically
similar to those of Scarlet Ibis and the Peacock, somewhat similar to those of Crocodylus
acutus and the Great Auk, and least similar to the Pelican, Whistling Swan, and alligator.
These results indicate that Pteranodon did not actively propel through the water, but may

have been capable of floating or treading water at the surface.

Dedicated to Dr. William Chaisson, whose continued support has always helped me
maintain focus and persistence in pursuing my career.

iii

ACKNOWLEDGEMENTS

This project would not have been possible without the help of many professionals
at several different institutions. The author wishes to thank Michael Gottfried and Danita
Brandt of Michigan State University for guidance and support during this research, and
Robert Anstey of Michigan State University for guidance, support, and instruction in
morphometric methodology. Thanks are also due to S. Christopher Bennett of the Fort
Hays State University Stemberg Museum (Kansas) for advice. The author thanks Laura
Abraczinskas for assistance in accessing extant bird and crocodilian specimens at the
Michigan State University Museum. The author also thanks Janet Hinshaw of the
University of Michigan Zoological Museum of Natural History and Mary Hennen, Paul
Baker, and David Willard of the Field Museum (Chicago) for assistance in accessing
extant bird specimens. Alan Resetar and James Ladonski of the Field Museum facilitated
access to extant crocodilian specimens. The author also acknowledges Larry Martin and
Daniel Williams of the University of Kansas, John Rebar Jr., Richard Zakrzewski, and
Scott Moses of the Stemberg Museum, and Walter Joyce of the Yale Peabody Museum
for allowing access to Pteranodon specimens. The author would like to thank Juan
Alvarez for his time and assistance in fixing and printing the poster used to present this
study at the 2006 GSA conference. This work was supported by a Stephen J. Gould
Student Grant from the Paleontological Society as well as a Shell Oil Company

Fellowship.

iv

TABLE OF CONTENTS

LIST OF TABLES ................................................................................... vii
LIST OF FIGURES ................................................................................. xii
LIST OF EQUATIONS ........................................................................... xvii
INTRODUCTION .................................................................................... 1
Pteranodont Habitat and Food ............................................................. 1
Proposed Terrestrial and Aerial Locomotion of Pteranodon .......................... 2
The Possibility of Pteranodont Aquatic Locomotion ................................... 4
The Extant Phylogenetic Bracket Surrounding Pteranodon ........................... 5
Avian Locomotion .......................................................................... 7
Crocodylian Locomotion .................................................................. 9
The Use of Quantitative Morphometrics .............................................. 10
MATERIALS AND METHODS ................................................................. ll
Specimens Studied ........................................................................ 1 1
Photograph Acquisition and Organization .............................................. 13
Photograph Manipulation ................................................................. 13
Raw Landmark Placement and Claw Orientation ...................................... 14
Raw Landmark Coordinate Input and Transformation ............................... 15
Morphometric Calculations ............................................................... 17
Curvature Equations ....................................................................... 20
Variable Correlation Calculations ....................................................... 22
Organization of Samples for Statistical Analyses ..................................... 22
Creation of Principal Components ...................................................... 23
Claw Phenogram Creation ............................................................... 24
ANOVA Analyses ........................................................................ 24
RESULTS ........................................................................................... 28
Bookstein Coordinates of Claw Landmarks ........................................... 28
Claw Centroid Locations and Sizes ..................................................... 31
Distances Between Claw Bookstein Landmarks ...................................... 32
Angles Between Claw Bookstein Landmarks ......................................... 33
Aspect and Angle Ratios of Claws ...................................................... 34
Claw Curvature Polynomial Coefficients .............................................. 35
Principal Component Variables Generated for Each Claw .......................... 37
Claw Phenograms ........................................................................ 38
ANOVA Results ......................................................................... 42
DISCUSSIONS ..................................................................................... 51
Conclusions Drawn from ANOVA Analyses ......................................... 51
Consistencies and Inconsistencies of the Study ....................................... 54

Arguments for Other Pterosaur Aquatic Locomotion: Soft Part Preservation

Evidence .............................................................................. 55

Arguments for Other Pterosaur Aquatic Locomotion: Ichnological Evidence.....57
Summary and Future Work ............................................................... 58
APPENDICES ....................................................................................... 60
Appendix 1: Photographs with Landmarks Used in Study ........................... 60
Appendix H: Notes on Photographs ..................................................... 65
Appendix III: Raw Coordinates of Claw Landmarks .................................. 66
Appendix IV: Claw Curvature Coordinates and Plots ................................ 67
Appendix V: Lists of Pairs of Correlated Variables ................................. 137

Appendix VI: Principal Component Data within Each Cluster of Each Claw

Phenogram ........................................................................ 139

Appendix VII: Morphometric Data from the Four Pteranodont Claws of Unknown
Articulation ....................................................................... 143

Appendix VIII: Tangential Claw Phenograms ........................................ 154

BIBLIOGRAPHY ................................................................................. 156

vi

LIST OF TABLES

TABLE 1. Classifications of animals used in study ............................................. 6
TABLE 2. Specimen pes types and characteristics .............................................. 7
TABLE 3. Specimens examined. ................................................................. 12
TABLE 4. The Bookstein coordinates of claw landmarks .................................... 29
TABLE 5. Claw centroid locations and sizes ................................................... 31
TABLE 6. Distances between the Bookstein landmarks of each claw ....................... 33

TABLE 7. Angle calculations (in degrees) between Bookstein landmarks l, 2, and 3 of
each claw ................................................................................ 34

TABLE 8. Aspect ratios and ratios of a to [3 of each claw .................................... 35

TABLE 9. Coefficients from polynomial (Y = AX2+BX+CX0) equations of outside and
inside curves with their R2 values, derived from Bookstein coordinates. . .....36

TABLE 10. Principal component variables generated for claw 1 using SYSTAT.........37
TABLE 11. Principal component variables generated for claw 2 using SYSTAT.........37
TABLE 12. Principal component variables generated for claw 3 using SYSTAT. . . . .....38

TABLE 13. Principal component variables generated for claw 4 using SYSTAT.........38

TABLE 14. ANOVA results of claw 1 ........................................................... 43
TABLE 15. ANOVA results of claw 2 ........................................................... 44
TABLE 16. ANOVA results of claw 3 ........................................................... 45

TABLE 17. AN OVA results of all clusters in phenogram, for all principal components of
claw 4 .................................................................................... 47

TABLE 18. List of pairs of clusters in the phenogram of the first claw with one or more
statistically different principal components ........................................ 48

TABLE 19. List of pairs of clusters in the phenogram of the second claw with one or
more statistically different principal components ................................. 49

vii

TABLE 20.

TABLE 21.

TABLE 22.

TABLE 23.

TABLE 24.

TABLE 25.

TABLE 26.

TABLE 27.

TABLE 28.

TABLE 29.

TABLE 30.

TABLE 31.

TABLE 32.

TABLE 33.

TABLE 34.

TABLE 35.

List of pairs of clusters in the phenogram of the third claw with one or more
statistically different principal components......................................50

Summary of AN OVA results for clusters containing claws of other taxa in
comparison with clusters containing the claws of Pteranodon longiceps,
with key ......................................................... . ...................... 51

Notes on photographs used in study ............................................... 65

Raw coordinates of all claw landmarks ........................................... 66

Raw and Bookstein coordinates taken from the outer and inner curves of
FHSM-VP2062, claw 1 ............................................................. 67

Raw and Bookstein coordinates taken from the outer and inner curves of
FHSM-VP2062, claw 2 .............................................................. 69

Raw and Bookstein coordinates taken from the outer and inner curves of
FHSM-VP2062, claw 3 ............................................................. 71

Raw and Bookstein coordinates taken from the outer and inner curves of
FHSM-VP2062, claw 4 .............................................................. 73

Raw and Bookstein coordinates taken from the outer and inner curves of
UM-P, claw 1 ......................................................................... 75

Raw and Bookstein coordinates taken from the outer and inner curves of
UM-P, claw 2 ......................................................................... 77

Raw and Bookstein coordinates taken from the outer and inner curves of
UM-P, claw 3 ......................................................................... 79

Raw and Bookstein coordinates taken from the outer and inner curves of
UM-P, claw 4 ........................................................................ 81

Raw and Bookstein coordinates taken from the outer and inner curves of
UM-WS, claw 2 ...................................................................... 83

Raw and Bookstein coordinates taken from the outer and inner curves of
UM—WS, claw 3 ...................................................................... 85

Raw and Bookstein coordinates taken from the outer and inner curves of
UM-WS, claw 4 ...................................................................... 87

Raw and Bookstein coordinates taken from the outer and inner curves of C-
GBBG, claw 2 ........................................................................ 89

viii

TABLE 36.

TABLE 37.

TABLE 38.

TABLE 39.

TABLE 40.

TABLE 41.

TABLE 42.

TABLE 43.

TABLE 44.

TABLE 45.

TABLE 46.

TABLE 47.

TABLE 48.

TABLE 49.

TABLE 50.

Raw and Bookstein coordinates taken from the outer and inner curves of C-
GBBG, claw 3 ........................................................................ 90

Raw and Bookstein coordinates taken from the outer and inner curves of C-
GBBG, claw 4 ....................................................................... 91

Raw and Bookstein coordinates taken from the outer and inner curves of C-
PI claw 2 .............................................................................. 93

Raw and Bookstein coordinates taken from the outer and inner curves of C-
PI claw 3 .............................................................................. 95

Raw and Bookstein coordinates taken from the outer and inner curves of C-
PI claw 3 .............................................................................. 97

Raw and Bookstein coordinates taken from the outer and inner curves of C-
81 claw 1 .............................................................................. 98

Raw and Bookstein coordinates taken from the outer and inner curves of C-
81 claw 2 .............................................................................. 99

Raw and Bookstein coordinates taken from the outer and inner curves of C-
81 claw 3 ............................................................................ 101

Raw and Bookstein coordinates taken from the outer and inner curves of C-
SI claw 4 ............................................................................ 102

Raw and Bookstein coordinates taken from the outer and inner curves of C-
PC claw 3 ............................................................................ 103

Raw and Bookstein coordinates taken from the outer and inner curves of C-
PC claw 4 ........................................................................... 104

Raw and Bookstein coordinates taken from the outer and inner curves of
MSU—PA claw l .................................................................... 106

Raw and Bookstein coordinates taken from the outer and inner curves of
MSU-PA claw 2 .................................................................... 108

Raw and Bookstein coordinates taken from the outer and inner curves of
MSU-PA claw 3 .................................................................... 110

Raw and Bookstein coordinates taken from the outer and inner curves of
MSU-PA claw 4 .................................................................... l 13

ix

TABLE 51.

TABLE 52.

TABLE 53.

TABLE 54.

TABLE 55.

TABLE 56.

TABLE 57.

TABLE 58.

TABLE 59.

TABLE 60.

TABLE 61.

TABLE 62.

TABLE 63.

TABLE 64.

TABLE 65.

Raw and Bookstein coordinates taken from the outer and inner curves of

C22026 claw 1 ...................................................................... l 16
Raw and Bookstein coordinates taken from the outer and inner curves of
C22026 claw 2 ..................................................................... 119
Raw and Bookstein coordinates taken from the outer and inner curves of
C22026 claw 3 ...................................................................... 122
Raw and Bookstein coordinates taken from the outer and inner curves of
C213395 claw l .................................................................... 124
Raw and Bookstein coordinates taken from the outer and inner curves of C-
CAD claw 2 .......................................................................... 126
Raw and Bookstein coordinates taken from the outer and inner curves of C-
CAD claw 3 .......................................................................... 128
Raw and Bookstein coordinates taken from the outer and inner curves of
C3101] claw 3 ...................................................................... 130
Raw and Bookstein coordinates taken from the outer and inner curves of
C3132] claw l ..................................................................... 132
Raw and Bookstein coordinates taken from the outer and inner curves of
C3132l claw 3 ...................................................................... 134
List of pairs of positively correlated morphometric variables ................ 137
List of pairs of negatively correlated morphometric variables ................ 138
Principal component data within each cluster in the phenogram of claw
l ...................................................................................... 139
Principal component data within each cluster in the phenogram of claw
2 ...................................................................................... 140
Principal component data within each cluster in the phenogram of claw
3 ....................................................................................... 141
Principal component data within each cluster in the phenogram of claw

4 ....................................................................................... 142

TABLE 66. Claw centroid locations and sizes of the four claws of unknown
articulations ............................................................................ 143

TABLE 67. Distances between the Bookstein landmarks of each claw of unknown
articulation .......................................................................... 143

TABLE 68. Angles (in degrees) between Bookstein landmarks 1, 2, and 3 of each claw of
unknown articulation .............................................................. 143

TABLE 69. Aspect ratios and ratios of a to B of each claw with unknown
articulation .......................................................................... 143

TABLE 70. Coefficients from polynomial (Y = AX2+BX+CX0) equations of outside and
inside curves of the four claws with unknown articulations with their R2
values, derived from Bookstein coordinates .................................... 144

TABLE 71. Raw and Bookstein coordinates taken from the outer and inner curves of
KU49399, unknown claw 1 ....................................................... 145

TABLE 72. Raw and Bookstein coordinates taken from the outer and inner curves of
KU49399, unknown claw 2 ....................................................... 146

TABLE 73. Raw and Bookstein coordinates taken from the outer and inner curves of
YPM2554, unknown claw 3 ...................................................... 149

TABLE 74. Raw and Bookstein coordinates taken from the outer and inner curves of
YPM2436, unknown claw 4 ...................................................... 151

xi

LIST OF FIGURES

FIGURE 1. Relationships of genera used in study ............................................... 6
FIGURE 2. Locations of the four landmarks on avian, crocodilian, and

pteranodont claws after reorientation ............................................. 15
FIGURE 3. Claw landmarks with an example set of Bookstein coordinates ................ 17

FIGURE 4. A. Example of superposition of a triangle (shown in dashed lines) drawn
from connecting landmarks l, 2, and 3. B. Locations of angle and line

designations in the triangle between landmarks 1, 2, and 3 .................... 19
FIGURE 5. The inner and outer curve of any given claw ...................................... 21
FIGURE 6. Bookstein coordinates of landmark 3 of all claws ................................ 30
FIGURE 7. Bookstein coordinates of landmark 4 of all claws ................................ 30
FIGURE 8. Phenogram of digit 1 claws, based on principal components .................. 39
FIGURE 9. Phenogram of digit 2 claws, based on principal components ................... 40
FIGURE 10. Phenogram of digit 3 claws, based on principal components ................. 41
FIGURE 1 1. Phenogram of digit 4 claws, based on principal components ................. 42
FIGURE 12. Photographs of FHSM-VP2062 left pes claws with landmarks ............... 60
FIGURE 13. Photographs of KU49399 left pes claws with landmarks ...................... 60

FIGURE 14. Photograph of YPM2554 left pes Unknown Claw 3 with landmarks ........ 61

FIGURE 15. Photograph of YPM2436 left pes Unknown Claw 4 with landmarks ........ 61

FIGURE 16. Photographs of UM-P left pes claws with landmarks .......................... 61
FIGURE 17. Photographs of UM-WS left pes claws with landmarks ....................... 62
FIGURE 18. Photographs of C—GBBG left pes claws with landmarks ...................... 62
FIGURE 19. Photographs of GP left pes claws with landmarks ............................ 62
FIGURE 20. Photographs of C-SI left pes claws with landmarks ............................ 62

xii

FIGURE 21. Photographs of C-PC left pes claws with landmarks ........................... 63

FIGURE 22. Photographs of MSU-PA left pes claws with landmarks ...................... 63
FIGURE 23. Photographs of C22026 left pes claws with landmarks ........................ 63
FIGURE 24. Photograph of C213395 left pes Claw 1 with landmarks ....................... 63
FIGURE 25. Photographs of C—CAD left pes claws with landmarks ......................... 64
FIGURE 26. Photograph of C3101] left pes Claw 3 with landmarks ........................ 64
FIGURE 27. Photographs of C3132] left pes claws with landmarks ......................... 64

FIGURE 28. Plotted Bookstein coordinates taken from the inner and outer curves of
FHSM-VP2062 claw 1, with trend lines and matching equations.............68

FIGURE 29. Plotted Bookstein coordinates taken from the inner and outer curves of
FHSM—VP2062 claw 2, with trend lines and matching equations.............70

FIGURE 30. Plotted Bookstein coordinates taken from the inner and outer curves of
FHSM-VP2062 claw 3, with trend lines and matching equations... ..........72

FIGURE 31. Plotted Bookstein coordinates taken from the inner and outer curves of
FHSM-VP2062 claw 4, with trend lines and matching equations. . . . . . . ......74

FIGURE 32. Plotted Bookstein coordinates taken from the inner and outer curves of UM-
P claw ], with trend lines and matching equations .............................. 76

FIGURE 33. Plotted Bookstein coordinates taken from the inner and outer curves of UM-
P claw 2, with trend lines and matching equations .............................. 78

FIGURE 34. Plotted Bookstein coordinates taken from the inner and outer curves of UM-
P claw 3, with trend lines and matching equations .............................. 80

FIGURE 35. Plotted Bookstein coordinates taken from the inner and outer curves of UM-
P claw 4, with trend lines and matching equations .............................. 82

FIGURE 36. Plotted Bookstein coordinates taken from the inner and outer curves of UM-
WS claw 2, with trend lines and matching equations ........................... 84

FIGURE 37. Plotted Bookstein coordinates taken from the inner and outer curves of UM-
WS claw 3, with trend lines and matching equations ........................... 86

FIGURE 38. Plotted Bookstein coordinates taken from the inner and outer curves of UM-
WS claw 4, with trend lines and matching equations ........................... 88

xiii

FIGURE 39. Plotted Bookstein coordinates taken from the inner and outer curves of C-
GBBG claw 2, with trend lines and matching equations ....................... 89

FIGURE 40. Plotted Bookstein coordinates taken from the inner and outer curves of C-
GBBG claw 3, with trend lines and matching equations ....................... 9]

FIGURE 41. Plotted Bookstein coordinates taken from the inner and outer curves of C-
GBBG claw 4, with trend lines and matching equations ....................... 92

FIGURE 42. Plotted Bookstein coordinates taken from the inner and outer curves of C-PI
claw 2, with trend lines and matching equations ................................ 94

FIGURE 43. Plotted Bookstein coordinates taken from the inner and outer curves of C-PI
claw 3, with trend lines and matching equations ................................ 96

FIGURE 44. Plotted Bookstein coordinates taken from the inner and outer curves of C-PI
claw 4, with trend lines and matching equations ................................ 97

FIGURE 45. Plotted Bookstein coordinates taken from the inner and outer curves of C-SI
claw 1, with trend lines and matching equations ................................ 99

FIGURE 46. Plotted Bookstein coordinates taken from the inner and outer curves of C-SI
claw 2, with trend lines and matching equations ............................... 100

FIGURE 47. Plotted Bookstein coordinates taken from the inner and outer curves of C-SI
claw 3, with trend lines and matching equations .............................. 102

FIGURE 48. Plotted Bookstein coordinates taken from the inner and outer curves of C—SI
claw 4, with trend lines and matching equations .............................. 103

FIGURE 49. Plotted Bookstein coordinates taken from the inner and outer curves of C-
PC claw 3, with trend lines and matching equations .......................... 104

FIGURE 50. Plotted Bookstein coordinates taken from the inner and outer curves of C-
PC claw 4, with trend lines and matching equations .......................... 105

FIGURE 51. Plotted Bookstein coordinates taken from the inner and outer curves of
MSU-PA claw 1, with trend lines and matching equations ................... 107

FIGURE 52. Plotted Bookstein coordinates taken from the inner and outer curves of
MSU-PA claw 2, with trend lines and matching equations .................. 109

FIGURE 53. Plotted Bookstein coordinates taken from the inner and outer curves of
MSU-PA claw 3, with trend lines and matching equations .................. 112

xiv

FIGURE 54.

FIGURE 55.

FIGURE 56.

FIGURE 57.

FIGURE 58.

FIGURE 59.

FIGURE 60.

FIGURE 61.

FIGURE 62.

FIGURE 63.

FIGURE 64.

FIGURE 65.

FIGURE 66.

FIGURE 67.

FIGURE 68.

Plotted Bookstein coordinates taken from the inner and outer curves of
MSU-PA claw 4, with trend lines and matching equations .................. 115

Plotted Bookstein coordinates taken from the inner and outer curves of
C22026 claw 1, with trend lines and matching equations .................... 1 18

Plotted Bookstein coordinates taken from the inner and outer curves of
C22026 claw 2, with trend lines and matching equations .................... 121

Plotted Bookstein coordinates taken from the inner and outer curves of
C22026 claw 3, with trend lines and matching equations .................... 123

Plotted Bookstein coordinates taken from the inner and outer curves of
C213395 claw 1, with trend lines and matching equations .................. 125

Plotted Bookstein coordinates taken from the inner and outer curves of C-
CAD claw 2, with trend lines and matching equations ........................ 127

Plotted Bookstein coordinates taken from the inner and outer curves of C-
CAD claw 3, with trend lines and matching equations ........................ 129

Plotted Bookstein coordinates taken from the inner and outer curves of
C3101] claw 3, with trend lines and matching equations .................... 131

Plotted Bookstein coordinates taken from the inner and outer curves of
C3132] claw l, with trend lines and matching equations .................... 134

Plotted Bookstein coordinates taken from the inner and outer curves of
C3132] claw 3, with trend lines and matching equations .................... 136

Plotted Bookstein coordinates taken from the inner and outer curves of
KU49399 unknown claw ], with trend lines and matching equations......146

Plotted Bookstein coordinates taken from the inner and outer curves of
KU49399 unknown claw 2, with trend lines and matching equations......148

Plotted Bookstein coordinates taken from the inner and outer curves of
YPM2554 unknown claw 3, with trend lines and matching equations...... 150

Plotted Bookstein coordinates taken from the inner and outer curves of
YPM2436 unknown claw 4, with trend lines and matching equations. .....]53

Phenogram of all claws regardless of articulation, without the four
pteranodont claws of unknown articulation ..................................... 154

XV

FIGURE 69. Phenogram of all claws regardless of articulation, with the four pteranodont
claws of unknown articulation .................................................... 155

xvi

LIST OF EQUATIONS

EQUATION 1. Transformation from raw coordinates to standardized. coordinates in any
given claw ........................................................................ 16

EQUATION 2. Transformation from standardized coordinates to Bookstein coordinates

in any given claw ................................................................ 16
EQUATION 3. Calculation of coordinates of centroid location in any given claw ........ 18
EQUATION 4. Calculation of the size of the centroid in any given claw ................... 18
EQUATION 5. Equation used for determining the distance between any two

landmarks ........................................................................ 18
EQUATION 6. Calculation of angle a in any given claw (in degrees) ...................... 19
EQUATION 7. Calculation of angle [3 in any given claw (in degrees) ...................... 19
EQUATION 8. Calculation of angle 7 in any given claw (in degrees) ...................... l9
EQUATION 9. Calculation oF-Ratio of angle a to angle [3 ................................... 20
EQUATION 10. Aspect ratio of any given claw ................................................ 20

EQUATION 1]. Transformation of raw coordinates to Bookstein coordinates, used for
determining the Bookstein coordinates of points found along claw
curves ............................................................................. 21

EQUATION 12. Calculation of degrees of freedom for use in Pearson correlation

coefficient table .................................................................. 22
EQUATION 13. Calculation of degrees of freedom within each cluster .................... 25
EQUATION 14. Calculation of the mean of a single cluster .................................. 25
EQUATION 15. Calculation of variance within a single cluster ............................. 25

EQUATION 16. Calculation of the sum of squared deviations within a single cluster. . .25
EQUATION 17. Calculation of the sum of all cluster sums of squared deviations ........ 25

EQUATION 18. Calculation of the sum of the degrees of freedom of all clusters... ......25

xvii

EQUATION l9. Calculation of the variance within all clusters ............................ 25

EQUATION 20. Calculation of the mean between all clusters .............................. 26
EQUATION 2]. Calculation of the between clusters sum of squared deviations
weighted by the clusters’ sample sizes ..................................... 26
EQUATION 22. Calculation of the degrees of freedom between clusters ................ 26
EQUATION 23. Calculation of the variance between clusters ............................. 26

xviii

INTRODUCTION

As with any extinct organism, the various aspects of the functional morphology of
Pteranodon must be inferred through multiple studies and testable hypotheses. One
convention for such a study is the use of an extant phylogenetic bracket (W itmer 1995).
Using this technique with the relatively novel technique of quantitative morphometrics,
this thesis explores the possibility that Pteranodon was capable of swimming on the
epicontinental seaway that covered the Western Interior of North America during the

Cretaceous period.

Pteranodont Habitat and Food

Two lines of evidence indicate that Pteranodon lived and fed in an oceanic
environment. First, Pteranodon fossils to date have been found only in the Cretaceous
chalk beds of Kansas. All four pteranodont specimens used in this study came from the
Niobrara Chalk Formation (Bennett 1994), which has also yielded fossils of mosasaurs
(the most commonly found vertebrate fossils in this formation), fish, the piscivorous birds
Hesperornus and Enionus (Bramwell and Whitfield 1974), plesiosaurs, and turtles
(Bennett 2000). Secondly, fossil evidence indicates that Pteranodon fed on fish in the
epicontinental seaway. This evidence includes a pteranodont specimen that contains fish
scales and bones in its stomach (Bramwell and Whitfield 1974), and a second specimen

that has a bolus of fish caught between its mandibular rami (Bennett 2001, part 2).

Proposed Terrestrial and Aerial Locomotion of Pteranodon

One of the more frequently discussed aspects of pteranodont terrestrial
locomotion has been the issue of plantigrade versus digitigrade stance. Although all birds
are digitigrade (Ede 1964), it was determined that Pteranodon, like crocodylians (Parrish
1987), was plantigrade (Bennett 2001, part 2). This is supported by the morphology of
the tarsal, metatarsal, and interphalangeal joints. For example, the joint found between
the distal tarsals and metatarsals (which were not fused to each other as is the condition in
birds (Padian 1983)) are thought to have permitted flexion of the pes in the vertical plane,
as well as permitting some lateral flexion. Furthermore, the metatarsal and
interphalangeal joints are simple ginglymoid joints that could not only permit flexion, but
probably extension as well (Bennett 2001, part 2).

The question of whether Pteranodon was bipedal or quadrupedal has been more
intensely debated. The argument for bipedalism can be supported first by examining the
terrestrial locomotion of large birds. For example, the limb disparity (the ratio of wing
length to leg length) of Pteranodon, which is 9: 1, is closest to that of the albatross, which
is 8:1 (Padian 1983). Although the hind limbs of both the albatross and Pteranodon are
small compared to their respective wingspans, the albatross is able to walk normally with
a bipedal gait. The possible bipedalism of Pteranodon can also be compared to the
bipedalism of birds with regards to the positioning of the femur. If the pteranodont femur
were positioned horizontally and parasagittally, then most of the puboischiadic would lie
behind and below the femur and the acetabulum, as is the condition in birds (Padian
1983). Additionally, it is possible that the weight of the body of Pteranodon could be

held over its feet, giving it adequate balance in a bipedal stance. To further promote

balance in a bipedal stance, flexion of the carpus and the subsequent rotation of the
radius, ulna, and humerus may have allowed for the wing to fold against the body with
the fourth manus digit directed posterodorsally (Bennett 2001, b).

On the other hand, several lines of evidence support the argument for a
quadrupedal stance in Pteranodon. Such evidence includes the reduction of the post-
acetabular part of the pelvis, which is thought to eliminate the possibility of bipedalism in
Pteranodon. This structure, in addition to the posterior position of the acetabulum,
hypothetically allowed the femur to move dorsally and ventrally, so that Pteranodon
could move along the ground by sliding on its stomach and pulling itself forwards with
its feet (Bramwell and Whitfield 1974).

Although Bramwell and Whitfield (1974) have suggested that Pteranodon could
hang from cliff edges like a bat, it has since been concluded that its claws were unsuitable
for climbing or perching, and were instead more suited to terrestrial locomotion due to
their minimal curvature (Bennett 2001, a). Furthermore, Pteranodon lacks the uniformly
parallel foot bones used for grasping branches as seen in bats (Padian 1983). These
evidences strongly indicate that Pteranodon could not perch or grab onto any surface.

Hypotheses of pteranodont aerial locomotion tend to correlate with hypotheses of
terrestrial locomotion. If Pteranodon were strictly quadrupedal, then it would not have
been able to run in order to take off for flight (Bramwell and Whitfield, 1974). Because
its wing finger was four times the length of its humerus and radius combined (Padian
1983), Pteranodon would have needed to take off from an object that was high enough to
prevent its wings from hitting the ground on the first downwards stroke. Moreover,

Bramwell and Whitfield (1974) hypothesized that Pteranodon could take off from the

ground by facing winds at speeds of at least seven meters per second and spreading its

wings, similar to the method of take-off used by the albatross.

The Possibility of Pteranodont Aquatic Locomotion

The possibility that Pteranodon landed on the water to feed has been mentioned
briefly (Bramwell and Whitfield 1974, Bennett 2001, b), but until now it has not been
examined as a hypothesis. The aquatic feeding habits of Pteranodon are most often
involved in the argument for pteranodont aquatic locomotion. Originally, most
hypotheses regarding methods of feeding suggested that Pteranodon fed by plunge
diving, or by sticking the beak into the water as it glided above the surface.

Plunge diving and feeding while gliding are congruent with the structure of the
jaws, which indicate that prey was caught between the jaws (Bennett 2001, b).
Furthermore, Pteranodon had strong neck bones with flexion thought to be suitable for
striking into the water (Bramwell and Whitfield 1974). However, both methods of
feeding seem improbable due to the lack of teeth or other structures in the jaw that would
facilitate catching fish in this manner. Additionally, the premaxilla extends forwards
beyond the tip of the mandible (Bennett 2001, b). If Pteranodon were a glider, it would
not have been able to gain enough speed necessary to plunge into the water (Bramwell
and Whitfield 1974).

An alternative hypothesis suggests that Pteranodon fed by floating on the surface
of the water and plunging its beak below the surface in order to grab fish (Bramwell and
Whitfield 1974). It is presumed that Pteranodon could dip its head 90 centimeters

(Bennett 2001, b) below the water’s surface with a range of roughly 1.2 meters

(Bramwell and Whitfield 1974), and could have used its elongate maxilla to slash through
the water and disorient fish (Bennett 2001, b). The disadvantages to this style of feeding
are that Pteranodon would be vulnerable to underwater predators and would not be able
to pursue quickly moving fish (Bramwell and Whitfield 1974).

The means by which Pteranodon may have launched into the air are also used in
the argument for possible aquatic locomotion. It is proposed that if Pteranodon could
take off directly from the ground, then it could probably take off from the surface of the
water in like manner (Bennett 2001, b). For example, if there were sufficient wind to
facilitate lift, Pteranodon may have either flapped its wings from the crest of a wave, or
launched itself form the crest of a wave as a glider (if Pteranodon could indeed glide). In
these two cases, the large expanse of the wings would permit a flapping downwards
without hitting the surface of the water or catching unfavorable air currents (Bramwell

and Whitfield 1974).

The Extant Phylogenetic Bracket Surrounding Pteranodon

The Extant Phylogenetic Bracket (EPB) method was developed by Witmer ( 1995)
primarily to test hypotheses regarding placement and/or functional morphologies of the
soft tissues of fossil organisms by comparing the tissues of at least two extant outgroups
to the fossil under study. However, an EPB can also be used to test hypotheses regarding
other topics of paleobiology, including the hypothesis that pteranodont claws have
functionally morphological characteristics similar to claws of the extant groups Aves and
Crocodylia (in regards to aquatic locomotion). In this case, the hypothesis was tested by

first examining the known swimming behaviors of the extant taxa, and then by making

inferences of the swimming ability of Pteranodon by comparing and contrasting claw
morphologies. These inferences are considered to be Level I inferences, due to the
homologies of the claws studied across all taxa. Level I inferences can generate a
decisive positive assessment, which minimizes speculation through the presence of

morphological congruence (Witmer 1995).

Order

rowdy/us porosus

ia ' rocodvlus acutus
[11' r
eranodon
longiceps
lecaniformes lecanidae

lecaniformes lecanidae us
'formes 0r columbianus

marinas

formes guzms

iconiiformes r ube r
iformes ' cristatus

 

TABLE I. Classifications of animals used in study (Brochu 2003, Raikow 1985, Bennett 1994).

«\‘S W‘s «“5 05°? toi “'5
Lows 9w?" $0906 pave“ 0W" 9090 ‘3th a“ ”“9," C

FIGURE 1. Relationships of genera used in study (Compiled from Thomas et. al 2004, Brochu 2003, Mayr
2003, Hedges and Sibley 1994, and Bennett 2003).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Genus/species (1:313:23: ngfillriliezi Webbinlg) Piesent on Foot type
on Pes Pes es. (bll‘dS)

Crocodylus porosus 4 2-3—4-4 significant webbing N/A
Crocodylus acutus 4 2-3-4-4 significant webbing N/A
Alligator mississippiens 4 2-3-4-4 ~2/3 webbed N/A
Pteranodon 4 2-3-4-5 N/A N/A
Pteranodon longiceps 4 2-3-4-5 N/A N/A
Pelecanus 4 2-3-4—5 totipalmate ectropodactyl
Olor columbianus 4 2-3-4-4 almate anisodactyl
Larus marinas 3 0-3-4-5 almate tridactyl
Pinguinis 3 0-3-4—5 almate tridactyl
Eudocimus ruber 4 2-3-4-4 basally anisodactyl
Pavo cristatus 4 2-3-4-4 none anisodactyl

 

 

TABLE 2. Specimen pes types and characteristics (Raikow 1985, Bennett 2001 part 1, Bellairs 1969).

It should be here noted that although Pinguinis (the Great Auk) is now extinct, it is used

as part of the EPB because its behavior has been observed and documented before its

extinction.

Avian Locomotion

Of the six different bird species used in this study (assuming that the two Pelican

specimens are either similar in functional morphology to each other, or are the same

species), two species swim by paddling along the water’s surface, two species

swim/swam both along the water’s surface and under the water, one species wades in

marshy areas, and one species is a terrestrial bird that occasionally perches.

Olor columbianus and Larus marinas perform most of their aquatic locomotion at

the surface of the water. Olor columbianus, the Whistling Swan, swims at the surface and

feeds by dipping its beak down into the water, usually in shallow areas (Wallace and

 

Mahan 1975). larus marinas, the Great Black-Backed Gull, floats on the water more
than it actively swims (Wallace and Mahan 1975). However, when it does swim, it does
so by paddling along the surface with its legs. Gulls occasionally dive into the water,
reaching depths no deeper than one to two meters below the water’s surface. When gulls
walk on the ground, it is with a lumbering gait, but they can sometimes hop onto perches
(Good 1998).

Pinguinis, the Great Auk, swam mostly underwater by propelling itself with its
flightless wings. The Auk could also flap its wings efficiently to plane along the surface
of the water. In spite of its skill in the water, however, the Auk walked clumsily on land
(Montevecchi and Kirk 1996). Like Pinguinis, Pelecanus has broad feet and webbing
between the toes that allow fast underwater swimming (Lockley 1974). However,
Pelicans feed mostly by flying close over the water and suddenly plunge diving into the
water to scoop up fish (Géroudet 1965).

Eudocimus ruber, the Scarlet Ibis, is similar to the White Ibis in both behavior
and choice of habitat. It walks slowly when feeding in shallow marshes, but walks more
quickly when feeding in aquatic habitats. The Scarlet Ibis can fly, and does so with rapid
beats of the wing; however, it swims only when pressed by danger (Kushlan and
Bildstein 1992).

Pavo cristatus, the Peacock, is a mostly terrestrial, non-swimming bird that is
used as a control in this study. It travels mainly by walking on the ground, but can run
when threatened. Furthermore, the Peacock flies only when crossing a ravine or alighting
into roost trees. Thus, the peacock spends most of its time on the ground, perching in

trees only when roosting (Ragupathy 1998).

Crocodylian Locomotion

Extant crocodylians are secondarily aquatic, in contrast to their terrestrial
ancestors (Parrish 1987). They perform many of their daily activities such as feeding,
social interactions, and reproduction, in the water (Seebacher et a1. 2003). As such,
crocodylian feet are webbed as an adaptation to their aquatic environment. Although both
the crocodylian manus and pes have webbing between the digits, the pes is extensively
more webbed than is the manus (Bellairs 1969). For example, the manus digits of
Alligator mississippiens are webbed almost halfway, whereas the pes digits are webbed
along two-thirds of their length. Similarly, Crocodylus acutus has slight webbing on the
third and fourth digits of its manus, whereas it has more extensive webbing on the outer
digits of its pes (Cope 1900).

Despite the presence of webbing, the feet are not the main source of propulsion in
adult crocodylian aquatic locomotion. Only hatchling crocodylians swim entirely by
paddling their feet, using their hind limbs to do so between 77% and 98.9% of the time.
On the other hand, medium—sized crocodylians paddle with their feet only at very slow
speeds, using their hind limbs between 71.3% and 92.9% of the time. Large crocodylians
do not use their feet for aquatic propulsion at all. Instead, the webbed feet of large and
medium-sized crocodylians that are swimming quickly are used to help maintain balance
and facilitate maneuverability in the water, while the tail facilitates propulsion (Seebacher

et al. 2003).

The Use of Quantitative Morphometrics

In contrast to qualitative descriptions, morphometrics are a quantitative way to
examine and compare shape data of organisms. These data can be then be analyzed using
algebra and statistics based on homologous landmarks placed on images of specimens.
Furthermore, using landmarks for shape comparison when performing morphometrics
better assures homology of data across specimens or taxa. However, landmarks can omit
data about curvature, unless another method is used to study curvature. Variation of the
coordinates of landmarks across studied specimens is removed by mathematically
removing the differences in specimen positions, sizes, and orientations (Zelditch et a1
2004). Morphometrics were used in this thesis to maintain homology across specimens,

and permit statistical analyses of these data.

10

MATERIALS AND METHODS

Specimens Studied

The two extant outgroups used in the EPB with the extinct genus Pteranodon
were Aves and Crocodylia. From one to four homologous claws were compared and
contrasted among the nine genera in this study. Sixteen total specimens (photographs of
which are shown in Appendix I) were examined, as described in Table 3. The four
pteranodont claws of unknown articulation were not used in the study, and were retained
in the overall data set (their data listed in Appendix VII) only for the creation of the

tangential claw phenograms in Appendix VIII.

1]

 

Body Parts Used in

 

Specimen Specimen Location Genus or Species Description Study
Fort Hays Stemberg . ‘ iarticulated foot in
FHSM-VP2062 Museum Pteranodon longzteps chalk block claws l, 2, 3, & 4

 

University of Kansas

disarticulated left
tibia. tarsals,

two disarticulated

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

KU49399 Museum Pteranodon metatarsals, and claws
halanges in chalk
iarticulated tarsals
Yale Peabody _ metatarsals, and one distarticulaled
YPM2554 Pteranodon
lMuseum disarticulated claw
claws in chalk
Yale Peabod disarticulated one distarticulated
YPM2436 Museum y Pteranodon metatarsals and claw
i claw in chalk
University of articulated
(UM-P) lMichigan Zoological Pelecanus skeleton claws l, 2, 3. & 4
Museum
University of .
(UM-WS) ichigan Zoological Olor columbianus flagged claws 2. 3, & 4
Museum
(C-GBBG) lags; F'e'd Larus marinas 23:52:“ claws 2, 3. a 4
(CPD Egg]: F‘e'd Pinguinis 3:63:15? claws 2, 3, & 4
(C-SI) 33:25; Field Eudocimus ruber :Eélcelifged claws l, 2, 3, & 4
(C-PC) hicago Field Pelecanus conspicillatus articulated claws 3 & 4
Museum skeleton
lMichi s '
_ gan tate . articulated
(MSU PA) University Museum Pavo crtstatus skeleton claws l, 2, 3, & 4
C22026 £11335; Field C rocodylus porosus jgliglceliljrjed klaws l, 2 & 3
Chicago Field ‘ articulated
C213395 [Museum C mood; [as acutus skeleton claw 1
(C-CAD) Mtggf; Field C rocodylus acutus 23:53:“ claws 2 & 3
Chicago Field . . . . . articulated
C310] 1 Museum Alligator missrssrpprens skeleton claw 3
C3132] 133:5; Field Alligator mississippiens $5513“ claws ] & 3

 

TABLE 3. Specimens examined. Specimens that have no catalog number are given an informal
abbreviation for reference in this paper (shown above in parentheses).

Photograph Acquisition and Organization

All photographs of specimens used in this study were taken with a Canon

Powershot A40 Digital Camera. Photographs were taken of the fronts of the specimens,

12

 

and where possible, also of both the left and right side and of the back of the specimen. A
Geological Society of America cardboard scale (in centimeters) was placed in the
photographs of many of the specimens. All photographs were taken in color, with the
highest possible resolution and with the camera set to automatically adapt to the lighting
conditions. Once acquired, the photographs were then labeled and organized according to
their location and catalog number or label on a computer hard drive. Notes about these

photographs can be found in Appendix 11.

Photograph Manipulation

Single elements of avian, crocodylian, and pteranodont feet had to be isolated and
then oriented in a manner that would allow for the placing of landmarks and for
morphometric measurement. Adobe Photoshop CS] was used for all manipulations and
calculations performed on the avian, crocodylian, and pteranodont claws. This program
has the advantages of the ability to adjust brightness, contrast, and other aspects of
photographs, a tool that measures distances between two points, and a built-in XY
coordinate system.

The first step was to load the photograph of a crocodylian, avian, or pteranodont
pes into Adobe Photoshop. Next, in instances where the cardboard scale was present in
the photograph, the photograph was first increased or decreased in percentages until one
centimeter of the scale measured as one centimeter in the program. (It should be noted,
however, that this is not a necessary step, as all size data were removed once certain
morphometric calculations of the landmarks were performed as shown below.) Each claw

image was then cropped and placed in its own file, and labeled by the specimen to which

13

it belonged and the number of the digit to which it corresponds. In order to define the
edges of the claw as precisely as possible, the brightness and contrast aspects of the
image were adjusted to make the claw stand out against its background, then the edges of
the claw were sharpened using the sharpen tool. The pictures remained in color because it
was easier to see the claw edges in color than in black and white. This method was

applied to 36 claws from 15 specimens.

Raw Landmark Placement and Claw Orientation

Once the claw image has been isolated and its edges had been sharpened,
landmarks were placed on homologous areas on each claw. Four landmarks were placed
on every claw (Figure 1); one landmark each was placed on the two proximal comers of
each claw where the claw meets the digit, a third was placed at the distal tip of the claw,
and the fourth was placed at the middle of the proximal edge of the claw where the claw
meets the digit. The claws were examined under a high magnification in order to place
the landmarks on the most specific coordinates possible. Although landmarks l, 2, and 3
were of the most interest, landmark 4 was included in morphometric computations and
was used to help determine the centroid coordinates and size.

Once landmarks were placed on the claw, the image was then reoriented so that
landmarks 1 and 2 rested parallel to each other on a horizontal baseline. This was done
with each claw. Furthermore, claws that curved upwards and towards the right were left
in this orientation, but claws that curved upwards to the left were flipped horizontally so

that all claws were in the same orientation. An assumption held here is that a horizontally

l4

flipped image of one side of the claw appears similar enough to the other side of said

claw that calculations will not significantly vary.

FIGURE 2. Locations of the four landmarks on avian, crocodylian, and pteranodont claws after
reorientation.

Raw Landmark Coordinate Input and Transformation

With the claws in their homologous orientation, the next step was to record the
XY coordinates of the landmarks from Photoshop’s XY display (see Appendix III). This
step was also performed in high zoom for accuracy in landmark coordinates. The line
along which landmarks 1 and 2 rested was the baseline, which was then considered to
occur at Y=0. The pencil tool and the measure tool work equally as well for pinpointing
the coordinates of landmarks; the XY coordinates are shown in the Info window. Y
coordinates for landmarks 3 and 4 were determined by subtracting the Y coordinate of
landmark 1 from the Y coordinates of landmark 3 and 4 respectively. The raw landmark
coordinates for each claw were placed in a Microsoft Excel spreadsheet, organized by

specimen and digit number.

15

Although equations exist to directly transform raw landmark data to Bookstein
(shape) data, the raw coordinates of each claw were first transformed into standardized
coordinates with Equation 1. This equation was placed directly into the cells of an Excel
spreadsheet for each set of coordinates. Transformation of landmarks from raw
coordinates to standardized coordinates placed all of the claws in a common plane of
existence, with all the landmarks l occurring at the coordinate (0, 0). Shape differences,
however, had not yet been removed from the landmark data.

Xs=X—X1 Ys=Y—Yr
EQUATION 1. Transformation from raw coordinates to standardized coordinates in any given claw.

Next, the standardized coordinates of the claw landmarks were transformed into
Bookstein coordinates with Equation 2. This equation was also placed directly into the
Excel worksheet and the calculations were carried out by the program. Transformation of
landmarks from standardized coordinates to Bookstein coordinates removed differences
between claw sizes by placing their baseline landmarks within a plane between X = O and
X = 1, as shown in Figure 3.

X3 = Xs/Ss 2 Y3 = Ys/Xs 2

EQUATION 2. Transformation from standardized coordinates to Bookstein coordinates in any given claw.

16

(1.343, 1.486)

    

(0.500, 0.125)

FIGURE 3. Claw landmarks with an example set of Bookstein coordinates. The Bookstein coordinates of
landmark 1 and landmark 2 for every claw involved in the study are (0,0) for landmark 1, and (0,1) for
landmark 2.

Morphometric Calculations

Several variables to be used in later calculations were extracted from geometric
and trigonometric calculations made with the Bookstein coordinates of the claw
landmarks. All of the equations for these calculations were placed directly into Excel and
computed by the program. First, the locations of the centroid coordinates in the center of
each claw were calculated, followed by the calculation of centroid size (Zelditch et al
2004). The centroid coordinates of each claw were calculated by averaging the X and Y
coordinates of the four landmarks, as demonstrated in Equation 3. The centroid size of
each claw was then determined by taking the square root of the sum of distances from

each of the four landmarks to the centroid, as in Equation 4.

XB1+XBZ+XB3+XB4 YBI+YBZ+YB3+YB4
XCT= 4 YCT= 4

 

 

EQUATION 3. Calculation of coordinates of centroid location in any given claw (Zelditch et al 2004).

17

 

centroid size = J2 [(XB— Xcr)2 + (YB+ Ycr)2]

EQUATION 4. Calculation of the size of the centroid in any given claw (Zelditch et al 2004).

The next set of calculations made with the Bookstein coordinates were the
distances between the four landmarks of each claw. The distances between landmarks 1
and 2, 1 and 3, l and 4, 2 and 3, and 3 and 4 were determined using the general distance
formula given in Equation 5. It should be noted that because size data were removed once
the landmark coordinates were transformed into Bookstein coordinates, the centimeter
was no longer an accurate metric for these distances. Instead, these distances represented
a set of data that was compared to the homologous distances of other claws, as apposed to

an absolute measurement.

 

D:\fi(XBr-Xaz)2 +(YBl—YBZ)2]

EQUATION 5. Equation used to determine the distance between any two landmarks.

Once the distances between landmarks were calculated, the angles between
landmarks 1, 2 and 3 were calculated. Angle 312 was labeled as angle (1, angle 123 was
labeled as angle [3, and angle 132 was labeled as angle 7, as demonstrated in Figure 4. All
angles were calculated and recorded in degrees; the equations used to calculate these

angles are shown in Equations 6, 7 and 8.

18

C

 

FIGURE 4. A. Example of superposition of a triangle (shown in dashed lines) drawn from connecting
landmarks l, 2, and 3. B. Locations of angle and line designations in the triangle between landmarks l, 2,
and 3.

BZ+C2—A2
2BC

 

Cosa =

EQUATION 6. Calculation of angle a in any given claw (in degrees).

A2+C2—B2
2AC

 

CosB =

EQUATION 7. Calculation of angle B in any given claw (in degrees).

A2+B2—C2
2AB

 

Cosy =

EQUATION 8. Calculation of angle 7 in any given claw (in degrees).

Another variable used for claw comparison was the ratio of angle a to angle B.

This was calculated by dividing angle a by angle B (Equation 9). This ratio represents the

19

amount of slant towards the right in each claw; for example, a smaller ratio implies that
the claw leans less towards the right, whereas a larger ratio implies that the claw leans
more towards the right.

a : B ratio = 0t/ B

EQUATION 9. Calculation oF-Ratio of angle a to angle B.

The last variable determined from the Bookstein landmarks of each claw was the
aspect ratio of the claw (Equation 10). For this variable, the X coordinate of landmark 2
was used to represent the width of the claw (which in all cases equaled one due to the
previous step of transforming all landmarks into Bookstein coordinates), and the Y
coordinate of landmark 3 was used to represent the height of the claw. It was assumed
that that any points on the claw outline that were higher than the Y coordinate of
landmark 3, or farther than the X coordinate of landmark 2, would not significantly
change the outcome of this calculation. Thus, an approximate ratio of width to height of

each claw was determined.

. X13 2 1
aspect 1'3th 2 =
YB 3 YB 3

 

EQUATION 10. Aspect ratio of any given claw.

Curvature Equations

Each claw was recognized as having two curves; the inner curve was the curve
that formed the right side of the claw, and the outer curve was the curve that formed the
left side of the claw (Figure 5). For each curve of each claw, raw coordinates of the curve

were extrapolated under high magnification in Photoshop and then recorded in the Excel

20

spreadsheet. The top and bottom ends of the curve were determined to occur at
coordinates where the curve began to change its direction (as shown in Figure 5). Once a
set of coordinates for a curve had been recorded, each coordinate was transformed into

Bookstein coordinates by placing Equation 11 (Zelditch et al 2004) into the spreadsheet.

OuterCm've InnerCurve

FIGURE 5. The inner and outer curve of any given claw.

 

: (X2-X1)(X3—Xi)+(Y2—Y1)(Y3—Y1)

X8 2 2
(Xz-Xr) +(Y2—Y1)

___ (X2-Xi)(Y3-X1)—(Y2-Y1)(Y3—Y1)

Y
B (X2—X1)2+(Y2—Yr)2

 

EQUATION 1]. Transformation of raw coordinates to Bookstein coordinates (Zelditch et al 2004) used in
curvature calculations. These calculations are based on the raw coordinates of landmarks l, 2 and 3.

The resulting Bookstein coordinates of each separate curve were plotted on their
own XY Scatter graph in Excel (listed in Appendix IV). Next, a polynomial (Y =
AX2+BX1+CX0) trend line of the data was plotted, with the equation for the trend line
and its R2 value shown on the graph. The coefficients of X2, X', and X0 were then

recorded as variables for both curves of every claw.

21

Variable Correlation Calculations

Before any statistical comparisons among variables could be completed, all
variables found from the above calculations (for all claws) had to be processed to identify
which variables significantly correlated with each other, in order to eliminate redundant
data. This process was carried out in a statistical analysis computer program called
SYSTAT. In the ANALYSIS menu, the command CORRELATIONS —> SIMPLE... was
selected. A Pearson analysis was selected, with the options continuous data, two sets, and
list wise deletion checked. All morphometric variables were added with the exception of
the X and Y baseline coordinates of landmarks 1 and 2, and the distance between these
coordinates. These five variables were excluded because they were identical throughout
all taxa, and thus could not be included in the correlation analysis. When the analysis was
run, a Pearson correlation value was produced for every combination of variable pairs.
The absolute values of these numbers were then compared to values found on the Pearson
correlation coefficient table (Upton and Cook 2004) at 26 degrees of freedom (see
Equation 12) and p = 0.05. Any pair of variables with an absolute value equal to or above
0.374, the correlation coefficient, denoted a significant correlation with each other. These

pairs are listed in Appendix V.

degrees of freedom = sample size - 2

EQUATION 12. Calculation of degrees of freedom for use in Pearson correlation coefficient table.

Organization of Samples for Statistical Analyses
Because this study examines the morphometric similarities and differences

between homologous claws across taxa, it was necessary to separate the data from digits

22

1, 2, 3, and 4 of all taxa into four data files to be used in statistical analyses. Each file was
individually processed in the following statistical procedures to ensure a comparison of
the same digit across taxa in each analysis. As an aside, statistical analyses were
performed on the data file that includes all digits from all taxa except the pteranodont
claws of unknown articulation, as well as the data files that include all digits from all taxa
with the pteranodont claws of unknown articulation; however, because these tests do not
compare strictly homologous structures, they are present in this study only for tangential

speculation.

Creation of Principal Components

In SYSTAT, a factor analysis was used to create uncorrelated principal.
component variables to be used in later statistical comparisons within each of the six data
files. This step removed redundant data by producing mathematical variables that did not
correlate with each other. Analysis —> Multivariate Analysis -—> Factor Analysis... was
selected from the menu bar. In the Model tab, the principal components method was used
with the correlation method of extraction. In the Rotation tab, varimax was selected; in
the Save tab, Factor Scores were selected to be saved with the option checked to save
data with scores. All other settings were left at their defaults. Next, all claw variables
except the X and Y values of the Bookstein coordinates of landmarks l and 2 as well as
the distance between these landmarks (these five variables omitted because they remain
constant throughout taxa) were added to the Model variable(s) field. When OK was
clicked, a data file containing the new principal component variables was created. This
process was performed on each of the individual digit data sets, yielding 4 new data files

containing principal component variables for each digit.

23

Claw Phenogram Creation

In order to create a phenogram of claw morphologies for each digit, 3 cluster
analysis was run in SYSTAT for each data file containing the newly created principal
components. Analysis ——> Multivariate Analysis —> Cluster Analysis —> Hierarchical...
was selected from the menu bar. In the Main tab, Ward Linkage, Euclidean Distance, and
Join: Rows were selected. Next, the principal component variables were entered into the
Selected Variables field. All other settings in this window were left at their defaults.
When OK was clicked, a dendrogram was created that had the taxa as its endpoints, with
a measure of distance below. This distance described where clusters joined together in the
dendrogram, in the sense that the shorter the distance was before two clusters joined, the
morphometrically closer to each other the clusters were. This process was performed for
all four individual claw data sets. It was also performed for the two all-inclusive data sets

for speculative purposes.

ANOVA Analyses

AN OVA was used to look for statistically significant similarities and differences
between the clusters produced within each of the four claw dendrograms. Each principal
component was analyzed individually, and all calculations were performed by entering
the necessary formulas into an Excel spreadsheet. Within each principal component, each
cluster was listed as an individual sample, and then calculations were performed in order
to find the degrees of freedom within each cluster (Equation 13), the mean of the cluster
(Equation 14), the variance within the cluster (Equation 15), and the sum of squared

deviations in the cluster (Equation 16).

24

df = n— 1, where n is the cluster sample size

EQUATION 13. Calculation of degrees of freedom of each cluster.

11
2..
Xj = i=1

n

EQUATION l4. Calculation of the mean of a single cluster.

32 _ ECG—XV _ 02
n—l dfwc

EQUATION 15. Calculation of variance within a single cluster.

 

 

202 =s2 odfwc

EQUATION 16. Calculation of the sum of squared deviations within a single cluster.

Next, seven calculations involving all of the clusters together were performed.
The sums of all cluster sums of squared deviations (Equation 17), as well as the sum of
all cluster degrees of freedom (Equation 18) were calculated. The variance within clusters

was then calculated using Equation 19.

k nj ‘—
sum of all clusters'z 02 = 21:1 21:1 (Xij— x02

EQUATION l7. Calculation of the sum of all cluster sums of squared deviations.

(if... = 2 df

EQUATION l8. Calculation of the sum of the degrees of freedom within clusters.

25

EQUATION l9. Calculation of the variance within all clusters.

The four remaining calculations yielded values between the clusters. The mean
between all clusters was first found with Equation 20. The between clusters sum of
squared deviations weighted by the clusters’ sample sizes was then found for the group of
clusters with Equation 21. Once the between clusters degrees of freedom was determined
with Equation 22, the between clusters variance was calculated using Equation 23
(Kachigan 1991). With these calculated values, it was then possible to determine and
analyze the F-ratios of cluster pairs for each principal component variable.

_ n 2
Xbc = Z; # clusters

EQUATION 20. Calculation of the mean between all clusters.

k _ _
Z 0'; =2 nj(Xj — Xbc)2
j=l

EQUATION 2]. Calculation of the between clusters sum of squared deviations weighted by the clusters’
sample sizes.

dfbc =# clusters -1

EQUATION 22. Calculation of the degrees of freedom between clusters.

22
2: Che

S
“C as.

EQUATION 23. Calculation of the variance between clusters.

26

The F-ratio for a group of clusters within a principal component variable was
calculated by dividing the variance between clusters by the variance within clusters
(Equation 24). Accordingly, the degrees of freedom for the F-ratio were the degrees of
freedom between clusters as the first number, followed by the degrees of freedom within
clusters as the second number. Upon holding the null hypothesis to be that there are no
significant differences between the clusters under each principal component variable, all
calculated F-ratios were compared to the F distribution values (at or =0.05) generated by
the >calc fif(0.95, dfbc, dfwc) command in SYSTAT, where dfbc represents the degrees of
freedom between clusters, and dfwc represents the degrees of freedom within clusters. In
the cases that the absolute value of the F—ratio was less than the critical value, the null
hypothesis was supported and the clusters were found not to be statistically different from
one another. However, in the cases when the absolute value of the calculated F-ratio was
equal to or greater than the critical value, the alternative hypothesis that the clusters are
significantly different from one another was instead supported (Kachigan 1991). Clusters
that yielded statistically significant F-ratio values within their first comparison to the rest
of the clusters as a group underwent analyses individually paired with every other cluster

in order to determine specific F-ratio values between pairs of clusters.

2

S

_ bc
F_ 2
SWC

EQUATION 24. Calculation of the F-ratio of two or more clusters.

27

RESULTS
Bookstein Coordinates of Claw Landmarks
Once homologous landmarks were placed on all claws used in the study, their
coordinates were transformed into standardized coordinates, which were then
transformed into Bookstein coordinates (Table 4). Because the Bookstein coordinates of
landmarks 1 and 2 are constant in all claws, only the Bookstein coordinates of landmarks
3 and 4 of all claws have been plotted on Figures 6 and 7 respectively for visual

comparison. (NOTE: Images in this thesis are presented in color.)

28

 

Specimen

Pes

Claw

Bookstein Coordinates

 

Landmark l

Landmark 2

Landmark 3

Landmark 4

 

X Y

X

Y

X

Y

X

Y

 

FHSM—VP2062

Left

0.500

3.321

0.464

0.107

 

0.973

3.405

0.459

-0.08 l

 

0.065

2.848

0.500

L0. 130

 

0.529

3.706

0.471

0.176

 

UM-P

Left

1.313

2.813

0.500

0.125

 

2.300

3.600

0.500

0.133

 

1.707

0.634

0.439

-0.085

 

1.692

1.173

0.577

0.135

 

UM-WS

Left

0.630

4.074

0.593

b0.148

 

1.941

3.765

0.471

-0. 147

 

0.795

4.077

0.590

-—0.256

 

C-GBBG

Left

0.900

2.500

0.500

~0.100

 

1.179

2.128

0.436

-0. 154

 

0.565

2.826

0.565

—0. l 74

 

C-PI

Left

1.000

4.143

0.429

-0.476

 

1.061

4.182

0.485

-0.242

 

1 .667

6.333

0.583

-0.167

 

C-SI

Left

-2.650

3.450

0.600

-0.300

 

1.588

3.059

0.412

-0.353

 

1.550

3.400

0.450

-0.400

 

1.333

2.500

0.556

00.333

 

C-PC

Left

0.719

2.063

0.500

0.094

 

1.261

3.261

0.478

-0.217

 

MSU—PA

Left

2.537

0.642

0.493

0.045

 

2.136

4.955

0.409

0.000

 

3.859

1.592

0.423

#0070

 

3.170

1.274

0.481

0.113

 

C22026

Left

1.566

2.823

0.496

0.142

 

1.944

3.204

0.500

0.000

 

1.810

2.983

0.569

+0.069

 

C213395

Left

1.282

2.373

0.473

-0.109

 

C-CAD

Left

0.896

2.167

0.573

0.156

 

0.392

2.608

0.431

-0.31

 

C3101]

Left

1 .465

2.433

0.446

0.015

 

C3132]

 

 

Left

1 .505

3.126

0.526

~0.137

 

 

'fiHWWN—WN-‘hWN—‘hWbUJN—wahWNhWNhWN—&WN—

 

 

COCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
COOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

 

-H~_-—~fl~—~_—-_H—_flH_H_H_H_H—--

 

COCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

 

0.449

 

3.808

 

0.385

 

 

—0.077

 

TABLE 4. The Bookstein coordinates of claw landmarks.

29

Bookstein Coordinates of Landmark 3

7 ,
6 . x , A, , L
$.03 5 . o I O Claw l
“-5 4< ‘-
‘5 g 3 g ’o'fif ‘A Claw 3
8 ‘3‘. ‘ X Claw 4
>-‘ 2 ‘ A“; A 0 Unknown Articulation
1 ‘ x x _._._. M W
A o
-4 -2 0 2 4 6

X Coordinates

FIGURE 6. Bookstein coordinates of landmark 3 of all claws (data from Table 4).

Bookstein Coordinates of Landmark 4

0.3
0.2 - x i
0.1 o! ”Agg _ V L

3 0-- IL; T , ., lOClawl

E -01 0 0.2 0. 0.6 0.8 1 1' Claw 2

E “ >4! A Claw 3

o -0.2 J

U )3 x . X Claw 4

V -03 *4 -° x ° ., °_ UslgoaaArtisslatim ,
-0.4 3 A
-0.5 - I
-O.6

X Coordinates

FIGURE 7. Bookstein coordinates of landmark 4 of all claws (data from Table 4).

30

Claw Centroid Locations and Sizes
The (X, Y) coordinates and the size of the centroid of the claws (based on

Bookstein coordinates) yielded two more variables for each claw, shown in Table 5.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Pes Claw Centrord Location Centroid Size
X Y
1 0.491 0.857 2.934
FHSM-VP20 62 Le ft 2 0.608 0.831 3.085
3 0.391 0.679 2.631
4 0.500 0.971 3.240
1 0.703 0.734 2.601
UM-P Left 2 0.950 0.933 3.525
3 0.787 0.137 1.402
4 0.817 0.327 1.578
2 0.556 0.981 3.644
UM-WS Left 3 0.853 0.904 3.606
4 0.596 0.955 3.687
2 0.600 0.600 2.332
C-GBBG Left 3 0.654 0.494 2.109
4 0.533 0.663 2.601
2 0.607 0.917 3.839
C-PI Left 3 0.636 0.985 3.796
4 0.813 1.542 5.667
1 -0.263 0.788 4.197
C-Sl Left 2 0.750 0.676 3.015
3 0.750 0.750 3.290
4 0.722 0.542 2.487
C-PC Left 3 0.555 0.492 1.957
4 0.685 0.761 3.05]
1 1.007 0.172 1.979
MSU-P A Left 2 0.886 1.239 4.583
3 1.320 0.380 3.325
4 1.163 0.347 2.651
1 0.765 0.741 2.673
C22026 Left 2 0.861 0.801 3.125
3 0.845 0.728 2.920
C213395 Left 1 0.689 0.566 2.309
C-CAD Left 2 0.617 0.581 1.994
3 0.456 0.574 2.468
C3101] Left 3 0.728 0.605 2.384
C3132] Left 1 0.758 0.747 2.967
3 0.458 0.933 3.396

 

 

 

TABLE 5. Claw centroid locations and sizes.

 

31

 

 

 

 

Distances Between Claw Bookstein Landmarks

The morphometric distances between each landmark yielded a total of 6 variables
(shown in Table 6) to be used in statistical analyses. Because the coordinates of
landmarks l and 2 remained constant throughout all claws, the distance between these

landmarks also remained constant.

32

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

S . Distances Between Landmarks (Bookstein)
peclmen Pes Claw
L1-L2 L2-L3 L1-L3 L3-L4 L1-L4 L2-L4
1 1 3.359 3.359 3.214 0.476 0.546
FHSM-VP2062 Left 2 1 3.406 3.542 3.524 0.467 0.547
3 1 2.997 2.849 3.010 0.517 0.517
4 1 3.736 3.744 3.530 0.503 0.558
1 1 2.830 3.104 2.808 0.515 0.515
UM-P Left 2 1 3.828 4.272 3.906 0.517 0.517
3 1 0.950 1.821 1.458 0.447 0.567
4 1 1.362 2.059 1.524 0.592 0.444
2 1 4.091 4.122 4.222 0.611 0.434
UM-WS Left 3 1 3.881 4.236 4.179 0.493 0.549
4 1 4.082 4.154 4.338 0.643 0.484
2 1 2.502 2.657 2.631 0.510 0.510
00330 Left 3 1 2.136 2.433 2.400 0.462 0.585
4 1 2.859 2.882 3.000 0.591 0.468
2 1 4.143 4.262 4.654 0.641 0.744
0131 L60 3 1 4.182 4.314 4.462 0.542 0.569
4 1 6.368 6.549 6.590 0.607 0.449
1 1 5.022 4.350 4.962 0.671 0.500
C-SI Left 2 1 3.1 15 3.447 3.609 0.542 0.686
3 1 3.444 3.737 3.956 0.602 0.680
4 1 2.522 2.833 2.938 0.648 0.556
C-PC Left 3 1 2.082 2.184 2.167 0.509 0.509
4 1 3.271 3.496 3.565 0.525 0.565
1 1 1.666 2.617 2.130 0.495 0.509
MSU-P A Left 2 1 5.083 5.396 5.247 0.409 0.591
3 1 3.272 4.174 3.817 0.428 0.582
4 1 2.516 3.416 2.928 0.494 0.531
1 1 2.879 3.228 2.887 0.515 0.524
C22026 Left 2 1 3 .340 3 .748 3.514 0.500 0.500
3 1 3.091 3.489 3.295 0.573 0.437
C213395 Left 1 1 2.389 2.697 2.610 0.485 0.538
C-C AD Left 2 1 2.169 2.345 2.036 0.594 0.455
3 1 2.678 2.637 2.922 0.533 0.649
C310] 1 Left 3 1 2.477 2.840 2.651 0.446 0.554
C 31321 Left 1 1 3.167 3.470 3.407 0.544 0.493
3 1 3.847 3.834 3.885 0.392 0.620

 

 

TABLE 6. Distances between the Bookstein landmarks of each claw.
Angles Between Claw Bookstein Landmarks
The angles described in Figure 4 were found by using the distances calculated in

Table 6. These yield three additional variables for each claw and are presented in Table 7.

33

 

Specimen

Pes

Claw

An les (degrees)

 

O

B

Y

 

FHSM-VP2062

Left

81.439

81.439

17.122

 

74.055

89.545

16.400

 

88.688

71.828

19.484

 

81.870

82.763

15.367

 

UM-P

64.983

96.340

18.677

 

57.426

109.855

12.719

 

20.376

138.122

21.501

 

34.729

120.548

24.723

 

UM-WS

Left

81.215

84.806

13.980

 

62.723

104.036

13.241

 

78.968

87.120

13.913

 

C-GBBG

Left

70.201

87.709

22.089

 

61.004

94.821

24.175

 

78.690

81.254

20.056

 

C—PI

Left

76.430

90.000

13.570

 

75.769

90.830

13.401

 

75.256

96.009

8.735

 

C—Sl

Left

127.528

43.386

9.085

 

62.560

100.886

16.554

 

65 .493

99.189

15.319

 

61.928

97.595

20.478

 

C-PC

Left

70.787

82.235

26.978

 

68.860

94.574

16.566

 

MSU-PA

Left

14.195

157.341

8.456

 

66.675

102.918

10.408

 

22.412

150.897

6.691

 

21.890

149.589

8.522

 

C22026

Left

60.976

101.344

17.680

 

58.745

106.425

14.830

 

58.745

105.199

16.056

 

C213395

Left

61.621

96.774

21.606

 

C-CAD

Left

67.537

87.248

25.216

 

81.448

76.880

21 .672

 

C3101]

Left

UJDJN—WN—-§UJN—bWAWN—bWNAWNhWNh'JN—AWNH

58.948

100.819

20.233

 

C3132]

 

 

Le ft

64.290

99.181

16.529

 

 

w—

 

83.279

 

81.762

 

14.959

 

TABLE 7. Angle calculations (in degrees) between Bookstein landmarks l. 2. and 3 of each claw.

Aspect and Angle Ratios of Claws

The aspect ratio and the ratio of a to B yielded one variable each for all claws and

are presented in Table 8.

34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Pes Claw Aspect Ratio Ratio of a to B
I 0.301 1.000
FHSM-VP2062 Left 2 0294 0327
3 0.351 1.235
4 0.270 0.989
I 0.356 0.675
UM-P Left 2 0.278 0.523
3 1.577 0.148
4 0.852 0.288
2 0.245 0.958
UM-WS Left 3 0.266 0.603
4 0.245 0.906
2 0.400 0.800
C-GBBG Left 3 0.470 0.643
4 0.354 0.968
2 0.241 0.849
C-PI Left 3 0.239 0.834
4 0.158 0.784
1 0.290 2.939
C-SI Left 2 0.327 0.620
3 0.294 0.660
4 0.400 0.635
C-PC Left 3 0.485 0.861
4 0.307 0.728
1 1.558 0.090
MSU-P A Left 2 0.202 0.648
3 0.628 0.149
4 0.785 0.146
1 0.354 0.602
C22026 Left 2 0.312 0.552
3 0.335 0.558
C213395 Left 1 0.421 0.637
C-C AD Left 2 0.462 0.774
3 0.383 1.059
C3101] Left 3 0.411 0.585
C3 1321 Left 1 0.320 0.648
3 0.263 1.019

 

 

TABLE 8. Aspect ratios and ratios of a to B of each claw.
Claw Curvature Polynomial Coefficients

The coefficients for functions in the format of Y = AX2+BX1+CXO that when
plotted, most closely match the inner and outer curvature of the claws, are detailed in

Table 9. The R2 value is also listed with the coefficients as a measure of accuracy.

35

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Curvature Equation Coefficients
S , Outer Curve Inner Curve

peclmen Pes Claw X2 X x0 R2 XI X x0 R2

Coeff. Coeff. Coeff. Value Coeff. Coeff. Coeff. Value
(A) (B) (C) (A) (B) (C)
1 -15.455 7.681 2.625 0.836 -0.595 -3.749 5.024 0.969
FHSM- 2 -3.515 4.931 1.571 0.934 -28.809 48.784 -18.602 0.055
Left

VP2062 3 6.265 —0.0681 1.569 0.014 0934 -5999 3.540 0.966
4 -4.664 6.368 2.091 0.799 3.077 -1 1.171 9.538 0.957
1 -l .819 3.559 0.968 0.923 -3.088 7.371 -2.425 0.039
UM-P Left 2 -0.955 3.205 0.884 0.968 2.330 -7.246 7.878 0.260
3 -0.552 1.190 0.172 0.984 -1 . 172 4.941 -2.914 0.971
4 -0.334 1.179 0.169 0.985 0.844 -1.180 0.829 0.608
2 -3.86 2.815 3.278 0.876 -1 1.562 17.706 -3.753 0.325
UM-WS Left 3 -1.034 3.404 0.785 0.982 -9.132 35.312 -30.955 0.935
4 -1.640 3.394 2.764 0.856 -27.085 41.063 -12.265 0.236
2 -4.340 4.756 0.700 0.89] 24.194 -51.157 27.556 0.863
00330 L60 3 -1.809 3.496 0.243 0.965 -34.266 69.085 -33.466 0.101
4 -4.950 3.494 2.197 0.644 12.141 -19.406 8.749 0.571
2 -3.088 4.842 2.034 0.923 -2.278 1.816 2.713 0.341
C-PI Left 3 -3.622 5.538 1.936 0.869 -l].757 21.063 -6.011 0.117
4 -1.495 4.055 3.382 0.932 -3.427 8.851 -1.171 0.315
1 -0.014 -1 .246 0.059 0.996 0.010 -0.805 1.151 0.994
0 SI Left 2 -0.629 2.546 0.671 0.986 1.031 0.817 -0.217 0.552
3 -1.022 3.451 0.515 0.997 1.894 -0.789 0.719 0.581
4 -l .262 3.164 0.465 0.989 4.087 —6.873 4.199 0.1 15
C-PC Left 3 -5.31 1 4.867 0.863 0.704 -3.715 2.715 1.270 0.678
4 -2.422 3.795 1.660 0.820 -2. 165 2.736 1.209 0.069
1 -0.472 1 .370 0.269 0.994 -0.747 2.950 -2.168 0.993
MSU-PA Left 2 -0.829 2.076 3.794 0.831 -1.111 4.511 0.379 0.649
3 -0.231 1.159 0.687 0.996 -0.233 1.473 -0.812 0.992
4 -0.032 1.147 0.822 0.994 -0.496 2.429 -1.689 0.976
1 -1.084 3.322 0.120 0.987 -1.966 9.825 -7.914 0.966
C22026 Left 2 —0.682 2.848 0.174 0.996 -0.408 3.836 -3. 152 0.989
3 -0.994 3.082 0.455 0.989 2.177 -2.723 0.834 0.977
C213395 Left 1 - l .569 3.392 0.472 0.991 -1.570 7.826 —5.1 19 0.646
C-C AD Left 2 0.171 1.888 0.279 0.996 6.754 -7.017 1.696 0.418
3 6.975 3.398 0.488 0.977 -3.75] 2.004 2.436 0.931
C310] 1 Left 3 -0.830 2.557 0.547 0.998 -0.634 4.310 -3095 0.982
C3 1321 Left 1 -0.669 2.303 1.176 0.946 1.618 -0.718 0.753 0.607
3 3.371 5.436 2.326 0.763 7.725 -16.428 9.065 0.755

 

 

TABLE 9. Coefficients from polynomial (Y = AX2+BX+CXO) equations of outside and inside curves with
their R2 values, derived from Bookstein coordinates.

36

Principal Component Variables Generated for Each Claw
A principal component analysis run in SYSTAT for each individual claw from the
above variables rendered principal component variables (shown in the data as PC], PC2,

etc.) for each claw. These variables, listed in Tables 10 through 13, were later used in

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA analyses.
Specimen PCl PC2 PC3
FHSM-VP2062 0.332 - l .974 1.024
UM-P 0.067 -0.219 -0.900
C-Sl 1.519 1.197 1.010
MSU-PA - l .871 0.667 1.036
C22026 0.024 0.109 -1 . 170
C213395 -0.229 -0.158 -0.800
C3 1321 0.158 0.379 -0. 199

 

 

TABLE 10. Principal component variables generated for claw 1 using SYSTAT.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen PCl PC2 PC3 PC4 PCS
FHSM-VP2062 -0.376 -0.349 -0.082 1.969 -1 .632
UM-P 0.308 1.302 -0.503 -0.389 -0. 100
UM-WS 0.948 -1 .622 -1.027 0.236 0.705
C-GBBG -0.830 -0.561 -0.233 -1.906 -1.463
C-P 0.591 -0.962 1.834 -0.256 0.217
C-SI -0.611 0.593 1.513 0.194 0.731
MSU-PA 1.781 0.786 -0.362 -0.254 0.010
C22026 -0.338 1.1 19 -0.256 0.331 0.082
C-CAD - l .473 -0.305 -0.884 0.075 1.449

 

 

 

37

TABLE 1 1. Principal component variables generated for claw 2 using SYSTAT.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen PCl PC2 PC3 PC4 PCS
FHSM-VP2062 0.019 1.396 -1.032 0.613 -0.615
UM-P -2.002 -1 .103 -0.254 -0.225 —0.2 16
UM-WS 1.116 -0.381 1.163 0.250 -0.230
C-GBBG -0.899 0.298 2.492 -0.408 -0.3 1 8
OP 1.384 0.267 0.603 0.369 0.743
C-SI 0.418 —0.339 -0.574 -1.247 2.013
C-PC -0.993 0.630 0.178 1.21 1 0.547
MSU-PA 0.606 -2.247 -0.439 -0.4 l 7 -0.745
C22026 0.216 -0.485 -0.475 2.094 0.705
C-CAD -0.553 0.973 -0.565 - l .381 0.850
C3101] -0.328 0.111 —0.899 -0.009 -1.318
C3132] 1.016 0.881 0199 -0.849 -1.416

TABLE 12. Principal component variables generated for claw 3 using SYSTAT.

Specimen PCl PC2 PC3 PC4 PCS
FHSM-VP2062 0.171 1.251 -0.943 -0.446 -1.386
UM-P -1.338 -0.594 1.396 0.021 -0.718
UM-WS 0.083 0.674 0.396 2.237 0.261
C-GBBG -0.349 0.901 0.816 -1.155 0.049
C-P 2.161 -0.424 0.883 -0.370 0.21 l
KI-Sl -0.615 -0.168 -0.399 -0.539 1.932
C-PC -0.070 0.245 -1 .284 0.156 0.397
MSU-PA -0.043 -1 .884 -0.865 0.096 -0.746

 

 

 

 

 

 

 

 

TABLE 13. Principal component variables generated for claw 4 using SYSTAT.

Claw Phenograms

The principal component variables underwent cluster analyses in SYSTAT and a
phenogram for each individual claw was produced. In the phenograms, taxa were paired
first to other taxa with the most morphometrically similar claws, then to other taxa or
clusters with claws in the order of decreasing morphometric similarity. The distance

metrics below the phenograms show at what distances the taxa and clusters join, and

represent the phenetic distances between the claws of the taxa.

The phenogram of claw 1, shown in Figure 8, pairs the claw of Pteranodon

longiceps most closely with that of the Scarlet Ibis. This cluster is then joined to the

38

Peacock, and these three claws are then joined to a group of clusters containing the two

crocodile species, the alligator, and the Pelican.

Ptaranodon longiceps

 

 

Eudocimus rubcr

 

Pavo cn'srams

Alligator mmissrppim

 

 

Crocodylus acutu: E

Pelecanus

 

Crocodylus poms-us D
6 i 2 1

Distance

 

FIGURE 8. Phenogram of digit 1 claws based on principal components. Clusters are labeled with capital
letters.

The phenogram of claw 2, shown in Figure 9, pairs P. longiceps with the Great
Black-Backed Gull. This cluster is then paired most closely with the cluster containing
one species of crocodile and the Whistling Swan. The next closest cluster to these
contains the Great Auk and Scarlet Ibis, and this cluster, combined with the
aforementioned clusters, joins group of nested clusters containing the Peacock, Pelican,

and the other species of crocodile.

39

 

Larus marinas - A

 

Pteranodon longiceps C
Olor columbianus
Crocodylus acutus
Eudocimus ruber

Pinguinis l

 

 

 

 

Pave cn’status

"’“""“‘ :r—J
Crocodylia porosus

r 1 I I
0.0 0.5 1.0 1.5 2.0

Distance

 

 

 

FIGURE 9. Phenogram of digit 2 claws based on principal components. Clusters are labeled with capital
letters.

P. longiceps is most closely joined to the two specimens of alligator in the third
claw phenogram (Figure 10). These nested clusters are equally joined to the clusters
containing the Pelican and Peacock and Crocodylus acutus and the Scarlet Ibis. The
combination of these clusters is then joined to clusters containing the other crocodile and
Pelican specimens, as well as the Great Black-Backed Gull, the Great Auk, and the

Whistling Swan, in nested configurations.

40

 

Lat-us marinas B
Olor columbianus—-1A l—_1

Pinguinis ——1 _ D
Crocodylus porosus 1C

Pelecamrs conspicillatus I

 

 

 

 

 

 

Pteranodon longiccps E
Alligator mminippim p
Alligator mississippim I

Pavo cnstarus G
Pelecarrus

Crocodylus acutus IE
I

r

l

 

 

 

 

 

 

 

Eudocimus rubcr
I

O

 

 

Distance

FIGURE 10. Phenogram of digit 3 claws based on principal components. Clusters are labeled with capital
letters.

The phenogram of the fourth claw, shown in Figure 11, places the fourth claw of
P. longiceps mostly closely to the cluster containing the fourth claws of the Pelican and
the Great Black-Backed Gull. These three taxa are joined at equal distances to the cluster
containing that Great Auk and the Whistling Swan, and the cluster containing the

Peacock, the Scarlet Ibis, and the other specimen of Pelican.

41

 

Pteranodon longiceps

 

 

 

 

 

 

 

 

 

 

B .
Lams marinas - . A I
Pelecanus
Olor columbianus F21
Pinguinis
Pavo cnlstatus ‘ E
Pelecamrs conspicillatus D
Eudocimus ruber
I l l 1 1
0.0 0.5 1.0 1.5 2.0
Distance

FIGURE 1 1. Phenogram of digit 4 claws based on principal components. Clusters are labeled with capital
letters.

ANOVA Results

In order to determine which clusters of claws were significantly similar or
different to each other, ANOVA was performed on groups of clusters within each
phenogram (see Appendix V1 for the cluster data used in these analyses). These analyses
were performed individually for each principal component variable.

In the phenogram for claw 1, all of the clusters were found to be statistically
similar to each other for two of the three principal components, as shown in Table 14A.
However, principal component 3 contained a statistically significant difference
somewhere within the group of all of the clusters in the phenogram. Narrowing down the
clusters tested for statistical differences yielded data in Table 14B, which shows a
statistically significant difference only for the group of clusters that contains cluster B.

Table 14C shows the AN OVA results for all clusters paired with clusters A and B. Of

42

these pairs, only clusters A and B were found to be significantly similar to each other; all

other tested cluster pairs revealed a significant difference.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A.
Claw 1
Principal Components PCl PC2 PC3
F-Ratio of {A, B, Q D, E} 0.527 0.056 43.993
F-Ratio DegLees of Freedom 4, 9 4, 9 4, 9
At a = 0.05, Significant Value is 3.630 3.630 3.630
Statistically Different? no no es
B.
Claw 1, Principal Component 3
F-Ratio of {B, C, D, E} 36.439
F-Ratio Degrees of Freedom 3, 8
At a = 0.05, Significant Value is 4.070
Statistically Different? es
F-Ratio of {C, D, E} 0.321
F-Ratio Degrees of Freedom 2, 6
At a = 0.05, Significant Value is 5.140
Statistically Different? no
F -Ratio of (D, E} 0.544
F-Ratio Dggrees of Freedom 1, 5
At a = 0.05, Significant Value is 6.610
Statistically Different? no
C.
Claw 1, Principal Component 3
Clusters in Comparison A+B A+C A+D A+E B+C B+D B+E
F-Ratio of {A, B, C, D, E} 0.356 1358.293 199.609 37.959 2452.385 320.375 55.719
F-RatioDegreesofFreedom 1,3 1,2 1,3 1,4 1,3 1,4 1,5
At a = 0.05, Significant Value is 10.13 18.51 10.13 7.71 10.13 7.71 6.61
Statistically Different? no es es es yes es es

 

 

 

 

 

 

 

 

 

 

TABLE 14. ANOVA results of claw l. A. ANOVA results of all clusters in phenogram, for all principal
components. B. ANOVA results for decreasing groups of clusters for principal component 3. C. ANOVA
results of cluster pairs for principal component 3.

Table 15A shows that all of the principal components except principal component
2 had statistical similarities among all of the clusters in the phenogram of claw 2. In spite

of narrowing down the clusters in each ANOVA analysis shown in Table 15B, all groups

43

of clusters in this table contain a statistically significant difference. Among the specific
pairs of clusters that were analyzed (their results shown in Table 15C), several pairs of

clusters show statistical differences between the two tested clusters.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A.
Claw 2

Principal Component PCl PC2 PC3 PC4 PCS
F-Ratio of {A, B, C, D, E, F, G} 0.441 4.562 2.716 0.012 1.156
F-Ratio Degees of Freedom 6, l4 6. l4 6, 14 6, l4 6, 14
At a = 0.05, SMcant Value is 2.850 2.850 2.850 2.850 2.850
Statistically Different? no es no no no

B.

Claw 2, Principal Component 2

F-Ratio oflB, C, D, E, F, G} 5.077

F-Ratio Degrees of Freedom 5, 13

At a = 0.05, Significant Value is 3.030

Statistically Different? es

F-Ratio of {C, D, E, F, G} 6.254

F -Ratio Dgrees of Freedom 4, 12

At a = 0.05, Significant Value is 3.260

Statistically Different? es

F -Ratio of {D, E, F, G} 6.253

F-Ratio Degrees of Freedom 3, 9

At a = 0.05, Significant Value is 3.860

Statistically Different? es

F-Ratio of {E, F, G} 12.478

F-Ratio Degees of Freedom 2. 8

At a = 0.05, Significant Value is 4.460

Statistically Different? es

F-Ratio of {F, G} 14.154

F-Ratio Dgrees of Freedom 1, 7

At a = 0.05, Significant Value is 5.590

Statistically Different? yes

 

 

 

 

44

C.

Claw 2, Principal Component 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Clusters in Comparison A+B A+C B+C A+B A+F B+E B+F C+E
F-Ratio oflA, B, C, D, E} 0.58] 0.331 0.192 141.831 54.766 10.691 15.429 18.979
F-RatingLeesofFreedom 1,2 1,4 1,4 1.2 1,3 1,2 1,3 1.4
At a = 0.05, Sigiificant Value is 18.51 7.71 7.71 18.51 10.13 18.51 10.13 7.71
Statistically Different? no no no es es no yes es
Clusters in Comparison C+F E+F A+D B+D C+D D+E D+F A+G
F-Ratio of {A, B, QQ E} 21.534 0.488 0.1 19 0.585 0.701 3.176 4.380 0.027
F-RatioDegreesofFreedom 1,5 1,3 1,2 1,2 1,4 1,2 1,3 1,6
At a = 0.05, finificant Value is 6.61 10.13 18.51 18.51 7.71 18.51 10.13 5.99
Statistically Different? yes no no no no no no no
Clusters in Comparison B+C C+G D+G E+G F+G

F-Ratio of {A, B, C, D, E} 0.615 0.158 0.373 13.329 14.154

F-Ratio Degrees of Freedom 1, 6 1, 8 1, 6 1, 6 1, 7

At a = 0.05, Significant Value is 5.99 5.32 5.99 5.99 5.59

Statistically Different? no no no yes yes

TABLE 15. ANOVA results of claw 2. A. ANOVA results of all clusters in phenogram, for all principal
components. B. ANOVA results for decreasing groups of clusters for principal component 2. C. ANOVA
results of cluster pairs for principal component 2.

In the phenogram of claw 3 (Figure 10), two of the five principal components

contained statistically significant differences within the group of all ten clusters (Table

16A). When this group was repeatedly narrowed down and analyzed, principal

components 3 and 4 showed significant differences only in groups that included clusters

B, C, and D (Table 16B and 16C). Table 16D shows which cluster pairs yielded

significant differences between the clusters.

 

 

 

 

 

 

A.

Claw 3
Principal Component PC 1 PC2 PC3 PC4 PCS
F -Ratio of {A, B, C, D, E, F, G, H, I, J} 0.646 1.261 5.263 4.093 1.790
F-Ratio Degrees of Freedom 9, 22 9, 22 9, 22 9, 22 9, 22
At a = 0.05, Sijnificant Value is 2.340 2.340 2.340 2.340 2.340
Statistically Different? no no yes yes no

 

 

 

 

 

 

 

45

 

B.
Claw 3, Principal Component 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F-Ratio of {B, C, D, E, F, G, H, I, J} 5.170
F-Ratio Degees of Freedom 8, 21
At a = 0.05, Significant Value is 2.420
Statistically Different? yes
F-Ratio 0113, D, E, F, G, H, I, J} 3.559
F-Ratio Dgegrees of Freedom 7, 19
At a = 0.05, Significant Value is 2.540
Statistically Different? es
F-Ratio of {D, E, F, G, H, I, J} 4.083
F -Ratio Degrees of Freedom 6, 18
At a = 0.05, Significant Value is 2.660
Statistically Different? es
F-Ratio of {E, F, G, H, I, J} 1.372
F -Ratio Degrees of Freedom 5. 14
At a = 0.05figgificant Value is 2.960
Statistically Different? no
F-Ratio of {F, G, H, I, J} 0.605
F-Ratio Degrees of Freedom 4, 13
At a = 0.05, Significant Value is 3.180
Statisticaglly Different? no
F-Ratio of {G, H, I, J} 0.563
F-Ratio Degrees of Freedom 3, l 1
At a = 0.05, Significant Value is 3.590
Statistically Different? no
F-Ratio of {11, I, J} 0.255]
F-Ratio Degrees of Freedom 2. 10
At a = 0.05, Significant Value is 4.100
Statistically Different? no
F-Ratio of {1, J} 0.449
F -Ratio Degrees of Freedom 1, 9
At a = 0.05, Significant Value is 5.120
Statistically Different? no

 

 

46

C.
Claw 3, Principal Component 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F-Ratio of {B, C, D, E, F, G, H, I, J} 4.308
F-Ratio Defies of Freedom 8. 21
At a = 0.05, Significant Value is 2.420
Statistically Different? es

F -Ratio of {C, D, E, F, G, H, I, J} 4.596
F -Ratio Degrees of Freedom 7, 19
At a = 0.05, Significant Value is 2.540
Statistically Different? yes
F-Ratio of {D, E, F, G, H, I, J} 3.072
F-Ratio Degrees of Freedom 6, 18
At a = 0.05, Siggificant Value is 2.660
Statistically Different? yes
F-Ratio of {E, F, G, H, I, J} 1.900
F-Ratio Degrees of Freedom 5, 14
At a = 0.05, Shflficant Value is 2.960
Statistically Different? no
F-Ratio of {F, G, H, I, J} 1.421
F-Ratio Degrees of Freedom 4, 13
At a = 0.05, Significant Value is 3.180
Statistically Different? no
F-Ratio of {G, H, I, J } 1.289
F-Ratio Degrees of Freedom 3, 11
At a = 0.05, Significant Value is 3.590
Statistically Different? no
F-Ratio of (H, I, J} 1.711
F-Ratio Degrees of Freedom 2, 10
At a = 0.05, Significant Value is 4.100
Statistically Different? no
F-Ratio of {I, J} 0.610
F-Ratio Degrees of Freedom 1, 9
At a = 0.05, Significant Value is 5.120
Statistically Different? no

 

 

 

 

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47

The phenogram for claw 4 showed no significant differences between any of the

five clusters analyzed (shown in Table 17). Thus, it was not necessary to perform further

ANOVA analyses on these clusters.

 

 

 

 

 

 

 

 

 

 

 

Claw 4
[Principal Component PC 1 PC2 PC3 PC4 PCS
[F-Ratio of {A, B, C, D, E} 1.952 0.549 3.204 1.032 1.454
[fiatio Degrees of Freedom 4, 7 4, 7 4, 7 4, 7 4, 7
At a = 0.05, Significant Value is 4.120 4.120 4.120 4.120 4.12
Statistically Different? no no no no no

 

 

TABLE I7. ANOVA results of all clusters in phenogram, for all principal components of claw 4.

Tables 18 through 20 summarize the number of statistically different principal
components for each cluster pairs with one or more differences. One or more
significantly different principal components indicate a statistical difference between the
morphologies of the claws within those clusters.

In the phenogram of claw 1 (Figure 8), cluster A was found to be statistically
different from every other cluster except for cluster B; likewise, cluster B was found to be
statistically different from all clusters except cluster A. However, clusters C, D, and E are
statistically similar to each other. These results separate the phenogram into two groups:
the group containing Pteranodon, the Scarlet Ibis, and the Peacock, and the group

containing two species of crocodile, the alligator, and the Pelican.

 

Cluster
A+C
A+D
A+E
B+C
B+D
B+E

Number of Different PCs (out of 3)

 

 

 

 

 

 

l
l
l
l
l
l

 

 

 

 

TABLE 18. List of pairs ofclusters in the phenogram ofthe first claw with one or more statistically dif-
ferent principal components.

48

Table 19 shows that in the phenogram of claw 2 (Figure 9), clusters E and F are
significantly different from clusters A, B, C, and G in one principal component. This
indicates a difference between the claws of the Peacock, Pelican, and C rocodylus porosus
and those of the Great Black-Backed Gull, Pteranodon, Whistling Swan, and Crocodylus
acutus. Furthermore, because cluster D is not found to be statistically different from any
of the other clusters, the second claws of the Great Auk and the Scarlet Ibis are

statistically similar to those of all other taxa in the analysis.

 

Cluster Number of Different PCs (out of 5)
A+E l
A+F
B+F
C+E
C+F
E+G
F+G

 

 

 

 

 

 

 

 

 

 

-_-—

 

TABLE I9. List of pairs of clusters in the phenogram of the second claw with one or more statistically dif-
ferent principal components.

Table 20 shows all of the pairs of clusters in the phenogram of claw 3 (Figure 10)
that have significant differences. Cluster pairs A+H and D+J are different in two
principal components, but the rest of the pairs listed in Table 20 are different in only one

principal component.

49

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Clusters Number of Different PCs (out of 5)
A+B l
A+F l
A+H 2
A+I 1
A+J l
B+E l
B+F 1
8+1 1
8+] 1
D+J 2
A+G l
B+C l
B+H l
C+G l
C+H l
C+I l
C+J 1
D+H l
D+I l

 

 

TABLE 20. List of pairs of clusters in the phenogram of the third claw with one or more statistically dif-
ferent principal components.

50

DISCUSSION
Conclusions Drawn from AN OVA Analyses
The ANOVA results between clusters for each of the four claws are graphically

summarized in Table 21 to facilitate comparison.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Taxon __ Claw l Claw 2 Claw 3 Claw 4
Pavo cristatus i i .
E udocimus ruber i G O O
Larus marinas * i
Olor columbianus 1' .
Pinguinis . i
Pelecanus i O
Pelecanus conspicillatus i t
Alligator mississippiens
Crocodylus acutus
Crocodylus porosus

 

 

 

 

 

 

   

Claw not analysed
Found in cluster statistically difl‘erent from cluster containing pteranodont claw
f ‘ Found in cluster statistically similar to cluster containing pteranodont claw

 

 

TABLE 21. Summary of ANOVA results for clusters containing claws of other taxa in comparison with
clusters containing the claws of Pteranodon longiceps, with key.

As shown in Table 21, the Scarlet Ibis (Eudocimus ruber) is the only taxon that
has all four claws in clusters found to be significantly similar to clusters containing the
pteranodont claws. The next taxon with the most similarity in pes claw morphometrics to
that of Pteranodon is the Peacock (Pavo cristatus), as its first, third, and fourth claws are
found in clusters that are statistically similar to those containing the homologous

pteranodont claws. Two out of three claws of the Great Black-Backed Gull (Larus

51

marinus), the Great Auk (Pinguim's), and Crocodylus acutus are morphometrically
similar to their pteranodont counterparts. Of the examined claws, the Whistling Swan
(Olor columbianus) and both specimens of Pelican (Pelecanus and Pelecanus
conspicillatus) were found to have only two out of four possible claws in clusters that
were statistically similar to clusters containing homologous pteranodont claws. The
remaining two specimens, Alligator mississippiens and C rocodylus acutus, each have
only one out of three possible claws (of the claws tested) in clusters found to be
statistically similar to clusters containing the homologous claws of Pteranodon.

One should bear in mind the both the various pes structures of different taxa as
well as their differing methods of aquatic locomotion when comparing and contrasting
claw morphometrics. For example, in spite of the similarities in claw morphometrics, it is
necessary to bear in mind that Pteranodon and the Scarlet Ibis have differing pes
structures, because the first digit of the Scarlet Ibis’s pes points backwards and is
elevated from the ground (Raikow 1985), whereas the first digit of the pteranodont pes
points forwards with the rest of the digits. The Scarlet Ibis has basally webbed pes, and
although it can swim, does so quite rarely (Kushlan and Bildstein 1992). Moreover, like
that of the Scarlet Ibis, the first digit of the Peacock’s pes is fully reversed and elevated
(Raikow 1985). However, there is no webbing present on the pes of the Peacock, and it
cannot swim under any circumstance (Ragupathy 1998).

Of the Great Black-Backed Gull, the Great Auk, and the crocodile, only the Great
Black-Backed Gull uses its webbed feet to paddle at the surface of the water. The Great
Auk instead propelled itself underwater with its wings (Montevecchi and Kirk 1996), and

the crocodile uses its tail for propulsion (Seebacher et al. 2003). The Whistling Swan and

52

the Pelican, in contrast, use their fully webbed feet to paddle through the water (Wallace
and Mahan 1975). Although Alligator mississippiens and Crocodylus acutus have
extensively webbed pes like the Whistling Swan and the Pelican, adult crocodiles and
alligators propel themselves in water with their tails, using their feet for balance and
stability (Seebacher et al. 2003).

If conclusions in regards to aquatic locomotion can be made from the comparison
of pteranodont claw morphometrics to those of extant organisms with known methods of
locomotion, then the significant similarities and differences among these claws indicate
that Pteranodon did not habitually paddle at or under the water’s surface with its pes.
First, the morphometrics of its claws most closely resemble those of the Scarlet Ibis,
which only swims when in danger, and second most closely resemble those of the
Peacock, which does not swim at all. Furthermore, clusters containing pteranodont claws
have found to be statistically different for two out of four claws for the Pelican and
Whistling Swan specimens, which use their feet to actively paddle through the water.
Therefore, it is highly unlikely that Pteranodon actively swam in the epicontinental
seaway that once covered Kansas.

On the other hand, it is possible that Pteranodon may have floated and/or treaded
water at the surface of the seaway. This is suggested because Crocodylus acutus and the
Great Auk, which both swim/swam by methods other than propulsion with the pes, have
two of their three claws in clusters that are statistically similar to clusters containing
pteranodont claws. These similarities indicate the option of some aquatic locomotion,
even if that locomotion is not actively traveling. Hypothetically, Pteranodon could alight

upon the water’s surface to feed, then float or tread water efficiently enough to not sink

53

but without forward motion, and then take off from the water with a method discussed in
the introduction.

Not all results of this analysis are exactly consistent with the above explanation.
For example, in contrast with Crocodylus acutus, Crocodylus porosus and Alligator
mississippiens only have one claw each in clusters statistically similar to clusters
containing pteranodont claws. It is presently unknown if part of this inconsistency is due
to the data missing from the missing claw 2 of Alligator mississippiens. This
inconsistency contradicts the idea that Pteranodon probably used its pes only for balance
in the water, and not for propulsion. A second inconsistency is that two of the three claws
of the Great Black-Backed Gull being in clusters that are statistically similar to those
containing pteranodont claws. Although the Great Black-Backed Gull floats at the suface
more often than it paddles through the water with its feet, these similarities somewhat
contradict the idea that Pteranodon probably did not actively paddle at the water’s

surface.

Consistencies and Inconsistencies of the Study

Several consistencies in the claw phenograms lend support to the validity of this
study. For example, in the phenogram of claw 1, the two species of crocodile and one
species of alligator are clustered closely together, as would be expected (in spite of the
presence of the Pelican in that cluster). A similar consistency is present in the phenogram
of claw 3, where the two alligator specimens are clustered closely together.

However, some inconsistencies are present in this study as well. One such
inconsistency lies in the significant difference between the cluster containing the second

Peacock claw and the cluster containing the second pteranodont claw. Examination of the

54

second Peacock claw in different lighting offers the possibility that the second and fourth
landmarks may be misplaced on the claw. If this is indeed the case, then this mistake may
have affected the data enough to cause the second claw of the Peacock to differ
morphometrically from that of Pteranodon.

Other apparent inconsistencies lie within the placement of taxa within the claw
phenograms. Although the phenogram of claw 3 has the two alligator specimens
clustered closely together, the two species of crocodile are in separate, different clusters.
Likewise, the phenogram of claw 4 places the two Pelican specimens in separate clusters.
The phenogram of claw 2 shares a similar situation with the two crocodile species.
However, since claws can be some variable in shape, it should be considered that no two
specimens from a single taxon will have identically-shaped claws, and this may account
for the apparent separation of phenotypically close taxa in the phenogram clusters.

Potential sources of error in this study lie in the missing data that are represented
in Table 21 as solid black boxes. It was not possible to obtain clear, useful photographs of
Olor columbianus claw 1, Pelecanus conspicillatus claws l and 2, and Alligator
mississippiens claw 2 because these specimens were stored in glass case, which made
photography difficult. Furthermore, some data were missing due to a lack of homologous
claws among some of the taxa. Larus marinas and Pinguinis did not have their first claw
analyzed because these taxa do/did not possess a first digit. Likewise, the three
crocodylian taxa do not have a claw on their fourth digit.

Arguments for Other Pterosaur Aquatic Locomotion: Soft Part Preservation
Evidence

Aquatic locomotion has been suggested as a possibility for at least three species in

55

addition to Pteranodon. These three suggestions stem from the observation of soft tissue
preservation found in specimens of Rhamphorhynchus muensteri, Pterodactylus sp., and
a specimen of ?Azhardichidae indet. studied by Frey et al (2003). All three of these
specimens show what appear to be imprints of webbing between the pes digits. The
Rhamphorhynchus muensteri specimen shows distinct traces of webbing between
metatarsals I through IV and digits I through V of the right pes. This webbing extends all
the way to the bases of the claws. The webbing found in the pes of the Pterodactylus sp.
specimen extends to the base of the ungula phalanx, and is thickest between digits HI and
IV. The ?Azhardchidae indet. specimen shows traces of webbing on its pes in the form of
a geotithic stain. It also shows these traces on its manus, implying that the manus was
webbed as well (Frey et al 2003).

The formations that yielded these three specimens are consistent with aquatic
paleoenvironments. The Rhamphorhynchus muensteri and Pterodactylus Sp. specimens
were both found in the Solnhofen formation (Frey et al 2003), which was deposited in a
marine environment during the Jurassic (Kemp and Trueman 2003). The ?Azhardchidae
indet. specimen was found in the Crato Formation (Frey et a1 2003), which consists of
lacustrine sediments deposited in the Early Cretaceous (Heimhofer et al 2006).

It is logical that webbing present between the pes digits implies the capability for
aquatic locomotion in pterosaurs within different clades and from different formations,
because although most aquatic birds have independently evolved, they all tend to have
feet that are expanded with partial or full webbing between the toes (Wallace and Mahan
1975). In fact, pterosaur phylogeny lends support to the idea of independent evolution of

pes structures designed for aquatic locomotion. Rhamphorhynchus and Pterodactylus are

56

primitive clades found closely together at the base of the pterosaur phylogeny. In
contrast, Azhdarcho is found in a separate, more derived clade (6 steps from
Pterodactylus) (Bennett 1994). Since it is improbable that webbing on the pes has
persisted throughout pterosaur evolution, this condition was likely an independently
acquired adaptation to aquatic environments in these taxa. This information does not
indicate whether or not Pteranodon also had webbing on the pes, but it does suggest a

possibility of webbing and/or some other form of adaptation to its aquatic environment.

Arguments for Other Pterosaur Aquatic Locomotion: Ichnological Evidence

Ichnofossils found in the western United States have also been proposed as
evidence supporting the possibility that some pterosaurs could swim or float in water.
The late Jurassic Sundance and Summerville formations contain tracks proposed by
Lockley and Wright (2003) to be the traces of pterosaurs floating in the shallow sea that
was regressing from the area at that time. The most definitive swim tracks were found at
the Del Monte Mines and Alcova lake localities. Some of these tracks show what appear
to be impressions of claws, phalangeal pads, and heels of floating pterosaurs. Other tracks
are proposed to be between one and four short toe impressions and elongate scratch
marks. These parallel scratch marks are interpreted as toe-tip traces in the substrate.
Additionally, some rocks containing these traces also show ripple marks. The
combination of these structures present in the rock are interpreted by Lockley and Wright
(2003) as the tracks of a buoyant pterosaur floating in shallow water.

It would be impossible to find any such ichnofossils in the Niobrara chalk, since

the Cretaceous epicontinental seaway was deep enough to serve as a habitat for

57

mososaurs and plesiosaurs (Bennett 1994, 2000). However, the interpretation of pterosaur
swim traces in the Sundance and Summerville formations opens the possibility that some
pterosaurs may have been able to float in the water. If this were to be the case, then it is

not unreasonable that Pteranodon could tread the water’s surface.

Summary and Future Work

The similarities of the morphometrics of pteranodont claws to those of the Scarlet
Ibis and the Peacock, along with the dissimilarities to those of the Whistling Swan and
the Pelican indicate that Pteranodon could not propel itself through the water with its
feet. However, the similarities between the morphometrics of pteranodont claws and
those of Crocodylus acutus and the Great Auk suggest the possibility that Pteranodon
could stay afloat and/or tread water at the surface, without necessarily moving forward.
This possibility is not unique to Pteranodon, as other pterosaurs (Rhamphorhynchus,
Pterodactylus, and ?Azhdarcho indet.) have shown what appear to be traces of webbing
on the pes. Proposed ichnofossils of pterosaurs treading water in what were once shallow
seas during the Jurassic also suggest the possibility of aquatic locomotion in pterosaurs.

Continuations of this work can be taken in several different directions. For
example, the techniques of morphometrics with use of an EPB can be applied to the
morphological analysis of the metatarsals and/or digits of Pteranodon in the question of
its potential for aquatic locomotion. However, the study of possible pteranodont aquatic
locomotion does not have to focus only on the pes of Pteranodon. The femoral index of
Pteranodon may be compared to that of swimming birds, birds of prey, wading birds,

etc., as presented in Zeffer et a1 (2003). It may also be possible to compare the beak of

58

Pteranodon to those of extant birds who feed in the water, to see if Pteranodon was
capable of plunging or diving based on beak morphology.

A tangential project could be performed on the pteranodont claws of unknown
articulation. These claws, included in the phenogram in Figure 69, can be compared to
the claws of known articulations in the phenogram in order to propose to which digit each
unknown claw may correspond. The morphometrics of the unknown claws may also be
included in digit-specific cluster analyses so that a more specific examination of their

possible placements may be performed.

59

APPENDIX I
PHOTOGRAPHS OF CLAWS WITH LANDMARKS

Note: The following images are not to scale.

   

 

FIGURE 12. Photographs of FHSM-VP2062 left pes claws with landmarks. A. Claw l. B. Claw 2. C. Claw

3. D. Claw 4.
A. 3'

FIGURE 13. Photographs of KU49399 left pes claws with landmarks. A. Unknown Claw l. B. Unknown
Claw 2.

 

6O

 

FIGURE 14. Photograph of YPM2554 left pes Unknown Claw 3 with landmarks.

 

FIGURE 15. Photograph of YPM2436 left pes Unknown Claw 4 with landmarks.

A. B.

FIGURE 16. Photographs of UMP left pes claws with landmarks. A. Claw 1. B. Claw 2. C. Claw 3. D.
Claw 4.

        

C.

61

B. . CI

FIGURE 17. Photographs of UM—WS left pes claws with landmarks. A. Claw 1. B. Claw 2. C. Claw 3.

BA CB

FIGURE 18. Photographs of C-GBBG left pes claws with landmarks. A. Claw 2. B. Claw 3. C. Claw 4.

t t as

FIGURE 19. Photographs of C-P left pes claws with landmarks. A. Claw 2. B. Claw 3. C. Claw 4.

.\ .1 at .1

FIGURE 20. Photographs of 081 left pes claws with landmarks. A. Claw 1. B. Claw 2. C. Claw 3.
D. Claw 4.

 

A.

 

A.

 

62

 

I

 

A. B.

FIGURE 21. Photographs of C—PC left pes claws with landmarks. A. Claw 3. B. Claw 4.

 

FIGURE 22. Photographs of MSU-PA left pes claws with landmarks. A. Claw 1. B. Claw 2. C. Claw 3. D.
Claw 4.

   

C.
FIGURE 23. Photographs of C22026 left pes claws with landmarks. A. Claw 1. B. Claw 2. C. Claw 3.
I ,

 

FIGURE 24. Photograph of C213395 left pes Claw l with landmarks.

63

   

B.

FIGURE 25. Photographs of C-CAD left pes claws with landmarks. A. Claw 2. B. Claw 3.

 

FIGURE 26. Photograph of C3101] left pes Claw 3 with landmarks.

 

A. B.

FIGURE 27. Photographs of C31 321 left pes claws with landmarks. A. Claw l. B. Claw 3.

APPENDIX II

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NOTES ON PHOTOGRAPHS
Specimen Pes Claw Notes
1
FHSM-VP2062 Left 3
4
KU49399 Unknown UNKl
Unknown UNK2
YPM2554 Unknown UNK3 Image flipped horizontally
YPM2436 Unknown UN K4
1 Image flipped horizontally
UM-P Left 3 Image flipped horizontally
4
2
UM-WS LCfl 3 Imagflipped horizontally
4 Image flipped horizontally
2
C-GBBG Left 3 Image flipped horizontally
4 Image flipped horizontally
2 Image flipped horizontally
C-PI Left 3 Imagg flipped horizontally
4 Image fljped horizontally
1 Strange shaped claw
051 Left 2 , ,
3 Image flipped horizontally
4 Image flipped horizontally
C-PC Left 3 Image flipped horizontally; no scale
4 Image flipped horizontally; no scale
1
2
MSU-Pa Left . ,
3 Image flipped horizontally
4 Image flipped horizontally
1 No scale
C22026 Left 2 N0 scale
3 No scale
C213395 Left 1 Image flipped horizontally; no scale
C—C AD Left 2 Image flipped horizontally; no scale
3 Image flipped horizontally; no scale
C310] 1 Left 3 No scale
C3132] Left 1 Image flipped horizontally; no scale
3 Image flipped horizontally; no scale

 

TABLE 22. Notes on photographs used in study.

65

 

APPENDD( IH

RAW COORDINATES OF CLAW LANDMARKS

 

Raw Coordinates

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Pes Claw Landmark l Landmark 2 Landmark 3 Landmark 4
X Y X Y X Y X Y
1 1.58 0 1.86 0 1.72 0.93 1.71 0.03
FHSM-VP2062 Left 2 1.74 0 2.1 'l 0 2.1 1.26 1.91 -0.03
3 2.81 0 3.27 0 2.84 1.31 3.04 -0.06
4 0.36 0 0.7 0 0.54 1.26 0.52 0.06
KU49399 Unknown UNKl 1.2 0 1.56 O 1.23 1.64 1.38 0.04
Unknown UNK2 0.52 0 0.95 0 1.1 2.17 0.77 0.08
YPM2554 Unknown UNK3 0.71 0 1.23 0 1.09 1.62 0.97 -0.08
YPM2436 Unknown UNK4 0.4 0 1.8 0 2.28 2.08 1.14 -0.16
1 0.83 0 1.31 0 1.46 1.35 1.07 0.06
UM-P Left 2 0.76 0 1.06 0 1.45 1.08 0.91 0.04
3 0.6 0 1.42 0 2 0.52 0.96 -0.07
4 0.75 0 1.27 0 1.63 0.61 1.05 0.07
2 0.54 0 0.81 0 0.71 1.1 0.7 -0.04
UM-WS LCfl 3 0.32 0 0.66 0 0.98 1.28 0.48 -0.05
4 0.36 0 0.75 0 0.67 1.59 0.59 -0.1
2 0.41 0 0.61 0 0.59 0.5 0.51 -0.02
C-GBBG Left 3 0.25 0 0.64 0 0.71 0.83 0.42 -0.06
4 0.75 0 0.98 0 0.88 0.65 0.88 -0.04
2 0.31 0 0.52 0 0.52 0.87 0.4 -0.1
0131 LCft 3 0.26 0 0.59 0 0.61 1.38 0.42 -0.08
4 0.22 0 0.34 0 0.42 0.76 0.29 -0.02
1 1.05 0 1.25 0 0.52 0.69 1.17 -0.06
C-SI Left 2 0.5 0 0.67 0 0.77 0.52 0.57 -0.06
3 0.5 0 0.7 0 0.81 0.68 0.59 -0.08
4 0.46 0 0.64 0 0.7 0.45 0.56 -0.06
C-PC Left 3 0.24 0 0.56 0 0.47 0.66 0.4 -0.03
4 0.23 0 0.46 0 0.52 0.75 0.34 -0.05
1 0.32 0 0.99 0 2.02 0.43 0.65 0.03
MSU-PA Left 2 0.86 0 1.3 0 1.8 2.18 1.04 0
3 2.32 0 3.03 0 5.06 1.13 2.62 -0.05
4 1.23 0 2.29 0 4.59 1.35 1.74 0.12
l 0.57 0 1.7 O 2.34 3.19 1.13 0.16
C22026 Left 2 0.56 0 1.64 0 2.66 3.46 1.1 0
3 1.93 0 2.51 0 2.98 1.73 2.26 -0.04
C213395 Left 1 0.63 0 1.73 0 2.04 2.61 1.15 -0.12
C-CAD Left 2 1.02 0 1.98 0 1.88 2.08 1.57 0.15
3 0.87 0 1.38 0 1.07 1.33 1.09 -0.16
C3101 1 Left 3 1.02 0 2.59 0 3.32 3.82 1.72 -0.023
C31321 Left 1 1.12 0 2.07 0 2.55 2.97 1.62 -0.13
3 0.84 0 1.62 0 1.19 2.97 1.14 -0.06

 

 

 

 

 

 

 

 

TABLE 23. Raw coordinates of all claw landmarks.

66

 

Note: In the following tables, “outer” refers to the left side curve of each claw, whereas

APPENDIX IV

CLAW CURVATURE COORDINATES AND PLOTS

“inner” refers to the right side curve of each claw.

TABLE 24. Raw and Bookstein coordinates taken from the outer and inner curves of FHSM-VP2062, claw
1.

 

FHSM-VP2062 Claw 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
1.700 0.910 0.429 3.250 1.720 0.910 0.500 3.250
1.650 0.890 0.250 3.179 1.740 0.860 0.571 3.071
1.600 0.860 0.071 3.071 1.740 0.790 0.571 2.821
1.590 0.810 0.036 2.893 1.740 0.750 0.571 2.679
1.570 0.750 -0.036 2.679 1.720 0.730 0.500 2.607
1.570 0.710 -0.036 2.536 1.740 0.720 0.571 2.571
1.570 0.650 -0.036 2.321 1.750 0.690 0.607 2.464
1.560 0.620 —0.071 2.214 1.760 0.660 0.643 2.357
1.550 0.550 -0.107 1.964 1.760 0.610 0.643 2.179
1.540 0.510 -0.143 1.821 1.780 0.570 0.714 2.036
1.540 0.430 -0. 143 1.536 1.780 0.540 0.714 1.929
1.530 0.370 -0.179 1.321 1.800 0.510 0.786 1.821
1.540 0.330 -0. 143 1.179 1.800 0.490 0.786 1.750
1.540 0.290 -0.143 1.036 1.810 0.430 0.821 1.536
1.550 0.220 -0.107 0.786 1.830 0.370 0.893 1.321
1.540 0.180 -0.143 0.643 1.830 0.330 0.893 1.179
1.530 0.130 -0.179 0.464 1.840 0.290 0.929 1.036
1 .530 0.090 -0.179 0.321 1.850 0.240 0.964 0.857
1.860 0.200 1.000 0.714
1.860 0.150 1.000 0.536
1.870 0.1 10 1.036 0.393
1.890 0.070 1.107 0.250

 

 

 

 

 

67

 

y = -15.455x3 + 7.6814x + 2.625 FHSM-VP2062 Claw 1

R2 = 0.8363 ,
4.000 9 Outer Curve (BS)
3500 I Inner Curve (BS)
. I i—Poly. (Outer Curve (B8))

4 . ‘
3.000 —Po]y. (Inner Curve (B8))
2.500 , ' ’ _ if I!

2.000 5
1.500 '
1.000 .
0.500 “ :

0.000 1 ~ “—4

-0.500 0.000 0.500 1.000 1.500 ,
y = -().5952x“ - 3.7491x + 5.0239

R3 = 0.9694

Y Coordinates

X Coordinates

FIGURE 28. Plotted Bookstein coordinates taken from the inner and outer curves of FHSM-VP2062 claw
1, with trend lines and matching equations.

68

TABLE 25. Raw and Bookstein coordinates taken from the outer and inner curves of FHSM-VP2062, claw
2.

 

FHSM-VP2062 Claw 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
2.050 1.260 0.838 3.405 2.1 10 1.220 1.000 3.297
2.020 1.240 0.757 3.351 2.080 1.200 0.919 3.243
2.000 1.220 0.703 3.297 2.060 1.170 0.865 3.162
1.970 1.200 0.622 3.243 2.040 1.140 0.81 1 3.081
1.950 1.180 0.568 3.189 2.020 1.090 0.757 2.946
1.940 1.150 0.541 3.108 2.020 1.050 0.757 2.838
1.920 1.120 0.486 3.027 2.020 0.990 0.757 2.676
1.910 1.090 0.459 2.946 2.020 0.910 0.757 2.459
1.890 1.060 0.405 2.865 2.020 0.840 0.757 2.270
1.870 1.020 0.351 2.757 2.020 0.810 0.757 2.189
1.840 0.990 0.270 2.676 2.020 0.740 0.757 2.000
1.830 0.960 0.243 2.595 2.020 0.700 0.757 1.892
1.820 0.920 0.216 2.486 2.030 0.640 0.784 1.730
1.810 0.880 0.189 2.378 2.010 0.590 0.730 1.595
1.790 0.840 0.135 2.270 2.010 0.550 0.730 1.486
1.780 0.800 0.108 2.162 2.000 0.510 0.703 1.378
1.760 0.770 0.054 2.081 2.010 0.460 0.730 1.243
1.750 0.700 0.027 1.892 1.990 0.420 0.676 1.135
1.740 0.650 0.000 1.757 2.010 0.390 0.730 1.054
1.730 0.610 -0.027 1.649 2.020 0.330 0.757 0.892
1.720 0.570 -0.054 1.541 2.020 0.270 0.757 0.730
1.710 0.520 -0.081 1.405 2.030 0.260 0.784 0.703
1.700 0.480 -0.108 1.297 2.050 0.180 0.838 0.486
1.690 0.430 -0.135 1.162 2.080 0.150 0.919 0.405
1.690 0.400 -0.135 1.081 2.090 0.120 0.946 0.324
1.700 0.340 -0.108 0.919 2.120 0.100 1.027 0.270
1.700 0.290 -0.108 0.784
1.680 0.240 -0.162 0.649
1.680 0.170 -0.162 0.459
1.690 0.120 -0.135 0.324
1.710 0.070 -0.081 0.189

 

 

 

 

 

69

 

y = 3515218 + 4.9313x + 1.5713 FHSM.vp2062 Claw 2
R2 = 0.934

4.000

3.500 —
3.000 ~
2.500 1
2.000 -
1.500 .
1.000 -
3:383. .2- . 2"

-0.500 0.000 0.500 1.000 1.500 .
y = —2s.s09\- + 48.784x — 18.0112

123:0.0552

0 Outer CurVe (B8)

I Inner Curve (BS)
— Poly. (Outer Curve (B8))
—Poly. (Inner Curve (B8))

Y Coordinates

 

X Coordinates

FIGURE 29. Plotted Bookstein coordinates taken from the inner and outer curves of FHSM-VP2062 claw
2, with trend lines and matching equations.

70

TABLE 26. Raw and Bookstein coordinates taken from the outer and inner curves of FHSM-VP2062, claw
3.

 

FHSM-VP2062 Claw 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
2.810 1.300 0.000 2.826 2.900 1.290 0.196 2.804
2.790 1.260 -0.043 2.739 2.890 1.250 0.174 2.717
2.760 1.230 -0.109 2.674 2.900 1.210 0.196 2.630
2.750 1.190 -0. 130 2.587 2.910 1.180 0.217 2.565
2.750 1.150 -0.130 2.500 2.910 1.150 0.217 2.500
2.740 1.120 -0.152 2.435 2.920 1.110 0.239 2.413
2.750 1.080 —0.130 2.348 2.920 1.070 0.239 2.326
2.740 1.040 -0. 152 2.261 2.920 1.040 0.239 2.261
2.730 1.000 -0.174 2.174 2.930 1.000 0.261 2.174
2.730 0.970 -0.174 2.109 2.920 0.970 0.239 2.109
2.720 0.930 -0.196 2.022 2.920 0.940 0.239 2.043
2.730 0.910 -0.174 1.978 2.920 0.910 0.239 1.978
2.730 0.880 -0.174 1.913 2.940 0.880 0.283 1.913
2.730 0.840 -0. 174 1.826 2.940 0.850 0.283 1.848
2.730 0.800 -0.174 1.739 2.960 0.810 0.326 1.761
2.730 0.760 -0.174 1.652 2.970 0.780 0.348 1.696
2.730 0.710 -0.174 1.543 2.980 0.750 0.370 1.630
2.720 0.660 —0. 196 1.435 3.000 0.720 0.413 1.565
2.730 0.620 —0. 174 1.348 3.010 0.680 0.435 1.478
2.730 0.580 -0.174 1.261 3.020 0.650 0.457 1.413
2.720 0.510 -0. 196 1.109 3.020 0.620 0.457 1.348
2.740 0.480 -0. 152 1.043 3.040 0.590 0.500 1.283
2.770 0.450 -0.087 0.978 3.060 0.570 0.543 1.239
2.790 0.430 -0.043 0.935 3.070 0.530 0.565 1.152
2.800 0.390 -0.022 0.848 3.090 0.490 0.609 1.065
2.790 0.310 -0.043 0.674 3.100 0.450 0.630 0.978
2.780 0.250 -0.065 0.543 3.120 0.420 0.674 0.913
2.760 0.150 -0.109 0.326 3.140 0.370 0.717 0.804
3.160 0.320 0.761 0.696
3.190 0.290 0.826 0.630
3.230 0.240 0.913 0.522
3.260 0.200 0.978 0.435
3.280 0.170 1.022 0.370

 

 

 

 

 

71

 

y = 6.2651x2 - 0.0681x + 1.5694 FHSM-VP2062 Claw 3

R2 = 0.0136
3.000
.0 0 Outer Curve (B8)

2500 I Inner Curve (BS)
g 2000 —Poly. (Outer Curve (B8))
.5 —Poly. (Inner Curve (88))
g 1.500 ’ *
c:
U ‘5

1.000 .
>7 } 3 : 3.9339x” - 5.999% + 3.5399

0500 .. R3 = 0.9656

0.000 ~

-0.500 0.000 0.500 1.000 1.500

X Coordinates

FIGURE 30. Plotted Bookstein coordinates taken from the inner and outer curves of FHSM-VP2062 claw
3, with trend lines and matching equations.

72

TABLE 27. Raw and Bookstein coordinates taken from the outer and inner curves of FHSM-VP2062, claw
4.

 

FHSM-VP2062 Claw 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.480 1.240 0.353 3.647 0.590 1.220 0.676 3.588
0.460 1.200 0.294 3.529 0.590 1 . 190 0.676 3.500
0.450 1.170 0.265 3.441 0.580 1.160 0.647 3.412
0.430 1.140 0.206 3.353 0.590 1.130 0.676 3.324
0.420 1.100 0.176 3.235 0.600 1 . 100 0.706 3.235
0.430 1.060 0.206 3.1 18 0.600 1.060 0.706 3.1 18
0.420 1.030 0.176 3.029 0.610 1.030 0.735 3.029
0.410 1.000 0.147 2.941 0.620 1.000 0.765 2.941
0.380 0.980 0.059 2.882 0.620 0.970 0.765 2.853
0.380 0.940 0.059 2.765 0.620 0.940 0.765 2.765
0.380 0.900 0.059 2.647 0.620 0.900 0.765 2.647
0.370 0.860 0.029 2.529 0.630 0.840 0.794 2.471
0.380 0.810 0.059 2.382 0.640 0.790 0.824 2.324
0.360 0.790 0.000 2.324 0.650 0.750 0.853 2.206
0.340 0.760 -0.059 2.235 0.660 0.700 0.882 2.059
0.340 0.730 -0.059 2.147 0.690 0.670 0.971 1.971
0.330 0.680 -0.088 2.000 0.700 0.640 1.000 1.882
0.330 0.640 -0.088 1.882 0.700 0.590 1.000 1.735
0.320 0.590 -0.1 18 1.735 0.710 0.540 1.029 1.588
0.330 0.550 -0.088 1.618 0.700 0.490 1.000 1.441
0.320 0.510 -0.1 18 1.500 0.700 0.440 1.000 1.294
0.320 0.470 -0.1 18 1.382 0.700 0.400 1.000 1.176
0.320 0.410 -0.1 18 1.206 0.710 0.350 1.029 1.029
0.320 0.370 -0.1 18 1.088 0.720 0.290 1.059 0.853
0.340 0.340 -0.059 1.000 0.730 0.250 1.088 0.735
0.350 0.310 -0.029 0.912 0.760 0.200 1.176 0.588
0.360 0.270 0.000 0.794 0.790 0.160 1.265 0.471
0.330 0.230 -0.088 0.676
0.300 0.190 -0.176 0.559
0.280 0.150 -0.235 0.441

 

 

 

 

 

73

 

y = -46635x’ + 6.3678x + 2.0906 FHSM-VP2062 Claw 4

 

R2 = 0.7986
4.000 -
0 Outer Curve (B8)
3.500
3000 I Inner Curve (BS)
53 2'500 —Poly. (Outer Curve (BS))
3:- ' —Poly. (Inner Curve (B8))
5 2.000 ‘ 55* 5555 5
8 1.500
>’ 1.000 §'2.3.()7(15\3- 1 1.171x + 9.5381
0.500 R3 = 0.9574
0.000 - ~ *-

-0.500 0.000 0.500 1.000 1.500

X Coordinates

FIGURE 31. Plotted Bookstein coordinates taken from the inner and outer curves of FHSM-VP2062 claw
4, with trend lines and matching equations.

74

 

UM-P Claw 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
1.410 1.330 1.208 2.771 1.440 1.320 1.271 2.750
1.390 1.320 1.167 2.750 1.420 1.280 1.229 2.667
1.360 1.300 1.104 2.708 1.400 1.260 1.188 2.625
1.330 1.290 1.042 2.688 1.390 1.230 1.167 2.563
1.300 1.270 0.979 2.646 1.380 1.200 1.146 2.500
1.280 1.260 0.938 2.625 1.370 1.170 1.125 2.438
1.250 1.250 0.875 2.604 1.360 1.150 1.104 2.396
1.220 1.230 0.813 2.563 1.340 1.120 1.063 2.333
1.200 1.220 0.771 2.542 1.340 1.090 1.063 2.271
1.180 1.200 0.729 2.500 1.320 1.070 1.021 2.229
1.160 1.180 0.688 2.458 1.310 1.030 1.000 2.146
1.150 1.170 0.667 2.438 1.290 1.010 0.958 2.104
1.130 1.160 0.625 2.417 1.280 0.970 0.938 2.021
1.110 1.140 0.583 2.375 1.280 0.950 0.938 1.979
1.080 1.110 0.521 2.313 1.260 0.920 0.896 1.917
1.060 1 . 100 0.479 2.292 1.260 0.890 0.896 1.854
1.040 1 .080 0.438 2.250 1.260 0.860 0.896 1.792
1.020 1.040 0.396 2.167 1.260 0.860 0.896 1.792
1.000 1.020 0.354 2.125 1.260 0.810 0.896 1.688
0.990 0.990 0.333 2.063 1.260 0.770 0.896 1.604
0.970 0.960 0.292 2.000 1.270 0.740 0.917 1.542
0.950 0.930 0.250 1.938 1.270 0.720 0.917 1.500
0.940 0.910 0.229 1.896 1.290 0.680 0.958 1.417
0.930 0.870 0.208 1.813 1.300 0.650 0.979 1.354
0.910 0.830 0.167 1.729 1.320 0.630 1.021 1.313
0.910 0.800 0.167 1.667 1.330 0.600 1.042 1.250
0.900 0.760 0.146 1.583 1.350 0.570 1.083 1.188
0.890 0.730 0.125 1.521 1.370 0.550 1.125 1.146
0.890 0.700 0.125 1.458 1.380 0.520 1.146 1.083
0.880 0.680 0.104 1.417 1.420 0.510 1.229 1.063
0.880 0.650 0.104 1.354 1.450 0.490 1.292 1.021
0.870 0.620 0.083 1.292
0.870 0.590 0.083 1.229
0.860 0.550 0.063 1.146
0.870 0.510 0.083 1.063
0.870 0.480 0.083 1.000
0.880 0.430 0.104 0.896
0.890 0.390 0.125 0.813

 

 

 

 

 

 

 

 

75

TABLE 28. Raw and Bookstein coordinates taken from the outer and inner curves of UM-P, claw 1.

 

y = -1.8185x2 + 3.5593x + 0.9675 UM-P Claw 1
R2 2 0.9228
3.000

2.500 5
I 0 63121 Curve(BS)

I Inner Curve (BS)
1—Poly. (Outer Curve (B8))
'—_~ Poly. (Inner Curve (B8))

Y Coordinates
La”
1

 

0.500 1
0.000 5 W5
0.000 0.500 1.000 1.500 3
,_ v : ~3.0879.\'~ + 7.371x - 2.425
X Coordinates ' .

R” = 0.0392

FIGURE 32. Plotted Bookstein coordinates taken from the inner and outer curves of UM-P claw 1, with
trend lines and matching equations.

76

 

UM—P Claw 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
1.380 1.090 2.067 3.633 1.420 1.010 2.200 3.367
1.340 1.080 1.933 3.600 1.400 1.000 2.133 3.333
1.320 1.070 1.867 3.567 1.390 0.970 2.100 3.233
1.290 1.060 1.767 3.533 1.370 0.940 2.033 3.133
1.260 1.050 1.667 3.500 1.350 0.930 1.967 3.100
1.230 1.040 1.567 3.467 1.340 0.910 1.933 3.033
1.200 1.020 1.467 3.400 1.320 0.880 1.867 2.933
1.180 1.000 1.400 3.333 1.290 0.860 1.767 2.867
1 . 150 0.990 1.300 3.300 1.270 0.830 1.700 2.767
1.130 0.970 1.233 3.233 1.250 0.810 1.633 2.700
1.090 0.960 1 . 100 3.200 1.240 0.790 1.600 2.633
1.070 0.930 1.033 3.100 1.220 0.750 1.533 2.500
1.040 0.920 0.933 3.067 1.210 0.710 1.500, 2.367
1.010 0.890 0.833 2.967 1.210 0.690 1.500 2.300
0.990 0.860 0.767 2.867 1.200 0.650 1 .467 2.167
0.970 0.830 0.700 2.767 1.210 0.620 1.500 2.067
0.950 0.800 0.633 2.667 1.210 0.590 1.500 1.967
0.930 0.780 0.567 2.600 1.230 0.570 1.567 1.900
0.920 0.750 0.533 2.500 1.260 0.550 1.667 1.833
0.910 0.710 0.500 2.367 1.280 0.530 1.733 1.767
0.900 0.680 0.467 2.267 1.320 0.520 1.867 1.733
0.880 0.650 0.400 2.167 1.350 0.510 1.967 1.700
0.870 0.610 0.367 2.033 1.380 0.500 2.067 1.667
0.860 0.570 0.333 1.900
0.850 0.530 0.300 1.767
0.840 0.500 0.267 1.667
0.830 0.460 0.233 1.533
0.820 0.430 0.200 1.433
0.830 0.380 0.233 1.267
0.820 0.340 0.200 1.133

 

 

 

 

 

77

TABLE 29. Raw and Bookstein coordinates taken from the outer and inner curves of UM-P, claw 2.

 

y = .0.9551x2 + 3.2045x + 0.8839 UM-P Claw 2

   

R2 = 0.9678
4.000
. ,
3.500 9 If, 0 Outer Curve (BS)
3 3.000 5 I Inner Curve (BS)
’g 2,500 -‘ —Poly. (Outer Curve (B8))
'2 2,000 —Poly. (Inner Curve (B8))
8 ..___ ~ - m
0 1.500 -
>7 1 000 O. . j 53‘ - ,3 ‘3 . 1
. * y:_.n_)5.\ — 7._46l\ +7.877‘)
0.500 - R3 = 0.3598
0.000 5* 555 5 ' 5 7"

0.000 0.500 1.000 1.500 2.000 2.500

X Coordinates

FIGURE 33. Plotted Bookstein coordinates taken from the inner and outer curves of UM-P claw 2, with
trend lines and matching equations.

78

 

UM-P Claw 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
1.860 0.560 1.537 0.683 1.940 0.510 1.634 0.622
1.830 0.580 1.500 0.707 1.900 0.520 1.585 0.634
1.800 0.580 1.463 0.707 1.860 0.510 1.537 0.622
1.770 0.600 1.427 0.732 1.820 0.510 1.488 0.622
1.740 0.620 1.390 0.756 1.790 0.510 1.451 0.622
1.710 0.630 1.354 0.768 1.770 0.510 1.427 0.622
1.690 0.650 1.329 0.793 1.720 0.520 1.366 0.634
1.650 0.660 1.280 0.805 1.690 0.510 1.329 0.622
1.630 0.660 1.256 0.805 1.670 0.500 1.305 0.610
1.600 0.660 1.220 0.805 1.650 0.490 1.280 0.598
1.570 0.670 1.183 0.817 1.620 0.480 1.244 0.585
1.540 0.680 1.146 0.829 1.590 0.460 1.207 0.561
1.520 0.690 1.122 0.841 1.570 0.440 1.183 0.537
1.480 0.690 1.073 0.841 1.540 0.430 1.146 0.524
1.450 0.680 1.037 0.829 1.530 0.410 1.134 0.500
1.420 0.690 1.000 0.841 1.510 0.400 1.1 10 0.488
1.390 0.670 0.963 0.817 1.490 0.380 1.085 0.463
1.360 0.670 0.927 0.817 1.470 0.350 1.061 0.427
1.330 0.660 0.890 0.805 1.460 0.330 1.049 0.402
1.300 0.640 0.854 0.780 1.450 0.310 1.037 0.378
1.290 0.630 0.841 0.768 1.440 0.270 1.024 0.329
1.260 0.620 0.805 0.756 1.420 0.250 1.000 0.305
1.230 0.600 0.768 0.732 1.410 0.220 0.988 0.268
1.210 0.600 0.744 0.732 1.400 0.190 0.976 0.232
1.170 0.590 0.695 0.720
1 . 150 0.570 0.671 0.695
1 . 120 0.560 0.634 0.683
1 . 100 0.540 0.610 0.659
1.060 0.520 0.561 0.634
1.040 0.500 0.537 0.610
1.010 0.500 0.500 0.610
0.980 0.490 0.463 0.598
0.940 0.490 0.415 0.598
0.920 0.470 0.390 0.573
0.910 0.460 0.378 0.561
0.880 0.450 0.341 0.549
0.850 0.420 0.305 0.512
0.830 0.400 0.280 0.488
0.810 0.380 0.256 0.463
0.780 0.350 0.220 0.427
0.750 0.320 0.183 0.390
0.740 0.290 0.171 0.354
0.710 0.260 0.134 0.317
0.690 0.230 0.1 10 0.280

 

 

 

 

 

79

TABLE 30. Raw and Bookstein coordinates taken from the outer and inner curves of UM-P, claw 3.

 

y = 05522112 + 1.1902x + 0.1724 UM.p Claw 3

R2 = 0.9835

0.900 ._ __

0 800 A 0 Outer Curve (BS)

0.700 4 I Inner Curve (BS)
m . —Pol .(Outer Curve BS))
30600 —1>1y I C (BS
._§ 0.500 . oy.( nnergrve( ))
8 0.400 5
U 0300 «
>~ ~ ,

0.200 . ° )* = —‘ 1.712315 + 4.9406x — 2.914

0.100 a R“ 21.1.9709

0.000 - 55 ~ 5 - 57

0.000 0.500 1.000 1.500 2.000

X Coordinates

FIGURE 34. Plotted Bookstein coordinates taken from the inner and outer curves of UM-P claw 3, with
trend lines and matching equations.

80

 

UM-P Claw 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
1.580 0.620 1.596 1.192 1.620 0.590 1.673 1.135
1.540 0.620 1.519 1.192 1.580 0.570 1.596 1.096
1.510 0.620 1.462 1.192 1.560 0.550 1.558 1.058
1.480 0.620 1.404 1.192 1.530 0.530 1.500 1.019
1.440 0.600 1.327 1.154 1.500 0.510 1.442 0.981
1.420 0.600 1.288 1.154 1.480 0.490 1.404 0.942
1.390 0.580 1.231 1.1 15 1.450 0.470 1.346 0.904
1.360 0.570 1.173 1.096 1.420 0.440 1.288 0.846
1.330 0.550 1.1 15 1.058 1.400 0.420 1.250 0.808
1.310 0.540 1.077 1.038 1.380 0.400 1.212 0.769
1.280 0.510 1.019 0.981 1.350 0.390 1.154 0.750
1.260 0.500 0.981 0.962 1.330 0.350 1.1 15 0.673
1.230 0.480 0.923 0.923 1.330 0.320 1.1 15 0.615
1.190 0.470 0.846 0.904 1.340 0.290 1.135 0.558
1.150 0.450 0.769 0.865 1.360 0.250 1.173 0.481
1 . 100 0.430 0.673 0.827 1.380 0.220 1.212 0.423
1.060 0.420 0.596 0.808 1.400 0.200 1.250 0.385
1.030 0.390 0.538 0.750 1.420 0.170 1.288 0.327
1.010 0.370 0.500 0.712
0.980 0.340 0.442 0.654
0.950 0.320 0.385 0.615
0.930 0.300 0.346 0.577
0.920 0.270 0.327 0.519
0.900 0.240 0.288 0.462
0.880 0.210 0.250 0.404
0.870 0.180 0.231 0.346

 

 

 

 

 

81

TABLE 31. Raw and Bookstein coordinates taken from the outer and inner curves of UM-P, claw 4.

 

y = 03338112 + 1.1788x + 0.169 UM-P Claw 4

R2 = 0.985

1.400 ;

1.200 I p 0 Outer Curve(BS)
3‘3 1.000 . I Inner Curve (BS)
(6
.5 0,300 o —Poly. (Outer Curve (BS))
g 0,600 —Poly. (Inner Eurve (BS))
>- 0.400 7'1. .

0 200 , ' y = 0s444x5 — 1.1796x + 0.14294

' ‘ R2 = 0.6076
0.000 ~ - - . -_ .-

0.000 0.500 1.000 1.500 2.000

X Coordinates

FIGURE 35. Plotted Bookstein coordinates taken from the inner and outer curves of UM-P claw 4, with
trend lines and matching equations.

82

 

UM-WS Claw 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.700 1.060 0.593 3.926 0.770 0.980 0.852 3.630
0.680 1.040 0.519 3.852 0.760 0.940 0.815 3.481
0.660 1.010 0.444 3.741 0.760 0.920 0.815 3.407
0.650 0.990 0.407 3.667 0.760 0.900 0.815 3.333
0.640 0.970 0.370 3.593 0.740 0.870 0.741 3.222
0.620 0.950 0.296 3.519 0.730 0.840 0.704 3.1 1 1
0.600 0.930 0.222 3.444 0.730 0.810 0.704 3.000
0.570 0.910 0.1 1 1 3.370 0.740 0.780 0.741 2.889
0.550 0.880 0.037 3.259 0.740 0.750 0.741 2.778
0.540 0.860 0.000 3.185 0.750 0.720 0.778 2.667
0.520 0.840 -0.074 3.1 11 0.760 0.690 0.815 2.556
0.510 0.820 -0.1 1 1 3.037 0.770 0.670 0.852 2.481
0.500 0.800 -0.148 2.963 0.780 0.650 0.889 2.407
0.480 0.770 -0.222 2.852 0.810 0.630 1.000 2.333
0.480 0.730 -0.222 2.704 0.820 0.620 1.037 2.296
0.470 0.710 -0.259 2.630
0.460 0.670 -0.296 2.481
0.460 0.630 -0.296 2.333
0.450 0.590 -0.333 2.185
0.450 0.550 -0.333 2.037
0.430 0.530 -0.407 1.963
0.430 0.490 —0.407 1.815
0.430 0.440 -0.407 1.630
0.420 0.400 -0.444 1.481
0.430 0.360 -0.407 1.333
0.430 0.310 -0.407 1.148
0.430 0.260 -0.407 0.963
0.430 0.220 -0.407 0.815
0.440 0. 1 80 -0.370 0.667

 

 

 

 

 

83

TABLE 32. Raw and Bookstein coordinates taken from the outer and inner curves of UM-WS, claw 2.

 

y = -3.8604x2 + 2.8148x + 3.2779 UM-WS Claw 2

R2 = 0.8758
4.500 6 Outer Curve (BS)
4.000 5 ,0 I Inner Curve (B8)
w 3500 ‘ o 0’ .- —Poly. (Outer Curve (B8))
9423 3.000 1 3 m ‘-—Poly. (Inner Curve (BS))___
5:5 2.500 55 g
8 2.000 -
if 1.500 - ,
1,000 : y z -1 1.56215 + 17.706x - 3.7353
0.500 5 ’ R2 = 0.325
-0.500 0.000 0.500 1.000 1.500

X Coordinates

FIGURE 36. Plotted Bookstein coordinates taken from the inner and outer curves of UM-WS claw 2. with
trend lines and matching equations.

84

 

UM-WS Claw 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
0.950 1.270 1.853 3.735 1.010 1.160 2.029 3.412
0.920 1.250 1.765 3.676 0.990 1 . 120 1.971 3.294
0.900 1.240 1.706 3.647 0.990 1.070 1.971 3.147
0.870 1.230 1.618 3.618 0.980 1.040 1.941 3.059
0.840 1.210 1.529 3.559 0.960 1.010 1.882 2.971
0.820 1.200 1.471 3.529 0.940 0.970 1.824 2.853
0.800 1.180 1.412 3.471 0.920 0.930 1.765 2.735
0.780 1.160 1.353 3.412 0.910 0.890 1.735 2.618
0.760 1.130 1.294 3.324 0.890 0.860 1.676 2.529
0.730 1.1 10 1.206 3.265 0.890 0.820 1.676 2.412
0.710 1.090 1.147 3.206 0.870 0.790 1.618 2.324
0.690 1.070 1.088 3.147 0.860 0.750 1.588 2.206
0.680 1.050 1.059 3.088 0.850 0.720 1.559 2.1 18
0.660 1 .030 1.000 3.029 0.850 0.680 1.559 2.000
0.640 1.010 0.941 2.971 0.840 0.640 1.529 1.882
0.620 1.000 0.882 2.941 0.830 0.600 1.500 1.765
0.600 0.970 0.824 2.853 0.820 0.560 1.471 1.647
0.580 0.940 0.765 2.765 0.820 0.520 1.471 1.529
0.560 0.930 0.706 2.735 0.820 0.490 1.471 1.441
0.550 0.900 0.676 2.647 0.810 0.440 1.441 1.294
0.540 0.880 0.647 2.588 0.810 0.400 1.441 1 . 176
0.520 0.850 0.588 2.500 0.810 0.380 1.441 1.118
0.510 0.820 0.559 2.412 0.810 0.350 1.441 1.029
0.500 0.790 0.529 2.324 0.810 0.320 1.441 0.941
0.480 0.760 0.471 2.235 0.810 0.290 1.441 0.853
0.460 0.730 0.412 2.147 0.810 0.250 1.441 0.735
0.440 0.690 0.353 2.029 0.810 0.200 1.441 0.588
0.430 0.670 0.324 1.971 0.800 0.150 1.412 0.441
0.420 0.630 0.294 1.853 0.800 0.100 1.412 0.294
0.410 0.600 0.265 1.765 0.800 0.060 1.412 0.176
0.400 0.560 0.235 1.647
0.390 0.540 0.206 1.588
0.380 0.500 0.176 1.471
0.360 0.460 0.1 18 1.353
0.360 0.430 0.1 18 1.265
0.350 0.390 0.088 1.147
0.340 0.340 0.059 1.000
0.340 0.300 0.059 0.882
0.330 0.260 0.029 0.765
0.320 0.240 0.000 0.706
0.310 0.200 -0.029 0.588
0.320 0.160 0.000 0.471
0.320 0.1 10 0.000 0.324

 

 

 

 

 

85

TABLE 33. Raw and Bookstein coordinates taken from the outer and inner curves of UM-WS, claw 3.

 

y = -1.034x2 + 3.40411 + 0.7846 UM-WS Claw 3

   
  
   
 
   

R2 = 0.9824
4.000 5
3.500 - ’ .61.... carting)
3.000 - p I Inner Curve (BS)
2.500 55 —Poly. (Outer Curve (BS))

Y Coordinates

2-000 ‘ —Poly. (Inner Curve (BS)) 1
1.500 , I ' I ‘7 *T ”T"
1.000 44‘ y = 91319.15 + 35.3121 - 30.955
0.500 3 R5 = 0.9354

0.000 44 ~ 444. . 41

0.000 0.500 1.000 1.500 2.000 2.500

X Coordinates

FIGURE 37. Plotted Bookstein coordinates taken from the inner and outer curves of UM-WS claw 3, with
trend lines and matching equations.

86

 

UM—WS Claw 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.580 1.590 0.564 4.077 0.700 1.520 0.872 3.897
0.560 1.570 0.513 4.026 0.680 1.500 0.821 3.846
0.540 1.550 0.462 3.974 0.670 1.470 0.795 3.769
0.520 1.530 0.410 3.923 0.660 1.440 0.769 3.692
0.510 1.500 0.385 3.846 0.650 1.400 0.744 3.590
0.500 1.470 0.359 3.769 0.640 1.370 0.718 3.513
0.490 1.440 0.333 3.692 0.630 1.320 0.692 3.385
0.480 1.410 0.308 3.615 0.630 1.290 0.692 3.308
0.470 1.390 0.282 3.564 0.620 1.250 0.667 3.205
0.450 1.370 0.231 3.513 0.620 1.230 0.667 3.154
0.440 1.340 0.205 3.436 0.610 1.200 0.641 3.077
0.430 1.310 0.179 3.359 0.610 1.170 0.641 3.000
0.420 1.260 0.154 3.231 0.610 1.140 0.641 2.923
0.410 1.270 0.128 3.256 0.620 1.120 0.667 2.872
0.400 1.240 0.103 3.179 0.620 1.080 0.667 2.769
0.390 1.190 0.077 3.051 0.640 1.060 0.718 2.718
0.380 1 . 150 0.051 2.949 0.650 1.040 0.744 2.667
0.370 1.130 0.026 2.897 0.670 1.000 0.795 2.564
0.360 1.090 0.000 2.795 0.680 0.970 0.821 2.487
0.340 1.060 -0.051 2.718 0.700 0.950 0.872 2.436
0.330 1.030 -0.077 2.641 0.720 0.920 0.923 2.359
0.310 1.000 -0.128 2.564 0.730 0.890 0.949 2.282
0.310 0.970 -0.128 2.487
0.300 0.940 -0.154 2.410
0.280 0.910 -0.205 2.333
0.260 0.870 -0.256 2.231
0.260 0.840 -0.256 2.154
0.250 0.800 -0.282 2.051
0.250 0.770 -0.282 1.974
0.230 0.720 -0.333 1.846
0.230 0.680 -0.333 1.744
0.220 0.640 -0.359 1.641
0.210 0.600 -0.385 1.538
0.200 0.550 -0.410 1.410
0.200 0.520 -0.410 1.333
0.210 0.470 -0.385 1.205
0.220 0.430 -0.359 1.103
0.220 0.370 -0.359 0.949
0.230 0.310 -0.333 0.795
0.240 0.280 -0.308 0.718
0.260 0.240 -0.256 0.615
0.290 0.200 —0. 179 0.513

 

 

 

 

 

87

TABLE 34. Raw and Bookstein coordinates taken from the outer and inner curves of UM-WS, claw 4.

 

y = —l.6399x2 + 3.3943x + 2.7639 UM-WS Claw 4

R2 = 0.856
4.500 5 L M L-..
4,000 - 0 Outer Curve (BS)
m 3.500 I Inner Curve (B8)
#3 3.000 5 1—Poly. (Outer Curve (B8))
Ta 250° ‘ . _—P09-(1nverC9mBS>)
8 2.000 5
31.5005 [fl )_3 _ .., -
1.000 - y = -_7.()1\5x‘ + 41,063.31 - 12.263
0.500 . .0 R" = 0.236
0.000 - ~ - -

-0.500 0.000 0.500 1.000 1.500
X Coordinates

FIGURE 38. Plotted Bookstein coordinates taken from the inner and outer curves of UM-WS claw 4, with
trend lines and matching equations.

88

 

C-GBBG Claw 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
0.540 0.410 0.650 2.050 0.570 0.450 0.800 2.250
0.520 0.400 0.550 2.000 0.570 0.420 0.800 2.100
0.510 0.380 0.500 1.900 0.580 0.380 0.850 1.900
0.490 0.370 0.400 1.850 0.580 0.350 0.850 1.750
0.480 0.350 0.350 1.750 0.580 0.300 0.850 1.500
0.470 0.330 0.300 1.650 0.580 0.260 0.850 1.300
0.450 0.310 0.200 1.550 0.580 0.220 0.850 1 . 100
0.430 0.280 0.100 1.400 0.600 0.180 0.950 0.900
0.420 0.230 0.050 1.150 0.610 0.130 1.000 0.650
0.410 0.200 0.000 1.000 0.620 0.090 1.050 0.450
0.410 0.170 0.000 0.850
0.410 0.140 0.000 0.700
0.410 0.110 0.000 0.550
0.410 0.090 0.000 0.450
0.410 0.050 0.000 0.250

 

 

 

 

 

 

TABLE 35. Raw and Bookstein coordinates taken from the outer and inner curves of C-GBBG, claw 2.

    
  

y = 4.3399112 + 4.7561 x + 0.6955 (3.9333 Claw 2
R2 = 0.8913
2.500
I 0 Outer Curve (BS)

w 2'000 . I I Inner Curve (BS)
‘3 —Poly. (Outer Curve (BS))
1: 1.500 -
'-§ ° q—Poly. (Inner Curve (BS))
0 _._ 3- __ _- __
5 1.000 t '
> v = 24.194.\'3 - 51.15731 + 27.556

0.500 .

R3 = 0.8625

0.000 L
0.000 0.200 0.400 0.600 0.800

X Coordinates

1.000 1.200

FIGURE 39. Plotted Bookstein coordinates taken from the inner and outer curves of C-GBBG claw 2, with
trend lines and matching equations.

89

 

C-GBBG Claw 3

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.630 0.770 0.974 1.974 0.680 0.790 1.103 2.026
0.600 0.760 0.897 1.949 0.670 0.760 1.077 1.949
0.580 0.740 0.846 1.897 0.650 0.730 1.026 1.872
0.540 0.720 0.744 1.846 0.640 0.700 1.000 1.795
0.510 0.700 0.667 1.795 0.640 0.670 1.000 1.718
0.500 0.690 0.641 1.769 0.640 0.630 1.000 1.615
0.480 0.670 0.590 1.718 0.630 0.590 0.974 1.513
0.450 0.650 0.513 1.667 0.630 0.550 0.974 1.410
0.440 0.630 0.487 1.615 0.610 0.510 0.923 1.308
0.430 0.600 0.462 1.538 0.610 0.490 0.923 1.256
0.420 0.570 0.436 1.462 0.610 0.460 0.923 1.179
0.410 0.450 0.410 1.154 0.610 0.430 0.923 1.103
0.400 0.520 0.385 1.333 0.620 0.400 0.949 1.026
0.490 0.490 0.615 1.256 0.620 0.370 0.949 0.949
0.380 0.460 0.333 1.179 0.630 0.340 0.974 0.872
0.360 0.430 0.282 1.103 0.640 0.320 1.000 0.821
0.350 0.390 0.256 1.000 0.650 0.300 1.026 0.769
0.340 0.370 0.231 0.949 0.650 0.260 1.026 0.667
0.330 0.340 0.205 0.872 0.670 0.240 1.077 0.615
0.320 0.300 0.179 0.769 0.690 0.210 1.128 0.538
0.300 0.280 0.128 0.718 0.690 0.180 1.128 0.462
0.290 0.250 0.103 0.641
0.290 0.230 0.103 0.590
0.270 0.190 0.051 0.487
0.270 0.160 0.051 0.410
0.260 0.120 0.026 0.308
0.270 0.1 10 0.051 0.282

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 36. Raw and Bookstein coordinates taken from the outer and inner curves of C-GBBG, claw 3.

90

y = -1.8089x2 + 3.4958x + 0.2431 C-GBBG Claw 3

R2 = 0.9647

2500 o OutefCurve (BS)

2 000 1 I Inner Curve (BS)
8 —Poly. (Outer Curve (BS))
is 0
g 1.500 . p—Poly1.(lnner Curve(BS))
E o
O 1.000
>1

0.500 ' l

y 2 342666 + 69.0.35x - 33.466
0000 i ' " " ' .__ R2 = 0.1009
0.000 0.200 0.400 0.600 0.800 1.000 1.200

X Coordinates

FIGURE 40. Plotted Bookstein coordinates taken from the inner and outer curves of C- GBBG claw 3, with
trend lines and matching equations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C-GBBG Claw 4

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.840 0.640 0.391 2.783 0.870 0.620 0.522 2.696
0.810 0.630 0.261 2.739 0.870 0.570 0.522 2.478
0.790 0.610 0.174 2.652 0.860 0.530 0.478 2.304
0.780 0.590 0.130 2.565 0.870 0.470 0.522 2.043
0.760 0.580 0.043 2.522 0.870 0.450 0.522 1.957
0.750 0.560 0.000 2.435 0.870 0.410 0.522 1.783
0.740 0.530 -0.043 2.304 0.870 0.380 0.522 1.652
0.730 0.500 —0.087 2.174 0.870 0.360 0.522 1.565
0.720 0.470 -0.130 2.043 0.870 0.330 0.522 1.435
0.710 0.430 -0.174 1.870 0.880 0.300 0.565 1.304
0.700 0.390 -0.217 1.696 0.900 0.290 0.652 1.261
0.700 0.350 —0.2 1 7 1.522 0.910 0.270 0.696 1.174
0.700 0.320 -0.217 1.391 0.930 0.260 0.783 1.130
0.700 0.300 -0.217 1.304 0.960 0.250 0.913 1.087
0.700 0.260 -0.217 1 . 130
0.700 0.220 -0.217 0.957
0.700 0.180 -0217 0.783
0.710 0.150 -0.174 0.652
0.730 0.120 0087 0.522

 

 

 

 

 

91

TABLE 37. Raw and Bookstein coordinates taken from the outer and inner curves of C-GBBG, claw 4.

 

y = 41.950438 + 3.493511 + 2.1969 C-GBBG Claw 4

 

R2 = 0.6436
3.000
I L . i
2.500 I 0 Outer Curve (B8)
so; 2000 I Inner Curve (BS)
g l—Poly. (Outer Curve (BS))
E 1500 '- 1—Poly.(1nner;Curve(BS))
: 1.000 7 '
\ = 12141.12 — 19.406x + 8.7488
0.500 5 . _
R” = (1.571
0.000 ‘ 5
~0.500 0.000 0.500 1.000

X Coordinates

FIGURE 41. Plotted Bookstein coordinates taken from the inner and outer curves of C-GBBG claw 4, with
trend lines and matching equations.

92

 

C-PI Claw 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.490 0.850 0.857 4.048 0.510 0.830 0.952 3.952
0.480 0.840 0.810 4.000 0.500 0.810 0.905 3.857
0.460 0.800 0.714 3.810 0.490 0.780 0.857 3.714
0.440 0.790 0.619 3.762 0.490 0.760 0.857 3.619
0.430 0.780 0.571 3.714 0.470 0.740 0.762 3.524
0.410 0.760 0.476 3.619 0.480 0.720 0.810 3.429
0.410 0.740 0.476 3.524 0.410 0.700 0.476 3.333
0.390 0.710 0.381 3.381 0.470 0.670 0.762 3.190
0.370 0.680 0.286 3.238 0.470 0.640 0.762 3.048
0.370 0.650 0.286 3.095 0.460 0.620 0.714 2.952
0.360 0.630 0.238 3.000 0.460 0.590 0.714 2.810
0.340 0.610 0.143 2.905 0.450 0.570 0.667 2.714
0.340 0.570 0.143 2.714 0.460 0.530 0.714 2.524
0.330 0.530 0.095 2.524 0.460 0.500 0.714 2.381
0.320 0.500 0.048 2.381 0.460 0.470 0.714 2.238
0.320 0.470 0.048 2.238 0.470 0.450 0.762 2.143
0.300 0.440 -0.048 2.095 0.480 0.420 0.810 2.000
0.300 0.410 -0.048 1.952 0.470 0.400 0.762 1.905
0.290 0.390 —0.095 1.857 0.490 0.370 0.857 1.762
0.280 0.270 -0.143 1.286 0.500 0.340 0.905 1.619
0.280 0.340 -0.143 1.619 0.510 0.310 0.952 1.476
0.270 0.310 -0. 190 1.476 0.530 0.290 1.048 1.381
0.270 0.280 -0. 190 1.333 0.550 0.260 1.143 1.238
0.270 0.260 -0.190 1.238 0.580 0.230 1.286 1.095
0.270 0.230 -0.190 1.095 0.610 0.200 1.429 0.952
0.270 0.190 -0. 190 0.905
0.280 0.150 -0.143 0.714
0.280 0.100 —0. 143 0.476
0.280 0.060 0143 0.286

 

 

 

 

 

93

TABLE 38. Raw and Bookstein coordinates taken from the outer and inner curves of C-PI claw 2.

 

y = -3.0883x2 + 4.8421x + 2.0337 (3.1)} Claw 2

R2 = 0.9234
4.500 - ——»-— —- -—-
4.000 0 Outer Curve (BS)
m 3.500 5 1 I Inner Curve (B8)
5% 3.000 5 —Poly. (Outer Curve (BS)),
"§ 2500 ‘ —Poly.(InnerCurve (BS))
8 2.000 1 T v "' 7*
u -_ o 7
>5 1338“ I. y = —2.2779.\5 + 1.8156x + 2.7134
0.500 1 § 16203407
0.000 5 *5 5i i i

-0.500 0.000 0.500 '1 .000 1.500 2.000

X Coordinates

FIGURE 42. Plotted Bookstein coordinates taken from the inner and outer curves of C-PI claw 2, with
trend lines and matching equations.

94

 

CePI Claw 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
0.590 1.370 1.000 4.152 0.600 1.360 1.030 4.121
0.560 1.350 0.909 4.091 0.590 1.330 1.000 4.030
0.550 1.330 0.879 4.030 0.580 1.320 0.970 4.000
0.520 1.310 0.788 3.970 0.570 1.290 0.939 3.909
0.510 1.290 0.758 3.909 0.550 1.260 0.879 3.818
0.480 1.270 0.667 3.848 0.540 1.240 0.848 3.758
0.470 1.260 0.636 3.818 0.530 1.210 0.818 3.667
0.450 1.240 0.576 3.758 0.520 1.170 0.788 3.545
0.430 1.220 0.515 3.697 0.510 1.140 0.758 3.455
0.420 1 . 190 0.485 3.606 0.500 1.130 0.727 3.424
0.400 1.170 0.424 3.545 0.500 1.1 10 0.727 3.364
0.390 1 . 140 0.394 3.455 0.490 1.080 0.697 3.273
0.380 1.120 0.364 3.394 0.490 1.050 0.697 3.182
0.360 1 . 100 0.303 3.333 0.490 1.020 0.697 3.091
0.350 1.060 0.273 3.212 0.490 0.990 0.697 3.000
0.340 1.030 0.242 3.121 0.490 0.960 0.697 2.909
0.320 1.000 0.182 3.030 0.500 0.930 0.727 2.818
0.320 0.980 0.182 2.970 0.510 0.910 0.758 2.758
0.310 0.950 0.152 2.879 0.510 0.880 0.758 2.667
0.300 0.930 0.121 2.818 0.520 0.850 0.788 2.576
0.290 0.890 0.091 2.697 0.530 0.830 0.818 2.515
0.290 0.860 0.091 2.606 0.550 0.820 0.879 2.485
0.280 0.830 0.061 2.515 0.580 0.800 0.970 2.424
0.270 0.900 0.030 2.727 0.610 0.790 1.061 2.394
0.270 0.780 0.030 2.364 0.640 0.780 1 . 152 2.364
0.250 0.740 -0.030 2.242
0.250 0.700 -0.030 2.121
0.250 0.670 -0.030 2.030
0.240 0.640 -0.061 1.939
0.230 0.600 -0.091 1.818
0.220 0.560 -0.121 1.697
0.220 0.530 -0.121 1.606
0.220 0.480 -0.121 1.455
0.220 0.440 -0.121 1.333
0.220 0.400 -0.121 1.212
0.220 0.360 -0.121 1.091
0.220 0.320 -0.121 0.970
0.220 0.290 -0.121 0.879
0.230 0.240 -0.091 0.727
0.240 0.210 -0.061 0.636
0.240 0.160 -0.061 0.485
0.250 0.120 -0.030 0.364

 

 

 

 

 

95

TABLE 39. Raw and Bookstein coordinates taken from the outer and inner curves of C-PI claw 3.

 

y = -3.6221x2 + 5.5375x + 1.9363 (3-121 Claw 3
R2 = 0.8693

4.500 ‘ 0 Outer Curve(BS)

 

' 22$ 4 I Inner Curve (BS)
g 3.000 —Poly. (Outer Curve (BS))
'5 2.500 ‘ t—Poly. (Inneir Curve (B8)) ‘
‘9 2.000
if 1.500 « 3 = -11.757\3+ 21.063x - 6.0107
1000 ' 143:0.1165
0.500 . \
0.000 ~+—~ -- --A,

-0.500 0.000 0.500 1.000 1.500

X Coordinates

FIGURE 43. Plotted Bookstein coordinates taken from the inner and outer curves of C-PI claw 3, with
trend lines and matching equations.

96

TABLE 40. Raw and Bookstein coordinates taken from the outer and inner curves of GP] claw 3.

 

C-PI Claw 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.390 0.760 1.417 6.333 0.400 0.740 1.500 6.167
0.370 0.740 1.250 6.167 0.390 0.720 1.417 6.000
0.360 0.730 1.167 6.083 0.380 0.710 1.333 5.917
0.350 0.710 1.083 5.917 0.380 0.690 1.333 5.750
0.330 0.690 0.917 5.750 0.370 0.680 1.250 5.667
0.320 0.660 0.833 5.500 0.370 0.650 1.250 5.417
0.300 0.640 0.667 5.333 0.360 0.620 1.167 5.167
0.290 0.620 0.583 5.167 0.350 0.590 1.083 4.917
0.280 0.590 0.500 4.917 0.350 0.560 1.083 4.667
0.270 0.560 0.417 4.667 0.340 0.530 1.000 4.417
0.250 0.530 0.250 4.417 0.330 0.500 0.917 4.167
0.240 0.500 0.167 4.167 0.330 0.470 0.917 3.917
0.230 0.470 0.083 3.917 0.330 0.450 0.917 3.750
0.220 0.450 0.000 3.750 0.340 0.420 1.000 3.500
0.210 0.420 -0.083 3.500 0.350 0.390 1.083 3.250
0.210 0.390 —0.083 3.250 0.360 0.370 1.167 3.083
0.200 0.350 -0.167 2.917 0.380 0.350 1.333 2.917
0.190 0.320 -0.250 2.667 0.400 0.340 1.500 2.833
0.180 0.290 -0.333 2.417 0.420 0.310 1.667 2.583
0.180 0.260 -0.333 2.167 0.420 0.280 1.667 2.333
0.170 0.210 -0.417 1.750 0.470 0.270 2.083 2.250
0.180 0.180 -0.333 1.500 0.490 0.250 2.250 2.083
0.180 0.130 -0.333 1.083
0.190 0.080 -0.250 0.667

 

 

 

 

 

 

 

y = — 1 4949112 + 4.0549x + 3.382.. C-PI Claw 4
R2 = 0.9317 ---_
7.000 0 Outer Curve (BS)
6.000 I Inner Curve (BS)
g 5000 ‘ —Poly. (Outer Curve (BS))
".3 4.000 5
15 —Poly. (Inner Curve (BS))
0 3.000 1 .-
U
>1 2.000 -
. o .
”’00 o 3 = —3.4266\" + 8.8508x— 1.1712
0000 4 ' ' R“ -.: 0.3146
-0.500 0.500 1.500 2.500

X Coordinates

FIGURE 44. Plotted Bookstein coordinates taken from the inner and outer curves of C-PI claw 4. with
trend lines and matching equations.

97

 

C-SI Claw 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
0.530 0.660 -2.600 3.300 0.540 0.680 -2.550 3.400
0.550 0.630 -2.500 3.150 0.550 0.660 -2.500 3.300
0.560 0.610 -2.450 3.050 0.580 0.630 -2.350 3.150
0.570 0.590 -2.400 2.950 0.590 0.610 -2.300 3.050
0.580 0.580 -2.350 2.900 0.620 0.590 -2.150 2.950
0.600 0.560 -2.250 2.800 0.630 0.560 -2. 100 2.800
0.610 0.530 -2.200 2.650 0.660 0.540 -1.950 2.700
0.630 0.510 -2. 100 2.550 0.680 0.510 -1.850 2.550
0.650 0.490 -2.000 2.450 0.710 0.490 -1.700 2.450
0.670 0.460 -1.900 2.300 0.730 0.480 -1.600 2.400
0.690 0.440 -1.800 2.200 0.770 0.450 -1.400 2.250
0.710 0.420 -1.700 2.100 0.790 0.430 -1.300 2.150
0.730 0.400 -1.600 2.000 0.830 0.410 -1 . 100 2.050
0.750 0.370 -1.500 1.850 0.860 0.380 -0.950 1.900
0.780 0.350 -1.350 1.750 0.900 0.360 -0.750 1.800
0.800 0.330 -1.250 1.650 0.920 0.340 -0.650 1.700
0.820 0.300 -1 . 150 1.500 0.950 0.320 -0.500 1.600
0.850 0.280 -1 .000 1.400 0.980 0.300 -0.350 1.500
0.870 0.250 -0.900 1.250 1.010 0.280 -0.200 1.400
0.900 0.220 -0.750 1 . 100 1.030 0.260 -0. 100 1.300
0.910 0.190 -0.700 0.950 1.050 0.240 0.000 1.200
0.930 0.160 -0.600 0.800 1.070 0.220 0.100 1 . 100
0.940 0.140 -0.550 0.700 1.1 10 0.190 0.300 0.950
0.960 0.1 10 -0.450 0.550 1.140 0.170 0.450 0.850
0.980 0.080 -0.350 0.400 1.160 0.140 0.550 0.700
1.010 0.060 -0.200 0.300 1 . 190 0.100 0.700 0.500

1.220 0.070 0.850 0.350

 

 

 

98

TABLE 41. Raw and Bookstein coordinates taken from the outer and inner curves of C-81 claw 1.

 

y = 00144312 — 1.2461x + 0.0589 (3.310,,W 1
R2 = 0.9956
4,000 0 Outer eerie (BS)
3.500 g . I Inner Curve (BS)
3 3.000 - l—Poly. (Outer Curve (BS))
2 2.500< emly.(hflrCuge(BS))_
“g 2.000 -
O 1
o 1.500 1
>3 1.000 . ,x=0.(10<_16,\341.80474 + 1.1513
0.500 1 R2 20.9939
0.000 -. V V 5*
-3500 -1500 0.500 2.500

X Coordinates

FIGURE 45. Plotted Bookstein coordinates taken from the inner and outer curves of C-81 claw 1, with
trend lines and matching equations.

 

 

 

TABLE 42. Raw and Bookstein coordinates taken from the outer and inner curves of C-81 claw 2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C-SI Claw 2
Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y

0.720 0.500 1.294 2.941 0.740 0.490 1.412 2.882
0.710 0.490 1.235 2.882 0.730 0.470 1.353 2.765
0.700 0.480 1.176 2.824 0.730 0.460 1.353 2.706
0.690 0.460 1.1 18 2.706 0.710 0.440 1.235 2.588
0.670 0.440 1.000 2.5 88 0.700 0.420 1.176 2.471
0.660 0.420 0.941 2.471 0.690 0.410 1.1 18 2.412
0.650 0.400 0.882 2.353 0.680 0.390 1.059 2.294
0.630 0.370 0.765 2.176 0.670 0.350 1.000 2.059
0.610 0.350 0.647 2.059 0.670 0.350 1.000 2.059
0.600 0.330 0.588 1.941 0.660 0.330 0.941 1.941
0.580 0.310 0.471 1.824 0.660 0.300 0.941 1.765
0.570 0.290 0.412 1.706 0.650 0.280 0.882 1.647
0.560 0.260 0.353 1.529 0.650 0.260 0.882 1.529
0.550 0.220 0.294 1.294 0.640 0.230 0.824 1.353
0.530 0.200 0.176 1.176 0.640 0.200 0.824 1.176
0.510 0.170 0.059 1.000 0.640 0.170 0.824 1.000
0.510 0.130 0.059 0.765 0.650 0.150 0.882 0.882
0.510 0.100 0.059 0.588 0.660 0.130 0.941 0.765
0.670 0.100 1.000 0.588

0.680 0.080 1.059 0.471

 

99

 

y = -O.6288x3 + 2.5457x + 0.6705 (3.3] Claw 2

 

R2 = 0.9859
3.500
3.000 0 Outer Curve (BS)
E), 2500 I Inner Curve (BS)
2 2.000 fl —Poly. (Outer Curve (BS))
'2 —Poly. (Inner Curve (BS))
0 - A _
o 1.500 '
U ,
> 1.000 . y : H)?» I \' + 0.817-ix - 0.217
0.000 5 7* - -- *
0.000 0.500 1.000 1.500

X Coordinates

FIGURE 46. Plotted Bookstein coordinates taken from the inner and outer curves of 081 claw 2, with
trend lines and matching equations.

100

 

C-SI Claw 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
0.790 0.690 1.450 3.450 0.790 0.670 1.450 3.350
0.770 0.670 1.350 3.350 0.780 0.650 1.400 3.250
0.760 0.650 1.300 3.250 0.770 0.640 1.350 3.200
0.740 0.630 1.200 3.150 0.760 0.630 1.300 3.150
0.730 0.6l0 l . 150 3.050 0.760 0.610 1.300 3.050
0.720 0.600 1 . 100 3.000 0.750 0.590 1.250 2.950
0.700 0.580 1.000 2.900 0.740 0.570 1.200 2.850
0.680 0.560 0.900 2.800 0.730 0.540 1.150 2.700
0.670 0.540 0.850 2.700 0.720 0.520 1 . 100 2.600
0.660 0.530 0.800 2.650 0.710 0.490 1.050 2.450
0.650 0.510 0.750 2.550 0.700 0.470 1.000 2.350
0.640 0.490 0.700 2.450 0.690 0.440 0.950 2.200
0.630 0.470 0.650 2.350 0.690 0.410 0.950 2.050
0.610 0.440 0.550 2.200 0.680 0.380 0.900 1.900
0.600 0.410 0.500 2.050 0.680 0.350 0.900 1.750
0.590 0.380 0.450 1.900 0.680 0.320 0.900 1.600
0.580 0.360 0.400 1.800 0.680 0.290 0.900 1.450
0.580 0.340 0.400 1.700 0.680 0.260 0.900 1.300
0.570 0.310 0.350 1.550 0.680 0.230 0.900 1.150
0.560 0.280 0.300 1 .400 0.690 0.190 0.950 0.950
0.550 0.250 0.250 1.250 0.710 0.170 1.050 0.850
0.540 0.220 0.200 1 . 100 0.730 0.140 1 . 150 0.700
0.530 0.200 0.150 1.000
0.520 0.170 0.100 0.850
0.510 0.140 0.050 0.700
0.500 0.1 10 0.000 0.550

 

 

 

 

 

101

TABLE 43. Raw and Bookstein coordinates taken from the outer and inner curves of C-SI claw 3.

 

y = -1 021818 + 3.450011 + 0.5149

C-SI Claw 3

0 Outer Curve (BS)

 
  
  

 

 

R2 = 0.9968

4.000 I Inner Curve (BS)

3500 ” —Poly. (Outer Curve (BS))
.0 3.000
{‘23 2.500 -—_Poly.(InnerCurve(BS))
E 2.000 .
8 1.500 , . . _
> 1.000 - I } : 1894\1-(7894x + 0.7185

0.500 ' R" = 0.5807

0.000 + ~

0.000 0.500 1.000 1.500 2.000

X Coordinates

FIGURE 47. Plotted Bookstein coordinates taken from the inner and outer curves of C-SI claw 3, with

trend lines and matching equations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C-SI Claw 4
Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y

0.680 0.450 1.222 2.500 0.690 0.430 1.278 2.389
0.670 0.440 1.167 2.444 0.680 0.420 1.222 2.333
0.650 0.420 1.056 2.333 0.670 0.410 1.167 2.278
0.630 0.410 0.944 2.278 0.660 0.390 1.11 1 2.167
0.610 0.400 0.833 2.222 0.640 0.370 1.000 2.056
0.590 0.380 0.722 2.1 1 1 0.640 0.360 1.000 2.000
0.580 0.370 0.667 2.056 0.630 0.350 0.944 1.944
0.570 0.340 0.61 1 1.889 0.620 0.330 0.889 1.833
0.550 0.320 0.500 1.778 0.600 0.310 0.778 1.722
0.540 0.300 0.444 1.667 0.590 0.290 0.722 1.61 1
0.530 0.270 0.389 1.500 0.590 0.270 0.722 1.500
0.520 0.250 0.333 1.389 0.580 0.260 0.667 1.444
0.510 0.230 0.278 1.278 0.580 0.230 0.667 1.278
0.510 0.200 0.278 1.1 11 0.590 0.220 0.722 1.222
0.480 0.170 0.1 1 1 0.944 0.590 0.190 0.722 1.056
0.480 0.140 0.1 1 1 0.778 0.610 0.160 0.833 0.889
0.470 0.100 0.056 0.556 0.620 0.130 0.889 0.722
0.640 0.110 1.000 0.611

0.660 0.090 1.1 1 1 0.500

0.670 0.060 1.167 0.333

 

 

 

 

 

102

TABLE 44. Raw and Bookstein coordinates taken from the outer and inner curves of 081 claw 4.

 

 

y = -1.2624x2 + 3.1642x + 0.4648 031 Claw 4
R2 = 0.9891
3.000
2.500 7 0 Outer Curile (BS)
§ 2 000 ‘ I Inner Curve (BS)
2 ' —Poly. (Outer Curve (BS))
E 1.500 —Poly. (Igng Curve 03,8»
0
if 1.000 .
y : 4.1)866x‘ - 6.87% + 4.1989
0500 ‘ R3 20.1146
0.000 a -
0.000 0.500 1.000 1.500

X Coordinates

FIGURE 48. Plotted Bookstein coordinates taken from the inner and outer curves of OS] claw 4, with
trend lines and matching equations.

 

 

 

TABLE 45. Raw and Bookstein coordinates taken from the outer and inner curves of C-PC claw 3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C-PC Claw 3

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.430 0.630 0.594 1.969 0.460 0.640 0.688 2.000
0.410 0.610 0.531 1.906 0.440 0.600 0.625 1.875
0.380 0.600 0.438 1.875 0.430 0.580 0.594 1.813
0.350 0.590 0.344 1.844 0.420 0.550 0.563 1.719
0.330 0.570 0.281 1.781 0.420 0.510 0.563 1.594
0.310 0.550 0.219 1.719 0.430 0.490 0.594 1.531
0.300 0.530 0.188 1.656 0.430 0.460 0.594 1.438
0.290 0.510 0.156 1.594 0.430 0.420 0.594 1.313
0.280 0.490 0.125 1.531 0.440 0.390 0.625 1.219
0.260 0.460 0.063 1.438 0.450 0.360 0.656 1.125
0.240 0.430 0.000 1.344 0.470 0.420 0.719 1.313
0.240 0.400 0.000 1.250 0.490 0.310 0.781 0.969
0.240 0.350 0.000 1.094 0.500 0.280 0.813 0.875
0.230 0.310 0031 0.969 0.520 0.250 0.875 0.781
0.240 0.250 0.000 0.781 0.530 0.220 0.906 0.688
0.230 0.200 -0.031 0.625 0.540 0.200 0.938 0.625
0.240 0.150 0.000 0.469
0.240 0.1 10 0.000 0.344
0.250 0.070 0.031 0.219

 

 

 

 

 

103

 

y = 5.311112 + 4.8667x + 0.8625
R2 = 0.7037

Y Coordinates

2.500

2.000 1

1.500 .

1.000

0.000 *
-0.500

0.000

C-PC Claw 3

0.500

 

0 Outer Curve (BS)
I Inner Curve (BS)
i — Poly. (Outer Curve (BS))

— Poly. (Inner Curve (BS))

y = 5.71.11“3 + 2.71451 +1.2701
182116785

1.000

FIGURE 49. Plotted Bookstein coordinates taken from the inner and outer curves of C-PC claw 3, with

X Coordinates

trend lines and matching equations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C-PC Claw 4

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.470 0.730 1.043 3.174 0.500 0.730 1.174 3.174
0.440 0.720 0.913 3.130 0.470 0.710 1.043 3.087
0.410 0.710 0.783 3.087 0.450 0.690 0.957 3.000
0.390 0.690 0.696 3.000 0.430 0.680 0.870 2.957
0.370 0.670 0.609 2.913 0.410 0.650 0.783 2.826
0.350 0.640 0.522 2.783 0.400 0.620 0.739 2.696
0.330 0.630 0.435 2.739 0.390 0.590 0.696 2.565
0.320 0.620 0.391 2.696 0.380 0.560 0.652 2.435
0.300 0.600 0.304 2.609 0.370 0.530 0.609 2.304
0.290 0.580 0.261 2.522 0.370 0.510 0.609 2.217
0.270 0.570 0.174 2.478 0.370 0.470 0.609 2.043
0.260 0.550 0.130 2.391 0.370 0.450 0.609 1.957
0.250 0.530 0.087 2.304 0.370 0.410 0.609 1.783
0.230 0.500 0.000 2.174 0.380 0.380 0.652 1.652
0.230 0.470 0.000 2.043 0.390 0.350 0.696 1.522
0.220 0.430 -0.043 1.870 0.400 0.320 0.739 1.391
0.210 0.400 -0.087 1.739 0.420 0.290 0.826 1.261
0.200 0.340 -O.130 1.478 0.430 0.260 0.870 1.130
0.210 0.310 -0.087 1.348 0.450 0.230 0.957 1.000
0.210 0.270 -0.087 1 . 174 0.460 0.210 1.000 0.913
0.210 0.230 -0.087 1.000 0.470 0.170 1.043 0.739
0.210 0.190 -0.087 0.826 0.490 0.150 1.130 0.652
0.210 0.160 -0.087 0.696 0.510 0.120 1.217 0.522
0.220 0.130 -0.043 0.565

 

 

 

 

 

104

TABLE 46. Raw and Bookstein coordinates taken from the outer and inner curves of C-PC claw 4.

 

y = -2.4215x3 + 3.7945x + 1.6597 0pc Claw 4

 

R2 = 0.82
3.500 f _ 7 .
3.000 , 0 Outer Curve (BS)
I Inner Curve (BS)
3 2.500 1
‘g '— Poly. (Outer Curve (BS))
'9 2'00” \—Poly- (61.16.16.166)
8 1.500 ~
U
> , .
1.000 } = —2.l()—19\‘ + 2.7357x + 1.21186
0500 ‘ #:1111691
0.000 - 7*

-0.500 0.000 0.500 1.000 1.500

X Coordinates

FIGURE 50. Plotted Bookstein coordinates taken from the inner and outer curves of C-PC claw 4, with
trend lines and matching equations.

105

 

MSU-PA Claw 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
1.980 0.490 2.478 0.731 1.960 0.400 2.448 0.597
1.970 0.510 2.463 0.761 1.910 0.420 2.373 0.627
1.940 0.540 2.418 0.806 1.880 0.440 2.328 0.657
1.910 0.570 2.373 0.851 1.860 0.450 2.299 0.672
1.890 0.590 2.343 0.881 1.830 0.450 2.254 0.672
1.860 0.610 2.299 0.910 1.800 0.460 2.209 0.687
1.830 0.640 2.254 0.955 1.770 0.470 2.164 0.701
1.800 0.660 2.209 0.985 1.740 0.480 2.1 19 0.716
1.770 0.690 2.164 1.030 1.720 0.490 2.090 0.731
1.740 0.710 2.1 19 1.060 1.690 0.490 2.045 0.731
1.720 0.730 2.090 1.090 1.650 0.500 1.985 0.746
1.690 0.740 2.045 1.104 1.600 0.500 1.910 0.746
1.650 0.760 1.985 1.134 1.560 0.500 1.851 0.746
1.620 0.780 1.940 1.164 1.520 0.480 1.791 0.716
1.580 0.790 1.881 1 . 179 1.490 0.470 1.746 0.701
1.550 0.810 1.836 1.209 1.450 0.450 1.687 0.672
1.510 0.820 1.776 1.224 1.420 0.440 1.642 0.657
1.480 0.830 1.731 1.239 1.390 0.430 1.597 0.642
1.440 0.840 1.672 1.254 1.370 0.410 1.567 0.612
1.400 0.860 1.612 1.284 1.330 0.390 1.507 0.582
1.350 0.860 1.537 1.284 1.300 0.380 1.463 0.567
1.320 0.860 1.493 1.284 1.280 0.350 1.433 0.522
1.270 0.860 1.418 1.284 1.250 0.320 1.388 0.478
1.220 0.850 1.343 1.269 1.220 0.310 1.343 0.463
1.170 0.840 1.269 1.254 1.200 0.280 1.313 0.418
1 . 140 0.830 1.224 1.239 1 . 160 0.260 1.254 0.388
1.1 10 0.820 1 . 179 1.224 1 . 140 0.230 1.224 0.343
1.070 0.810 1.119 1.209 1.130 0.210 1.209 0.313
1.030 0.790 1.060 1.179 1.1 10 0.180 1.179 0.269
0.990 0.760 1.000 1.134 1.090 0.140 1.149 0.209
0.960 0.750 0.955 1.119 1.070 0.110 1.119 0.164
0.930 0.730 0.910 1.090
0.900 0.720 0.866 1.075
0.870 0.700 0.821 1.045
0.850 0.680 0.791 1.015
0.820 0.670 0.746 1.000
0.790 0.650 0.701 0.970
0.770 0.640 0.672 0.955
0.740 0.620 0.627 0.925
0.720 0.600 0.597 0.896
0.680 0.590 0.537 0.881
0.640 0.570 0.478 0.851

 

 

 

 

 

106

TABLE 47. Raw and Bookstein coordinates taken from the outer and inner curves of MSU-PA claw 1.

 

TABLE 47 (cont’d)

0.630 0.550 0.463 0.821
0.600 0.520 0.418 0.776
0.580 0.490 0.388 0.731
0.550 0.460 0.343 0.687
0.530 0.440 0.313 0.657
0.510 0.420 0.284 0.627
0.470 0.390 0.224 0.582
0.440 0.360 0.179 0.537
0.420 0.330 0.149 0.493
0.400 0.290 0.1 19 0.433
0.380 0.260 0.090 0.388
0.350 0.220 0.045 0.328
0.340 0.180 0.030 0.269

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

y = -0.4722x2 + 1.3696x + 0.2689 MSU-PA Claw 1

Y Coordinates

R2 = 0.9942
1.400 -

1200 if 0‘ Outer—Curye (BS)
1.000 ~ 1 I Inner Curve (BS)
I—Poly. (Outer Curve (BS)) 1

0.800
—Poly. (Inner Curve (BS))
0.600 1 ‘ ’ 7 “‘ '
0-400 - _\= = —0.7471x3+ 2.94991 — 2.1684
0.200 ~' 83 : 0.9932
0.000 ~ ~ ~ . 7 . __2
0.000 1 .000 2.000 3.000

X Coordinates

FIGURE 51. Plotted Bookstein coordinates taken from the inner and outer curves of MSU-PA claw 1, with
trend lines and matching equations.

107

 

MSU-PA Claw 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
1.720 2.230 1.955 5.068 1.650 2.100 1.795 4.773
1.670 2.220 1.841 5.045 1.610 2.080 1.705 4.727
1.630 2.220 1.750 5.045 1.580 2.060 1.636 4.682
1.590 2.220 1.659 5.045 1.540 2.030 1.545 4.614
1.540 2.210 1.545 5.023 1.520 2.010 1.500 4.568
1.510 2.190 1.477 4.977 1.480 2.000 1.409 4.545
1.460 2.180 1.364 4.955 1.460 1.980 1.364 4.500
1.420 2.170 1.273 4.932 1.430 1.960 1.295 4.455
1.380 2.160 1.182 4.909 1.400 1.930 1.227 4.386
1.350 2.150 1.114 4.886 1.370 1.910 1.159 4.341
1.310 2.130 1.023 4.841 1.360 1.870 1.136 4.250
1.270 2.100 0.932 4.773 1.330 1.840 1.068 4.182
1.220 2.080 0.818 4.727 1.310 1.820 1.023 4.136
1.190 2.050 0.750 4.659 1.290 1.780 0.977 4.045
1 . 160 2.020 0.682 4.591 1.270 1.750 0.932 3.977
1 . 130 2.010 0.614 4.568 1.250 1.730 0.886 3.932
1.1 10 1.990 0.568 4.523 1.230 1.700 0.841 3.864
1.080 1.970 0.500 4.477 1.220 1.660 0.818 3.773
1.050 1.940 0.432 4.409 1.200 1.630 0.773 3.705
1.020 1.910 0.364 4.341 1 . 180 1.590 0.727 3.614
0.990 1.880 0.295 4.273 1 . 160 1.550 0.682 3.523
0.970 1.860 0.250 4.227 1 . 140 1.510 0.636 3.432
0.940 1.830 0.182 4.159 1.110 1.470 0.568 3.341
0.910 1.800 0.114 4.091 1.100 1.440 0.545 3.273
0.860 1.770 0.000 4.023 1.080 1.400 0.500 3.182
0.840 1.740 -0.045 3.955 1.070 1.360 0.477 3.091
0.810 1.710 -0.114 3.886 1.060 1.310 0.455 2.977
0.780 1.670 -0. 182 3.795 1.060 1.270 0.455 2.886
0.750 1.650 -0.250 3.750 1.060 1.230 0.455 2.795
0.730 1.620 -0.295 3.682 1.060 1.200 0.455 2.727
0.710 1.580 -0.341 3.591 1.060 1.160 0.455 2.636
0.690 1.540 -0.386 3.500 1.060 1 . 130 0.455 2.568
0.680 1 .500 -0.409 3.409 1.060 1.080 0.455 2.455
0.670 1.460 -0.432 3.318 1.060 1.040 0.455 2.364
0.650 1.420 -0.477 3.227 1.060 0.990 0.455 2.250
0.630 1.390 -0.523 3.159 1.050 0.960 0.432 2.182
0.620 1.360 -0.545 3.091 1.050 0.920 0.432 2.091
0.600 1.320 -0.591 3.000 1.050 0.880 0.432 2.000
0.580 1.270 -0.636 2.886 1.050 0.850 0.432 1.932
0.580 1.220 -0.636 2.773 1.050 0.810 0.432 1.841
0.560 1.180 -0.682 2.682 1.060 0.770 0.455 1.750
0.560 1 . 140 -0.682 2.591 1.060 0.740 0.455 1.682

 

108

TABLE 48. Raw and Bookstein coordinates taken from the outer and inner curves of MSU-PA claw 2.

 

TABLE 48 (cont’d)

0.540 1.090 -0.727 2.477 1.080 0.720 0.500 1.636
0.540 1.040 -0.727 2.364 1.090 0.680 0.523 1.545
0.540 1.010 -0.727 2.295 1 . 100 0.660 0.545 1.500
0.540 0.970 -0.727 2.205 1.120 0.620 0.591 1.409
0.530 0.920 -0.750 2.091 1 . 140 0.600 0.636 1.364
0.530 0.880 -O.750 2.000 1 . 150 0.570 0.659 1.295
0.520 0.840 -0.773 1.909 1.170 0.540 0.705 1.227
0.520 0.800 -0.773 1.818 1.180 0.510 0.727 1.159
0.510 0.750 -0.795 1.705
0.510 0.720 -0.795 1.636
0.520 0.680 -0.773 1.545
0.520 0.630 -0.773 1.432
0.520 0.580 -0.773 1.318
0.520 0.550 -0.773 1.250
0.540 0.500 -0.727 1.136
0.540 0.460 -0.727 1.045
0.560 0.420 -0.682 0.955
0.560 0.380 -0.682 0.864
0.570 0.330 -0.659 0.750
0.580 0.290 -0.636 0.659
0.600 0.260 -0.591 0.591
0.620 0.210 -0.545 0.477

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

y = -0.8294x2 + 2.0764x + 3.7941 MSU-pA Claw 2

 

R2 = 0.8306

6.000

5.000 - 0 Outer Curve (BS) —
m g I Inner Curve (BS)
55:: 4'000 1 l—Poly. (Outer Curve (BS))
‘g 3.000 . L—Poly. (Inner Curve (BS))
8
>1 2.000

1 y =—1.1 109x- +4.511.\'+().3785
””0 ' R:=().6485
0.000 1 AAA - ~

-1 .000 0.000 1.000 2.000 3.000

X Coordinates

FIGURE 52. Plotted Bookstein coordinates taken from the inner and outer curves of MSU-PA claw 2, with
trend lines and matching equations.

109

 

MSU-PA Claw 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
5.020 1.200 3.803 1.690 4.930 1.060 3.676 1.493
4.990 1.240 3.761 1.746 4.890 1.060 3.620 1.493
4.960 1.260 3.718 1.775 4.850 1.060 3.563 1.493
4.930 1.280 3.676 1.803 4.820 1.060 3.521 1.493
4.890 1.320 3.620 1.859 4.770 1.060 3.451 1.493
4.860 1.340 3.577 1.887 4.730 1.060 3.394 1.493
4.830 1.370 3.535 1.930 4.680 1.070 3.324 1.507
4.800 1.390 3.493 1.958 4.640 1.060 3.268 1.493
4.770 1.390 3.451 1.958 4.590 1.070 3.197 1.507
4.720 1.410 3.380 1.986 4.550 1.070 3.141 1.507
4.680 1.430 3.324 2.014 4.500 1.070 3.070 1.507
4.650 1.440 3.282 2.028 4.440 1.070 2.986 1.507
4.620 1.450 3.239 2.042 4.390 1.070 2.915 1.507
4.590 1.470 3.197 2.070 4.340 1.070 2.845 1.507
4.550 1.480 3.141 2.085 4.290 1.060 2.775 1.493
4.500 1.490 3.070 2.099 4.210 1.040 2.662 1.465
4.470 1.480 3.028 2.085 4.220 1.040 2.676 1.465
4.430 1.490 2.972 2.099 4.190 1.020 2.634 1.437
4.380 1.490 2.901 2.099 4.150 1.010 2.577 1.423
4.340 1.500 2.845 2.113 4.110 1.010 2.521 1.423
4.300 1.510 2.789 2.127 4.070 1.000 2.465 1.408
4.250 1.520 2.718 2.141 4.040 0.980 2.423 1.380
4.210 1.520 2.662 2.141 4.000 0.970 2.366 1.366
4.170 1.520 2.606 2.141 3.970 0.950 2.324 1.338
4.130 1.520 2.549 2.141 3.940 0.940 2.282 1.324
4.100 1.520 2.507 2.141 3.900 0.920 2.225 1.296
4.060 1.510 2.451 2.127 3.860 0.910 2.169 1.282
4.020 1.510 2.394 2.127 3.830 0.890 2.127 1.254
3.980 1.510 2.338 2.127 3.790 0.880 2.070 1.239
3.950 1.510 2.296 2.127 3.750 0.860 2.014 1.211
3.910 1.500 2.239 2.113 3.720 0.850 1.972 1.197
3.880 1.490 2.197 2.099 3.680 0.830 1.915 1.169
3.860 1.490 2.169 2.099 3.650 0.800 1.873 1.127
3.820 1.490 2.1 13 2.099 3.620 0.790 1.831 1.113
3.800 1.480 2.085 2.085 3.580 0.780 1.775 1.099
3.770 1.470 2.042 2.070 3.560 0.760 1.746 1.070
3.750 1 .460 2.014 2.056 3.520 0.740 1.690 1.042
3.700 1.450 1.944 2.042 3.490 0.720 1.648 1.014
3.680 1.440 1.915 2.028 3.460 0.700 1.606 0.986
3.650 1.440 1.873 2.028 3.440 0.680 1.577 0.958
3.620 1.430 1.831 2.014 3.400 0.650 1.521 0.915
3.590 1.420 1.789 2.000 3.370 0.620 1.479 0.873

 

 

 

 

 

 

 

 

110

TABLE 49. Raw and Bookstein coordinates taken from the outer and inner curves of MSU-PA claw 3.

 

TABLE 49 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.560 1.410 1.746 1.986 3.330 0.600 1.423 0.845
3.530 1.400 1.704 1.972 3.310 0.570 1.394 0.803
3.510 1.390 1.676 1.958 3.280 0.540 1.352 0.761
3.470 1.380 1.620 1.944 3.250 0.500 1.310 0.704
3.440 1.380 1.577 1.944 3.230 0.460 1.282 0.648
3.410 1.360 1.535 1.915 3.230 0.410 1.282 0.577
3.380 1.340 1.493 1.887
3.340 1.330 1.437 1.873
3.310 1.320 1.394 1.859
3.280 1.300 1.352 1.831
3.250 1.280 1.310 1.803
3.220 1.270 1.268 1.789
3.190 1.260 1.225 1.775
3.170 1.240 1.197 1.746
3.140 1.220 1.155 1.718
3.110 1.210 1.113 1.704
3.080 1.200 1.070 1.690
3.060 1 . 180 1.042 1.662
3.030 1 . 160 1.000 1.634
3.010 1 . 150 0.972 1.620
2.980 1 . 140 0.930 1.606
2.960 1.1 10 0.901 1.563
2.920 1.090 0.845 1.535
2.890 1.060 0.803 1.493
2.860 1.040 0.761 1.465
2.840 1.020 0.732 1.437
2.820 1.000 0.704 1.408
2.780 0.970 0.648 1.366
2.760 0.950 0.620 1.338
2.730 0.920 0.577 1.296
2.710 0.900 0.549 1.268
2.690 0.880 0.521 1.239
2.660 0.850 0.479 1.197
2.630 0.820 0.437 1.155
2.610 0.790 0.408 1.113
2.580 0.760 0.366 1.070
2.550 0.730 0.324 1.028
2.530 0.700 0.296 0.986
2.500 0.680 0.254 0.958
2.490 0.640 0.239 0.901
2.470 0.590 0.21 1 0.831

 

111

 

y = -0.2308x2 + 1.1591 x + 0.6866 MSU-” Claw 3

R2 = 0.9957

2.500 .

2.000 ONOuter Curve (BS)
6’5 I Inner Curve (BS)
E 1500 '7 —Poly. (Outer Curve (BS))
g —Poly. (Inner Curve (BS))
81.00098 W —* -
>‘ ‘ ‘3

y = —().2326\“ + 1.473711 - (1.81 16
0.500 - 3
R = (1.992
0.000 3

0.000 1 .000 2.000 3.000 4.000

X Coordinates

FIGURE 53. Plotted Bookstein coordinates taken from the inner and outer curves of MSU-PA claw 3, with
trend lines and matching equations.

112

 

MSU-PA Claw 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
4.530 1.530 3.113 1.443 4.450 1.210 3.038 1.142
4.500 1.570 3.085 1.481 4.400 1.240 2.991 1 . 170
4.450 1.600 3.038 1.509 4.340 1.260 2.934 1.189
4.420 1.630 3.009 1.538 4.310 1.270 2.906 1.198
4.380 1.660 2.972 1.566 4.280 1.280 2.877 1.208
4.340 1.690 2.934 1.594 4.250 1.280 2.849 1.208
4.290 1.720 2.887 1.623 4.210 1.300 2.811 1.226
4.260 1.750 2.858 1.651 4.170 1.300 2.774 1.226
4.210 1.760 2.811 1.660 4.130 1.310 2.736 1.236
4.170 1.780 2.774 1.679 4.090 1.310 2.698 1.236
4.120 1.810 2.726 1.708 4.040 1.320 2.651 1.245
4.090 1.820 2.698 1.717 4.000 1.330 2.613 1.255
4.040 1.850 2.651 1.745 3.960 1.330 2.575 1.255
3.990 1.860 2.604 1.755 3.900 1.330 2.519 1.255
3.960 1.880 2.575 1.774 3.870 1.330 2.491 1.255
3.910 1.890 2.528 1.783 3.830 1.340 2.453 1.264
3.870 1.900 2.491 1.792 3.790 1.340 2.415 1.264
3.830 1.920 2.453 1.811 3.750 1.340 2.377 1.264
3.790 1.930 2.415 1.821 3.700 1.340 2.330 1.264
3.740 1.940 2.368 1.830 3.650 1.340 2.283 1.264
3.710 1.960 2.340 1.849 3.600 1.330 2.236 1.255
3.660 1.980 2.292 1.868 3.550 1.310 2.189 1.236
3.620 1.990 2.255 1.877 3.510 1.300 2.151 1.226
3.570 2.000 2.208 1.887 3.470 1.290 2.113 1.217
3.510 2.010 2.151 1.896 3.420 1.270 2.066 1.198
3.450 2.030 2.094 1.915 3.380 1.260 2.028 1.189
3.410 2.040 2.057 1.925 3.350 1.240 2.000 1.170
3.370 2.040 2.019 1.925 3.310 1.230 1.962 1.160
3.320 2.030 1.972 1.915 3.260 1.210 1.915 1.142
3.280 2.030 1.934 1.915 3.220 1.190 1.877 1.123
3.240 2.030 1.896 1.915 3.190 1.170 1.849 1.104
3.190 2.030 1.849 1.915 3.150 1.150 1.811 1.085
3.130 2.030 1.792 1.915 3.110 1.140 1.774 1.075
3.100 2.030 1.764 1.915 3.080 1.120 1.745 1.057
3.050 2.030 1.717 1.915 3.040 1.100 1.708 1.038
2.990 2.030 1.660 1.915 3.000 1.080 1.670 1.019
2.910 2.040 1.585 1.925 2.960 1.060 1.632 1.000
2.870 2.020 1.547 1.906 2.930 1.030 1.604 0.972
2.830 2.010 1.509 1.896 2.900 1.000 1.575 0.943
2.790 1.990 1.472 1.877 2.860 0.980 1.538 0.925
2.750 1.970 1.434 1.858 2.830 0.940 1.509 0.887
2.700 1.950 1.387 1.840 2.790 0.920 1.472 0.868

 

113

TABLE 50. Raw and Bookstein coordinates taken from the outer and inner curves of MSU-PA claw 4.

 

TABLE 50 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.660 1.920 1.349 1.81 1 2.760 0.890 1.443 0.840
2.620 1.900 1.31 1 1.792 2.730 0.850 1.415 0.802
2.600 1.880 1.292 1.774 2.710 0.820 1.396 0.774
2.570 1.860 1.264 1.755 2.690 0.770 1.377 0.726
2.530 1.840 1.226 1.736 2.660 0.740 1.349 0.698
2.500 1.820 1.198 1.717 2.650 0.690 1.340 0.651
2.460 1.800 1 . 160 1.698 2.630 0.640 1.321 0.604
2.420 1.780 1.123 1.679 2.610 0.600 1.302 0.566
2.370 1.760 1.075 1.660 2.600 0.560 1.292 0.528
2.320 1.750 1.028 1.651 2.590 0.520 1.283 0.491
2.290 1.740 1.000 1.642
2.260 1.710 0.972 1.613
2.230 1.690 0.943 1.594
2.200 1.680 0.915 1.585
2.160 1.660 0.877 1.566
2.120 1.640 0.840 1.547
2.090 1.620 0.811 1.528
2.040 1.600 0.764 1.509
2.000 1.570 0.726 1.481
1.960 1.550 0.689 1.462
1.920 1.530 0.651 1.443
1.870 1.500 0.604 1.415
1.830 1.470 0.566 1.387
1.780 1.450 0.519 1.368
1 .750 1.420 0.491 1.340
1.710 1.400 0.453 1.321
1.680 1.380 0.425 1.302
1.650 1.350 0.396 1.274
1.610 1.320 0.358 1.245
1.590 1.280 0.340 1.208
1.560 1.260 0.311 1.189
1.530 1.230 0.283 1.160
1.490 1.190 0.245 1.123
1.460 1.170 0.217 1.104
1.430 1.130 0.189 1.066
1.400 1.100 0.160 1.038
1.380 1.050 0.142 0.991
1.350 1.010 0.113 0.953
1.300 0.970 0.066 0.915
1.270 0.930 0.038 0.877
1.230 0.890 0.000 0.840
1.210 0.840 -0.019 0.792
1.190 0.810 -0.038 0.764
1 . 160 0.760 -0.066 0.717
I . 150 0.720 -0.075 0.679
1.130 0.670 -0.094 0.632

 

 

 

 

 

114

 

y = 0302112 + 1.1469x + 0.8216 Msu.pA Claw 4

R2 = 0.9938
2.500
2.000 ” ' ’
0 Outer Curve (BS)

5.5 I Inner Curve (BS)
2 1.500 -
-.§ —Poly. (Outer Curve (BS))
0 —
8 1.000 . . mil-Elmer Curve (BS):
>_‘ 1

0.500 ~ 524149633 + 2.4293x — 1.6894

R3 = 0.9763
0.000 ~ -' - — **

-0.500 0.500 1.500 2.500 3.500

X Coordinates

FIGURE 54. Plotted Bookstein coordinates taken from the inner and outer curves of MSU-PA claw 4, with
trend lines and matching equations.

115

 

C22026 Claw l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
2.240 3.210 1.478 2.841 2.350 3.090 1.575 2.735
2.210 3.190 1.451 2.823 2.340 3.040 1.566 2.690
2.170 2.170 1.416 1.920 2.310 3.000 1.540 2.655
2.140 3.150 1.389 2.788 2.300 2.970 1.531 2.628
2.130 3.120 1.381 2.761 2.260 2.930 1.496 2.593
2.100 3.100 1.354 2.743 2.240 2.880 1.478 2.549
2.080 3.070 1.336 2.717 2.250 2.830 1.487 2.504
2.070 3.030 1.327 2.681 2.250 2.780 1.487 2.460
2.050 3.000 1.310 2.655 2.230 2.730 1.469 2.416
2.020 2.980 1.283 2.637 2.220 2.680 1.460 2.372
2.000 2.960 1.265 2.619 2.210 2.650 1.451 2.345
1.970 2.930 1.239 2.593 2.200 2.590 1.442 2.292
1.950 2.900 1.221 2.566 2.210 2.550 1.451 2.257
1.920 2.870 1.195 2.540 2.210 2.500 1.451 2.212
1.890 2.850 1.168 2.522 2.220 2.470 1.460 2.186
1.870 2.820 1.150 2.496 2.240 2.440 1.478 2.159
1.840 2.800 1.124 2.478 2.260 2.400 1.496 2.124
1.820 2.770 1.106 2.451 2.240 2.370 1.478 2.097
1.800 2.740 1.088 2.425 2.230 2.330 1.469 2.062
1.770 2.720 1.062 2.407 2.220 2.300 1.460 2.035
1.750 2.680 1.044 2.372 2.200 2.270 1.442 2.009
1.720 2.650 1.018 2.345 2.180 2.240 1.425 1.982
1.710 2.620 1.009 2.319 2.170 2.200 1.416 1.947
1.690 2.600 0.991 2.301 2.160 2.150 1.407 1.903
1.680 2.570 0.982 2.274 2.150 2.120 1.398 1.876
1.650 2.540 0.956 2.248 2.140 2.080 1.389 1.841
1.630 2.510 0.938 2.221 2.130 2.040 1.381 1.805
1.610 2.490 0.920 2.204 2.130 2.000 1.381 1.770
1.590 2.460 0.903 2.177 2.1 10 1.970 1.363 1.743
1.570 2.430 0.885 2.150 2.100 1.920 1.354 1.699
1.550 2.400 0.867 2.124 2.080 1.890 1.336 1.673
1.520 2.380 0.841 2.106 2.070 1.860 1.327 1.646
1.490 2.350 0.814 2.080 2.060 1.810 1.319 1.602
1.460 2.320 0.788 2.053 2.060 1.770 1.319 1.566
1.440 2.270 0.770 2.009 2.040 1.730 1.301 1.531
1.400 2.240 0.735 1.982 2.030 1.690 1.292 1.496
1.380 2.200 0.717 1.947 2.010 1.640 1.274 1.451
1.350 2.160 0.690 1.912 2.000 1.600 1.265 1.416
1.340 2.140 0.681 1.894 1.980 1.560 1.248 1.381
1.310 2.090 0.655 1.850 1.960 1.520 1.230 1.345
1.290 2.060 0.637 1.823 1.950 1.470 1.221 1.301
1.270 2.030 0.619 1.796 1.940 1.430 1.212 1.265

 

116

TABLE 51. Raw and Bookstein coordinates taken from the outer and inner curves of C22026 claw 1.

 

TABLE 51 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.240 1.980 0.593 1.752 1.940 1.390 1.212 1.230
1.230 1.950 0.584 1.726 1.930 1.350 1.204 1.195
1.210 1.920 0.566 1.699 1.920 1.300 1.195 1.150
1.200 1.880 0.558 1.664 1.910 1.270 1.186 1.124
1 . 180 1.850 0.540 1.637 1.910 1.220 1.186 1.080
1.160 1.820 0.522 1.611 1.900 1.180 1.177 1.044
1.150 1.790 0.513 1.584 1.900 1.140 1.177 1.009
1 . 140 1.760 0.504 1.558 1.890 1.090 1.168 0.965
1.120 1.710 0.487 1.513 1.890 1.050 1.168 0.929
1 . 100 1.670 0.469 1.478 1.890 1.010 1.168 0.894
1.080 1.640 0.451 1.451 1.880 0.970 1 . 159 0.858
1.070 1.600 0.442 1.416 1.880 0.930 1 . 159 0.823
1.060 1.570 0.434 1.389 1.870 0.880 1 . 150 0.779
1.050 1.530 0.425 1.354 1.860 0.830 1.142 0.735
1.040 1.490 0.416 1.319 1.850 0.800 1.133 0.708
1.030 1.430 0.407 1.265 1.840 0.760 1.124 0.673
1.010 1.400 0.389 1.239 1.830 0.710 1.115 0.628
0.990 1.350 0.372 1 . 195 1.830 0.670 1.1 15 0.593
0.980 1.320 0.363 1.168 1.820 0.620 1.106 0.549
0.970 1.270 0.354 1.124 1.830 0.580 1.115 0.513
0.950 1.240 0.336 1.097 1.830 0.540 1.1 15 0.478
0.930 1.200 0.319 1.062 1.830 0.500 1.1 15 0.442
0.910 1.160 0.301 1.027 1.850 0.450 1.133 0.398
0.900 1 . 120 0.292 0.991 1.850 0.400 1 . 133 0.354
0.870 1.080 0.265 0.956
0.850 1.040 0.248 0.920
0.840 0.990 0.239 0.876
0.830 0.950 0.230 0.841
0.810 0.900 0.212 0.796
0.800 0.860 0.204 0.761
0.790 0.820 0.195 0.726
0.780 0.790 0.186 0.699
0.770 0.740 0.177 0.655
0.750 0.700 0.159 0.619
0.730 0.670 0.142 0.593
0.720 0.640 0.133 0.566
0.710 0.590 0.124 0.522
0.710 0.550 0.124 0.487
0.690 0.530 0.106 0.469
0.690 0.490 0.106 0.434
0.670 0.440 0.088 0.389
0.660 0.400 0.080 0.354
0.640 0.360 0.062 0.319
0.630 0.310 0.053 0.274
0.620 0.270 0.044 0.239
0.610 0.230 0.035 0.204

 

117

 

y = —1.0837x2 + 3.3219x + 0.1195 C22026 Claw 1

R2 = 0.9871
3.000 .
. 2, .7 . 2 ,2-
2.500 1 0 Outer Curve (BS)
g 2.000 I Inner Curve (BS)
.5. —Poly. (Outer Curve (BS))
-o
(E; 1500 ' —Poly. (Inner Curye (BS))
if 1.000 W
5 = —l.9659.\"+9.82~15x - 7.9137
0500 R3 = 0.9663
0.000 4. - - — 7"

0.000 0.500 1.000 1.500 2.000

X Coordinates

FIGURE 55. Plotted Bookstein coordinates taken from the inner and outer curves of C22026 claw 1, with
trend lines and matching equations.

118

 

C22026 Claw 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
2.520 3.410 1.815 3.157 2.720 3.340 2.000 3.093
2.480 3.390 1.778 3.139 2.730 3.310 2.009 3.065
2.440 3.370 1.741 3.120 2.730 3.260 2.009 3.019
2.410 3.350 1.713 3.102 2.730 3.210 2.009 2.972
2.370 3.320 1.676 3.074 2.720 3.180 2.000 2.944
2.350 3.290 1.657 3.046 2.720 3.130 2.000 2.898
2.320 3.280 1.630 3.037 2.710 3.090 1.991 2.861
2.290 3.250 1.602 3.009 2.700 3.050 1.981 2.824
2.250 3.220 1.565 2.981 2.700 3.020 1.981 2.796
2.220 3.190 1.537 2.954 2.680 2.990 1.963 2.769
2.190 3.150 1.509 2.917 2.660 2.960 1.944 2.741
2.170 3.120 1.491 2.889 2.650 2.930 1.935 2.713
2.130 3.080 1.454 2.852 2.630 2.900 1.917 2.685
2.1 10 3.050 1.435 2.824 2.620 2.850 1.907 2.639
2.080 3.030 1.407 2.806 2.600 2.810 1.889 2.602
2.050 3.000 1.380 2.778 2.590 2.770 1.880 2.565
2.020 2.960 1.352 2.741 2.570 2.750 1.861 2.546
1.990 2.930 1.324 2.713 2.560 2.720 1.852 2.519
1.970 2.900 1.306 2.685 2.540 2.690 1.833 2.491
1.930 2.850 1.269 2.639 2.530 2.660 1.824 2.463
1.910 2.820 1.250 2.611 2.510 2.630 1.806 2.435
1.890 2.780 1.231 2.574 2.500 2.600 1.796 2.407
1.860 2.740 1.204 2.537 2.490 2.560 1.787 2.370
1.830 2.710 1.176 2.509 2.480 2.530 1.778 2.343
1.790 2.680 1.139 2.481 2.470 2.490 1.769 2.306
1.760 2.640 1.1 1 1 2.444 2.460 2.460 1.759 2.278
1.740 2.610 1.093 2.417 2.440 2.440 1.741 2.259
1.710 2.570 1.065 2.380 2.420 2.410 1.722 2.231
1.680 2.530 1.037 2.343 2.410 2.380 1.713 2.204
1.650 2.490 1.009 2.306 2.390 2.350 1.694 2.176
1.630 2.460 0.991 2.278 2.380 2.330 1.685 2.157
1.600 2.420 0.963 2.241 2.370 2.290 1.676 2.120
1.560 2.370 0.926 2.194 2.350 2.260 1.657 2.093
1.540 2.330 0.907 2.157 2.340 2.220 1.648 2.056
1.510 2.290 0.880 2.120 2.330 2.180 1.639 2.019
1.470 2.260 0.843 2.093 2.320 2.150 1.630 1.991
1.450 2.220 0.824 2.056 2.310 2.110 1.620 1.954
1.430 2.190 0.806 2.028 2.290 2.070 1.602 1.917
1.410 2.160 0.787 2.000 2.280 2.030 1.593 1.880
1.390 2.120 0.769 1.963 2.260 1.990 1.574 1.843
1.370 2.090 0.750 1.935 2.240 1.940 1.556 1.796
1.350 2.050 0.731 1.898 2.220 1.890 1.537 1.750

 

 

 

 

 

119

TABLE 52. Raw and Bookstein coordinates taken from the outer and inner curves of C22026 claw 2.

 

TABLE 52 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.330 2.030 0.713 1.880 2.200 1.840 1.519 1.704
1.310 2.010 0.694 1.861 2.180 1.800 1.500 1.667
1.290 1.980 0.676 1.833 2.170 1.760 1.491 1.630
1.280 1.960 0.667 1.815 2.150 1.720 1.472 1.593
1.260 1.930 0.648 1.787 2.140 1.680 1.463 1.556
1.240 1.900 0.630 1.759 2.130 1.640 1.454 1.519
1.230 1.880 0.620 1.741 2.100 1.600 1.426 1.481
1.220 1.860 0.61 1 1.722 2.080 1.550 1.407 1.435
1.200 1.820 0.593 1.685 2.060 1.510 1.389 1.398
1 . 180 1.790 0.574 1.657 2.040 1.460 1.370 1.352
1.160 1.760 0.556 1.630 2.020 1.410 1.352 1.306
1.140 1.730 0.537 1.602 2.000 1.370 1.333 1.269
1.120 1.700 0.519 1.574 1.980 1.330 1.315 1.231
1 . 100 1.650 0.500 1.528 1.950 1.300 1.287 1.204
1.080 1.610 0.481 1.491 1.930 1.260 1.269 1.167
1.070 1.560 0.472 1.444 1.920 1.240 1.259 1.148
1.060 1.520 0.463 1.407 1.900 1.200 1.241 1.111
1.040 1.480 0.444 1.370 1.880 1.160 1.222 1.074
1.030 1.450 0.435 1.343 1.870 1.1 10 1.213 1.028
1.020 1.420 0.426 1.315 1.850 1.080 1.194 1.000
1.020 1.390 0.426 1.287 1.830 1.030 1. 176 0.954
1.020 1.360 0.426 1.259 1.840 0.990 1.185 0.917
1.010 1.330 0.417 1.231 1.830 0.930 1.176 0.861
1.000 1.230 0.407 1.139 1.800 0.890 1.148 0.824
0.990 1.240 0.398 1 . 148 1.780 0.850 1.130 0.787
0.970 1.210 0.380 1.120 1.780 0.830 1.130 0.769
0.970 1 . 170 0.380 1.083 1.770 0.780 1 . 120 0.722
0.950 1 . 130 0.361 1.046 1.770 0.750 1.120 0.694
0.920 1.100 0.333 1.019 1.760 0.710 1.111 0.657
0.900 1.070 0.315 0.991 1.740 0.660 1.093 0.61 1
0.880 1.040 0.296 0.963 1.740 0.630 1.093 0.583
0.860 1.000 0.278 0.926 1.730 0.600 1.083 0.556
0.860 0.960 0.278 0.889 1.720 0.550 1.074 0.509
0.860 0.920 0.278 0.852 1.730 0.510 1.083 0.472
0.820 0.880 0.241 0.815 1.730 0.470 1.083 0.435
0.800 0.840 0.222 0.778 1.720 0.420 1.074 0.389
0.770 0.790 0.194 0.731 1.720 0.390 1.074 0.361
0.750 0.750 0.176 0.694 1.720 0.350 1.074 0.324
0.740 0.710 0.167 0.657 1.730 0.310 1.083 0.287
0.730 0.680 0.157 0.630 1.730 0.260 1.083 0.241
0.710 0.680 0.139 0.630 1.720 0.220 1.074 0.204
0.700 0.590 0.130 0.546

0.690 0.540 0.120 0.500

0.680 0.510 0.1 l 1 0.472

0.670 0.450 0.102 0.417

0.660 0.420 0.093 0.389

 

 

 

 

 

120

 

TABLE 52 (cont’d)

 

0.650 0.380 0.083 0.352
0.640 0.330 0.074 0.306
0.640 0.290 0.074 0.269
0.640 0.260 0.074 0.241

 

 

 

 

 

 

 

 

 

y = 06817142 + 2.847911 + 0.1736 C22026 Claw 2

R2 = 0.9962
3.500 -
3000 o OuteFC-urve (BS)
33 2.500 «
g 2000 4 I Inner Curve (BS)
‘5
8 L500 —Poly. (Outer Curve
>- 1.0001 ,__ (BS))
0500 - ‘ '—P61y. (Inner Curve (BS))
0.000 4 - . . -22.

0.000 0.500 1.000 1.500 2.000 2.500

X Coordinates

FIGURE 56. Plotted Bookstein coordinates taken from the inner and outer curves of C22026 claw 2, with
trend lines and matching equations.

121

 

C22026 Claw 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
2.930 1.720 1.724 2.966 2.980 1.670 1.810 2.879
2.890 1.710 1.655 2.948 2.970 1.630 1.793 2.810
2.870 1.690 1.621 2.914 2.960 1.590 1.776 2.741
2.840 1.670 1.569 2.879 2.950 1.570 1.759 2.707
2.800 1.650 1.500 2.845 2.930 1.530 1.724 2.638
2.770 1.630 1.448 2.810 2.920 1.490 1.707 2.569
2.740 1.600 1.397 2.759 2.910 1.450 1.690 2.500
2.720 1.590 1.362 2.741 2.900 1.420 1.672 2.448
2.690 1.580 1.310 2.724 2.890 1.400 1.655 2.414
2.660 1.560 1.259 2.690 2.890 1.370 1.655 2.362
2.630 1.540 1.207 2.655 2.880 1.340 1.638 2.310
2.610 1.520 1.172 2.621 2.860 1.320 1.603 2.276
2.600 1.510 1.155 2.603 2.870 1.280 1.621 2.207
2.580 1.500 1.121 2.586 2.870 1.250 1.621 2.155
2.550 1.480 1.069 2.552 2.850 1.220 1.586 2.103
2.540 1.460 1.052 2.517 2.840 1.180 1.569 2.034
2.520 1.440 1.017 2.483 2.840 1.160 1.569 2.000
2.350 1.410 0.724 2.431 2.830 1.130 1.552 1.948
2.470 1.390 0.931 2.397 2.820 1.100 1.534 1.897
2.450 1.360 0.897 2.345 2.820 1.070 1.534 1.845
2.420 1.330 0.845 2.293 2.810 1.040 1.517 1.793
2.400 1.300 0.810 2.241 2.800 1.010 1.500 1.741
2.370 1.270 0.759 2.190 2.800 0.980 1.500 1.690
2.350 1.260 0.724 2.172 2.790 0.960 1.483 1.655
2.330 1.230 0.690 2.121 2.800 0.930 1.500 1.603
2.320 1.200 0.672 2.069 2.800 0.900 1.500 1.552
2.290 1.180 0.621 2.034 2.800 0.860 1.500 1.483
2.290 1.150 0.621 1.983 2.790 0.830 1.483 1.431
2.260 1 . 120 0.569 1.931 2.790 0.800 1.483 1.379
2.240 1.090 0.534 1.879 2.770 0.760 1.448 1.310
2.230 1.060 0.517 1.828 2.760 0.730 1.431 1.259
2.220 1.030 0.500 1.776 2.740 0.690 1.397 1 . 190
2.200 1.000 0.466 1.724 2.730 0.660 1.379 1.138
2.190 0.970 0.448 1.672 2.730 0.620 1.379 1.069
2.170 0.940 0.414 1.621 2.710 0.580 1.345 1.000
2.160 0.910 0.397 1.569 2.700 0.550 1.328 0.948
2.150 0.880 0.379 1.517 2.670 0.530 1.276 0.914
2.130 0.860 0.345 1.483 2.640 0.490 1.224 0.845
2.1 10 0.830 0.310 1.431 2.630 0.440 1.207 0.759
2.100 0.800 0.293 1.379 2.600 0.400 1.155 0.690
2.090 0.760 0.276 1.310 2.590 0.360 1.138 0.621
2.080 0.720 0.259 1.241 2.580 0.320 1.121 0.552

 

122

TABLE 53. Raw and Bookstein coordinates taken from the outer and inner curves of C22026 claw 3.

 

TABLE 53 (cont’d)

Y Coordinates

2.070 0.680 0.241 1.172 2.580 I 0.290 I 1.121 | 050M

2.060 0.640 0.224 1.103

2.050 0.610 0.207 1.052

2.030 0.580 0.172 1.000

2.020 0.550 0.155 0.948

2.010 0.520 0.138 0.897

2.000 0.490 0.121 0.845

1.990 0.450 0.103 0.776

1.990 0.420 0.103 0.724

1.970 0.380 0.069 0.655

1 .960 0.350 0.052 0.603

1.960 0.300 0.052 0.517

1.950 0.260 0.034 0.448

1.950 0.220 0.034 0.379

1.950 0.180 0.034 0.310

y = 09939112 + 3.0815x + 0.4545 C22026 Claw 3
R2 = 0.9893
3.500
3.000 -' . . -
2 500 0 Outer Curve (BS)
’ ° . I Inner Curve (BS)
2000 " —Poly. (Outer Curve (BS)) .
1.500 *1 —Poly. (Inner Curve (BS)) _
1.000 - ,
= 2. (8.“ - 2. 33.4 1.83
0500‘ ) 171\ 7 51+( 41
R" = 0.9708
0.000 ‘ 2 2
0.000 0.500 1.000 1.500 2.000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

X Coordinates

FIGURE 57. Plotted Bookstein coordinates taken from the inner and outer curves of C22026 claw 3, with
trend lines and matching equations.

123

 

C213395 Claw 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
1.940 2.610 1.191 2.373 2.060 2.550 1.300 2.318
1.910 2.600 1.164 2.364 2.040 2.520 1.282 2.291
1.870 2.590 1.127 2.355 2.030 2.500 1.273 2.273
1.830 2.580 1.091 2.345 2.020 2.470 1.264 2.245
1.800 2.560 1.064 2.327 2.020 2.430 1.264 2.209
1.770 2.540 1.036 2.309 2.010 2.380 1.255 2.164
1.750 2.520 1.018 2.291 1.990 2.360 1.236 2.145
1.720 2.490 0.991 2.264 1.980 2.330 1.227 2.118
1.700 2.470 0.973 2.245 1.970 2.300 1.218 2.091
1.670 2.460 0.945 2.236 1.950 2.260 1.200 2.055
1.640 2.430 0.918 2.209 1.940 2.230 1.191 2.027
1.600 2.410 0.882 2.191 1.910 2.190 1.164 1.991
1.550 2.380 0.836 2.164 1.890 2.160 1.145 1.964
1.510 2.360 0.800 2.145 1.880 2.130 1.136 1.936
1.490 2.340 0.782 2.127 1.850 2.090 1.109 1.900
1.460 2.300 0.755 2.091 1.830 2.040 1.091 1.855
1.430 2.270 0.727 2.064 1.820 2.010 1.082 1.827
1.410 2.240 0.709 2.036 1.820 1.960 1.082 1.782
1.380 2.220 0.682 2.018 1.800 1.930 1.064 1.755
1.350 2.180 0.655 1.982 1.790 1.870 1.055 1.700
1.320 2.150 0.627 1.955 1.780 1.830 1.045 1.664
1.300 2.1 10 0.609 1.918 1.770 1.800 1.036 1.636
1.280 2.080 0.591 1.891 1.770 1.760 1.036 1.600
1.250 2.040 0.564 1.855 1.760 1.720 1.027 1.564
1.220 2.020 0.536 1.836 1.750 1.690 1.018 1.536
1.200 1.980 0.518 1.800 1.740 1.640 1.009 1.491
1 . 190 1.940 0.509 1.764 1.730 1.590 1.000 1.445
1.170 1.900 0.491 1.727 1.720 1.560 0.991 1.418
1 . 140 1.870 0.464 1.700 1.720 1.510 0.991 1.373
1 . 120 1.840 0.445 1.673 1.710 1.470 0.982 1.336
1.090 1.800 0.418 1.636 1.710 1.430 0.982 1.300
1.070 1.770 0.400 1.609 1.700 1.390 0.973 1.264
1.040 1.720 0.373 1.564 1.700 1.350 0.973 1.227
1.030 1.690 0.364 1.536 1.690 1.320 0.964 1.200
1.010 1.660 0.345 1.509 1.690 1.280 0.964 1 . 164
0.980 1.620 0.318 1.473 1.680 1.230 0.955 1.1 18
0.970 1.590 0.309 1.445 1.680 1.190 0.955 1.082
0.950 1.540 0.291 1.400 1.670 1 . 150 0.945 1.045
0.930 1.500 0.273 1.364 1.650 1.1 10 0.927 1.009
0.920 1.450 0.264 1.318 1.650 1.060 0.927 0.964
0.900 1.410 0.245 1.282 1.640 1.010 0.918 0.918
0.900 1.370 0.245 1.245 1.640 0.980 0.918 0.891

 

124

TABLE 54. Raw and Bookstein coordinates taken from the outer and inner curves of C2 1 3395 claw l.

 

TABLE 54 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.880 1.340 0.227 1.218 1.630 0.930 0.909 0.845
0.870 1.300 0.218 1 . 182 1.630 0.890 0.909 0.809
0.860 1.260 0.209 1.145 1.630 0.850 0.909 0.773
0.840 1.220 0.191 1.109 1.620 0.800 0.900 0.727
0.820 1 . 170 0.173 1.064 1.640 0.760 0.918 0.691
0.800 1 . 140 0.155 1.036 1.650 0.720 0.927 0.655
0.790 1.090 0.145 0.991 1.660 0.680 0.936 0.618
0.790 1.050 0.145 0.955 1.660 0.630 0.936 0.573
0.790 1.000 0.145 0.909 1.660 0.600 0.936 0.545
0.760 0.970 0.1 18 0.882 1.670 0.560 0.945 0.509
0.750 0.920 0.109 0.836 1.680 0.510 0.955 0.464
0.730 0.880 0.091 0.800 1.690 0.470 0.964 0.427
0.730 0.830 0.091 0.755 1.710 0.430 0.982 0.391
0.720 0.790 0.082 0.718 1.730 0.390 1.000 0.355
0.710 0.760 0.073 0.691 1.750 0.350 1.018 0.318
0.710 0.730 0.073 0.664 1.770 0.310 1.036 0.282
0.700 0.670 0.064 0.609 1.780 0.280 1.045 0.255
0.680 0.630 0.045 0.573 1.800 0.250 1.064 0.227
0.680 0.580 0.045 0.527
0.680 0.530 0.045 0.482
0.680 0.480 0.045 0.436
y = - 1 5693113 + 3.391911 + 0.4716 C213395 Claw 1
R7- = 0.9913
3.000 -
0 Outer Curve (BS)
2500 I Inner Curve (BS)
U)
54,; 2.000 —Poly. (Outer Curve (BS))
:
E 1. 5 00 :Pgly. (Inner Curve (BS))
8
1.000 - 1
>‘ y = — 1 .57021- + 7.8262.\ — 5.1189
0.500 7 113 = 0.6459
1
0.000 « - ~ 4
0.000 0.500 1.000 1.500

X Coordinates

FIGURE 58. Plotted Bookstein coordinates taken from the inner and outer curves of C213395 claw 1, with
trend lines and matching equations.

125

 

C-CAD Claw 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein lnner Raw Inner Bookstein
X Y X Y X Y X Y
1.870 2.040 0.885 2.125 1.910 2.030 0.927 2.115
1.860 2.000 0.875 2.083 1.930 2.000 0.948 2.083
1.830 1.960 0.844 2.042 1.940 1.980 0.958 2.063
1.830 1.930 0.844 2.010 1.960 1.960 0.979 2.042
1.810 1.910 0.823 1.990 1.980 1.940 1.000 2.021
1.760 1.870 0.771 1.948 1.990 1.900 1.010 1.979
1.790 1.830 0.802 1.906 1.990 1.860 1.010 1.938
1.770 1.780 0.781 1.854 2.000 1.840 1.021 1.917
1.760 1.740 0.771 1.813 2.000 1.810 1.021 1.885
1.760 1.710 0.771 1.781 2.010 1.780 1.031 1.854
1.740 1.670 0.750 1.740 2.010 1.750 1.031 1.823
1.730 1.640 0.740 1.708 2.010 1.730 1.031 1.802
1.710 1.610 0.719 1.677 2.010 1.700 1.031 1.771
1.690 1.570 0.698 1.635 2.020 1.660 1.042 1.729
1.680 1.530 0.688 1.594 2.020 1.620 1.042 1.688
1.640 1.490 0.646 1.552 2.020 1.560 1.042 1.625
1.620 1.440 0.625 1.500 2.020 1.520 1.042 1.583
1.590 1.400 0.594 1.458 2.020 1.460 1.042 1.521
1.590 1.360 0.594 1.417 2.020 1.420 1.042 1.479
1.570 1.340 0.573 1.396 2.020 1.370 1.042 1.427
1.550 1.300 0.552 1.354 2.010 1.320 1.031 1.375
1.530 1.270 0.531 1.323 2.010 1.280 1.031 1.333
1.510 1.240 0.510 1.292 2.000 1.240 1.021 1.292
1.500 1.220 0.500 1.271 2.000 1.200 1.021 1.250
1.490 1.190 0.490 1.240 1.990 1.160 1.010 1.208
1.470 1.160 0.469 1.208 1.990 1.100 1.010 1.146
1.450 1.130 0.448 1.177 1.990 1.090 1.010 1.135
1.430 1.1 10 0.427 1.156 1.970 1.060 0.990 1.104
1.410 1.070 0.406 1.1 15 1.970 1.030 0.990 1.073
1.390 1.030 0.385 1.073 1.950 0.990 0.969 1.031
1.370 1.000 0.365 1.042 1.940 0.960 0.958 1.000
1.360 0.970 0.354 1.010 1.920 0.930 0.938 0.969
1.250 0.710 0.240 0.740 1.910 0.910 0.927 0.948
1.220 0.670 0.208 0.698 1.900 0.870 0.917 0.906
1.210 0.630 0.198 0.656 1.880 0.850 0.896 0.885
1 . 190 0.590 0.177 0.615 1.870 0.820 0.885 0.854
1 . 170 0.560 0.156 0.583 1.870 0.790 0.885 0.823
1.160 0.530 0.146 0.552 1.860 0.760 0.875 0.792
1.140 0.490 0.125 0.510 1.860 0.730 0.875 0.760
1.1 10 0.440 0.094 0.458 1.860 0.700 0.875 0.729
1 .090 0.390 0.073 0.406 1.860 0.670 0.875 0.698
1.080 0.370 0.063 0.385 1.850 0.620 0.865 0.646

 

126

TABLE 55. Raw and Bookstein coordinates taken from the outer and inner curves of C-CAD claw 2.

 

TABLE 55 (cont’d)

y = 0.1713112 + 1.8876x + 0.2786 OCAD Claw 2

 

 

 

 

 

 

 

 

 

 

 

 

 

1.060 0.330 0.042 0.344 1.850 0.580 0.865 0.604
1.040 0.290 0.021 0.302 1.850 0.550 0.865 0.573
1.020 0.260 0.000 0.271 1.860 0.500 0.875 0.521
1.860 0.460 0.875 0.479
1.880 0.420 0.896 0.438
1.910 0.380 0.927 0.396
1.930 0.350 0.948 0.365
1.940 0.320 0.958 0.333
1.950 0.270 0.969 0.281
1.960 0.220 0.979 0.229

 

 

 

 

 

R2 = 0.9963
2.500
2.000 0 Outer Curve (BS)
{3 ' I Inner Curve (BS)
E 1500 —Poly. (Outer Curve (BS))
1% ‘—Poly. (Inner Curve (BS))
5 1.000 ~ - - -+- w» v
>— . ,
0.500 1 }'=(1.75—l—1.\’ — 7.071211" + 1.6959
R’- = 0.4184
0.000 - , .
0.000 0.500 1.000 1.500

X Coordinates

FIGURE 59. Plotted Bookstein coordinates taken from the inner and outer curves of C-CAD claw 2, with

trend lines and matching equations.

127

 

 

C-CAD Claw 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
1.050 1.290 0.353 2.529 1.080 1.290 0.412 2.529
1.050 1.270 0.353 2.490 1 . 100 1.270 0.451 2.490
1.040 1.240 0.333 2.431 1 . 120 1.240 0.490 2.431
1.030 1.210 0.314 2.373 1.140 1.210 0.529 2.373
1.030 1.180 0.314 2.314 1.160 1.180 0.569 2.314
1.020 1.150 0.294 2.255 1 . 190 1 . 160 0.627 2.275
1.020 1.120 0.294 2.196 1.220 1.120 0.686 2.196
1.020 1.100 0.294 2.157 1.230 1.100 0.706 2.157
1.010 1.070 0.275 2.098 1.240 1.060 0.725 2.078
1.010 1.040 0.275 2.039 1.260 1.020 0.765 2.000
1.010 1.010 0.275 1.980 1.260 1.000 0.765 1.961
1.010 0.980 0.275 1.922 1.270 0.970 0.784 1.902
1.010 0.940 0.275 1.843 1.280 0.940 0.804 1.843
1.010 0.920 0.275 1.804 1.290 0.910 0.824 1.784
1.000 0.890 0.255 1.745 1.290 0.880 0.824 1.725
1.000 0.860 0.255 1.686 1.290 0.860 0.824 1.686
1.000 0.840 0.255 1.647 1.300 0.830 0.843 1.627
0.990 0.810 0.235 1.588 1.300 0.800 0.843 1.569
0.990 0.790 0.235 1.549 1.310 0.760 0.863 1.490
0.990 0.760 0.235 1.490 1.310 0.740 0.863 1.451
0.980 0.740 0.216 1.451 1.310 0.700 0.863 1.373
0.970 0.720 0.196 1.412 1.310 0.670 0.863 1.314
0.970 0.700 0.196 1.373 1.320 0.640 0.882 1.255
0.960 0.670 0.176 1.314 1.320 0.610 0.882 1.196
0.950 0.650 0.157 1.275 1.320 0.590 0.882 1.157
0.940 0.590 0.137 1 . 157 1.320 0.550 0.882 1.078
0.930 0.560 0.1 18 1.098 1.320 0.530 0.882 1.039
0.930 0.540 0.1 18 1.059 1.330 0.500 0.902 0.980
0.930 0.520 0.1 18 1.020 1.330 0.470 0.902 0.922
0.920 0.490 0.098 0.961 1.340 0.430 0.922 0.843
0.910 0.470 0.078 0.922 1.340 0.400 0.922 0.784
0.910 0.430 0.078 0.843 1.350 0.380 0.941 0.745
0.910 0.400 0.078 0.784 1.350 0.340 0.941 0.667
0.890 0.380 0.039 0.745 1.370 0.320 0.980 0.627
0.890 0.340 0.039 0.667 1.370 0.290 0.980 0.569
0.890 0.320 0.039 0.627 1.390 0.270 1.020 0.529
0.890 0.290 0.039 0.569 1.400 0.240 1.039 0.471
0.880 0.270 0.020 0.529 1.410 0.210 1.059 0.412
0.880 0.230 0.020 0.451 1.430 0.170 1.098 0.333
0.880 0.200 0.020 0.392 1.440 0.150 1.1 18 0.294

1.440 0.120 1.118 0.235

 

128

TABLE 56. Raw and Bookstein coordinates taken from the outer and inner curves of C-CAD claw 3.

 

y = 0.9749112 + 3.39831 + 0.4878 C.CAD Claw 3
R2 = 0.9771

3.000 ’ '7 i ‘
. q o OuterCurve (BS)

 

2500 I Inner Curve (BS)
g 2.000 —Poly. (Outer Curve (BS))
.5 —Poly. (Inner Curve (BS))
"15’ 1.500 ‘ * “ '“" ’
8
>" 1'000 ‘ _\= = 37506113 + 2.00411 + 2.43.64

0.500 R3 = (1.93119

1
0.000 *-
0.000 0.500 1.000 1.500

X Coordinates

FIGURE 60. Plotted Bookstein coordinates taken from the inner and outer curves of C-CAD claw 3, with
trend lines and matching equations.

129

 

C31011Claw3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
2.960 3.840 1.236 2.446 3.510 3.440 1.586 2.191
2.920 3.820 1.210 2.433 3.510 3.370 1.586 2.146
2.870 3.800 1.178 2.420 3.510 3.330 1.586 2.121
2.820 3.780 1.146 2.408 3.490 3.290 1.573 2.096
2.790 3.750 1.127 2.389 3.480 3.270 1.567 2.083
2.740 3.720 1.096 2.369 3.460 3.230 1.554 2.057
2.700 3.690 1.070 2.350 3.430 3.190 1.535 2.032
2.650 3.670 1.038 2.338 3.410 3.160 1.522 2.013
2.620 3.610 1.019 2.299 3.390 3.110 1.510 1.981
2.610 3.570 1.013 2.274 3.380 3.070 1.503 1.955
2.580 3.530 0.994 2.248 3.350 3.020 1.484 1.924
2.560 3.500 0.981 2.229 3.330 2.960 1.471 1.885
2.520 3.470 0.955 2.210 3.310 2.910 1.459 1.854
2.490 3.430 0.936 2.185 3.280 2.850 1.439 1.815
2.450 3.410 0.911 2.172 3.260 2.800 1.427 1.783
2.400 3.380 0.879 2.153 3.250 2.750 1.420 1.752
2.370 3.340 0.860 2.127 3.230 2.700 1.408 1.720
2.350 3.290 0.847 2.096 3.210 2.640 1.395 1.682
2.310 3.270 0.822 2.083 3.190 2.580 1.382 1.643
2.290 3.230 0.809 2.057 3.180 2.510 1.376 1.599
2.260 3.180 0.790 2.025 3.160 2.430 1.363 1.548
2.220 3.150 0.764 2.006 3.140 2.400 1.350 1.529
2.190 3.090 0.745 1.968 3.110 2.350 1.331 1.497
2.150 3.050 0.720 1.943 3.100 2.300 1.325 1.465
2.1 10 3.010 0.694 1.917 3.070 2.240 1.306 1.427
2.070 2.970 0.669 1.892 3.050 2.180 1.293 1.389
2.040 2.930 0.650 1.866 3.020 2.130 1.274 1.357
2.010 2.880 0.631 1.834 3.000 2.070 1.261 1.318
1.980 2.830 0.61 1 1.803 2.970 2.020 1.242 1.287
1.950 2.790 0.592 1.777 2.930 1.990 1.217 1.268
1.920 2.740 0.573 1.745 2.910 1.940 1.204 1.236
1.900 2.680 0.561 1.707 2.890 1.900 1.191 1.210
1.870 2.650 0.541 1.688 2.860 1.850 1.172 1.178
1.850 2.600 0.529 1.656 2.850 1.820 1.166 1 . 159
1.830 2.560 0.516 1.631 2.830 1.760 1.153 1.121
1.810 2.530 0.503 1.611 2.820 1.710 1.146 1.089
1.790 2.490 0.490 1.586 2.810 1.650 1.140 1.051
1.750 2.440 0.465 1.554 2.790 1.600 1.127 1.019
1.730 2.400 0.452 1.529 2.780 1.540 1.121 0.981
1.710 2.350 0.439 1.497 2.780 1.490 1.121 0.949
1.680 2.320 0.420 1.478 2.770 1.450 1.1 15 0.924
1.660 2.280 0.408 1.452 2.770 1.400 1.1 15 0.892

 

 

 

 

 

 

 

 

130

TABLE 57. Raw and Bookstein coordinates taken from the outer and inner curves of C31011 claw 3.

 

TABLE 57 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.630 2.240 0.389 1.427 2.770 1.370 1.115 0.873
1.610 2.210 0.376 1.408 2.780 1.320 1.121 0.841
1.590 2.170 0.363 1.382 2.800 1.290 1.134 0.822
1.570 2.140 0.350 1.363 2.820 1.240 1.146 0.790
1.540 2.100 0.331 1.338
1.520 2.060 0.318 1.312
1.510 2.020 0.312 1.287
1.480 1.960 0.293 1.248
1.460 1.920 0.280 1.223
1.430 1.870 0.261 1.191
1.410 1.830 0.248 1.166
1.380 1.780 0.229 1.134
1.360 1.740 0.217 1.108
1.350 1.680 0.210 1.070
1.330 1.630 0.197 1.038
1.320 1.580 0.191 1.006
1.310 1.530 0.185 0.975
1.290 1.490 0.172 0.949
1.270 1.450 0.159 0.924
1.260 1.400 0.153 0.892
1.240 1.340 0.140 0.854
1.220 1.290 0.127 0.822
1.200 1.240 0.1 15 0.790
1.180 1.190 0.102 0.758
1.150 1.150 0.083 0.732
1.130 1.1 10 0.070 0.707

 

y = 0.8299113 + 2.5568x + 0.5469 C31011 Claw 3

R2 = 09984 O OUICI'CUI’VE (BS)
3000 l I Inner Curve (BS)
2.500 ~
w ' — Poly. (Outer Curve
0 .
"g 1,500 1 —Poly. (Inner Curve (BS))
0 I
U
>_‘ 1.000 *-
0.500 - y = 41.634111" + 4.311991 — 3.0953
0.000 . R2 = (1.9818
0.000 0.500 1.000 1.500 2.000

X Coordinates

FIGURE 61. Plotted Bookstein coordinates taken from the inner and outer curves of C3101 1 claw 3. with
trend lines and matching equations.

131

 

C3132] Claw 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
2.420 2.950 1.368 3.105 2.530 2.930 1.484 3.084
2.400 2.930 1.347 3.084 2.510 2.880 1.463 3.032
2.370 2.910 1.316 3.063 2.490 2.840 1.442 2.989
2.340 2.890 1.284 3.042 2.470 2.810 1.421 2.958
2.310 2.860 1.253 3.011 2.460 2.780 1.411 2.926
2.270 2.840 1.21 1 2.989 2.440 2.760 1.389 2.905
2.240 2.820 1 . 179 2.968 2.420 2.720 1.368 2.863
2.220 2.800 1.158 2.947 2.410 2.680 1.358 2.821
2.190 2.770 1.126 2.916 2.390 2.660 1.337 2.800
2.170 2.750 1.105 2.895 2.380 2.620 1.326 2.758
2.130 2.720 1.063 2.863 2.360 2.580 1.305 2.716
2.100 2.700 1.032 2.842 2.340 2.560 1.284 2.695
2.070 2.680 1.000 2.821 2.330 2.530 1.274 2.663
2.050 2.650 0.979 2.789 2.310 2.500 1.253 2.632
2.020 2.620 0.947 2.758 2.300 2.470 1.242 2.600
2.000 2.590 0.926 2.726 2.290 2.450 1.232 2.579
1.970 2.560 0.895 2.695 2.270 2.410 1.211 2.537
1.940 2.530 0.863 2.663 2.260 2.370 1.200 2.495
1.910 2.510 0.832 2.642 2.250 2.340 1 . 189 2.463
1.890 2.480 0.811 2.611 2.240 2.310 1.179 2.432
1.860 2.460 0.779 2.589 2.220 2.280 1.158 2.400
1.830 2.430 0.747 2.558 2.200 2.230 1.137 2.347
1.810 2.400 0.726 2.526 2.180 2.200 1.116 2.316
1.800 2.360 0.716 2.484 2.170 2.160 1.105 2.274
1.780 2.320 0.695 2.442 2.160 2.120 1.095 2.232
1.780 2.280 0.695 2.400 2.140 2.080 1.074 2.189
1.750 2.250 0.663 2.368 2.130 2.050 1.063 2.158
1.740 2.220 0.653 2.337 2.120 2.020 1.053 2.126
1.720 2.180 0.632 2.295 2.1 10 1.990 1.042 2.095
1.700 2.140 0.611 2.253 2.100 1.940 1.032 2.042
1.670 2.100 0.579 2.211 2.080 1.900 1.011 2.000
1.650 2.050 0.558 2.158 2.070 1.860 1.000 1.958
1.620 2.020 0.526 2.126 2.050 1.810 0.979 1.905
1.590 1.990 0.495 2.095 2.040 1.770 0.968 1.863
1.560 1.960 0.463 2.063 2.030 1.730 0.958 1.821
1.530 1.920 0.432 2.021 2.010 1.690 0.937 1.779
1.500 1.890 0.400 1.989 2.000 1.650 0.926 1.737
1.480 1.850 0.379 1.947 1.990 1.610 0.916 1.695
1.450 1.790 0.347 1.884 1.980 1.560 0.905 1.642
1.420 1.760 0.316 1.853 1.980 1.520 0.905 1.600
1.400 1.720 0.295 1.81 1 1.960 1.480 0.884 1.558
1.380 1.680 0.274 1.768 1.940 1.440 0.863 1.516

 

 

 

 

 

 

 

 

132

TABLE 58. Raw and Bookstein coordinates taken from the outer and inner curves of C31 321 claw 1.

 

TABLE 58 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.360 1.660 0.253 1.747 1.940 1.410 0.863 1.484
1.340 1.620 0.232 1.705 1.940 1.380 0.863 1.453
1.310 1.600 0.200 1.684 1.920 1.340 0.842 1.41 1
1.280 1.570 0.168 1.653 1.910 1.300 0.832 1.368
1.260 1.540 0.147 1.621 1.890 1.270 0.811 1.337
1.230 1.510 0.116 1.589 1.890 1.220 0.811 1.284
1.220 1.480 0.105 1.558 1.880 1 . 190 0.800 1.253
1.200 1.440 0.084 1.516 1.890 1.160 0.811 1.221
1.170 1.390 0.053 1.463 1.890 1.130 0.811 1.189
1.160 1.340 0.042 1.411 1.900 1.100 0.821 1.158
1.140 1.300 0.021 1.368 1.890 1.060 0.811 1.116
1.110 1.260 -0.011 1.326 1.910 1.000 0.832 1.053
1.080 1.220 -0.042 1.284 1.920 0.960 0.842 1.01 1
1.050 1 . 190 -0.074 1.253 1.920 0.930 0.842 0.979
1.030 1 . 150 -0.095 1.21 1 1.940 0.890 0.863 0.937
1.020 1.1 10 -0.105 1 . 168 1.960 0.860 0.884 0.905
1.000 1.070 -0.126 1.126 2.120 0.530 1.053 0.558
0.970 1.030 -0.158 1.084 2.150 0.490 1.084 0.516
0.970 1.000 -0.158 1.053 2.170 0.460 1.105 0.484
0.940 0.950 -0. 189 1.000 2.190 0.430 1.126 0.453
0.930 0.900 -0.200 0.947 2.210 0.400 1.147 0.421
0.930 '0.870 -0.200 0.916
0.910 0.820 -0.221 0.863
0.910 0.770 -0.221 0.811
0.910 0.710 -0.221 0.747
0.910 0.660 -0.221 0.695
0.910 0.610 -0.221 0.642
0.920 0.570 -0.21 1 0.600
0.930 0.530 -0.200 0.558
0.930 0.480 -0.200 0.505
0.950 0.440 -0. 179 0.463
0.960 0.380 -0. 168 0.400
0.980 0.340 -0.147 0.358
0.990 0.300 -0.137 0.316
1.000 0.260 -0.126 0.274
1.020 0.220 -0.105 0.232
1.040 0.180 -0.084 0.189

 

133

 

y = 06693113 + 2.303311 + 1.1758 C31321 Claw 1

R2 = 0.9459
3.500 *
3.000 . 0 Outer Curve (BS)
0:3 2.500 , I Inner Curve (BS)
E 2 000 —Poly. (Outer Curve (BS))
‘5 ' I
15 —Poly. (Inner Curve (BS))
0 1.500 1 ‘ ' A ‘7 "
U
>‘ 1-000 3 = 1.6183“: — (1.717711 + (1.7531
0.500 1 \ 123:0.6072
0.000 - 1 ~ ' 7-. 7

-0.500 0.000 0.500

X Coordinates

1.000 1.500 2.000

FIGURE 62. Plotted Bookstein coordinates taken from the inner and outer curves of C3 1 321 claw 1, with
trend lines and matching equations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C3132] Claw 3

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
1.060 2.850 0.282 3.654 1.270 2.790 0.551 3.577
1.020 2.810 0.231 3.603 1.280 2.750 0.564 3.526
1.010 2.770 0.218 3.551 1.270 2.710 0.551 3.474
0.990 2.730 0.192 3.500 1.270 2.670 0.551 3.423
0.980 2.680 0.179 3.436 1.270 2.620 0.551 3.359
0.970 2.630 0.167 3.372 1.260 2.560 0.538 3.282
0.960 2.590 0.154 3.321 1.270 2.500 0.551 3.205
0.970 2.540 0.167 3.256 1.260 2.420 0.538 3.103
0.950 2.500 0.141 3.205 1.250 2.370 0.526 3.038
0.940 2.450 0.128 3.141 1.250 2.320 0.526 2.974
0.940 2.390 0.128 3.064 1.250 2.270 0.526 2.910
0.920 2.360 0.103 3.026 1.240 2.230 0.513 2.859
0.910 2.310 0.090 2.962 1.240 2.190 0.513 2.808
0.900 2.270 0.077 2.910 1.230 2.140 0.500 2.744
0.880 2.230 0.051 2.859 1.230 2.090 0.500 2.679
0.870 2.190 0.038 2.808 1.230 2.060 0.500 2.641
0.850 2.130 0.013 2.731 1.230 2.000 0.500 2.564
0.850 2.090 0.013 2.679 1.240 1.940 0.513 2.487
0.840 2.040 0.000 2.615 1.250 1.880 0.526 2.410
0.840 1.990 0.000 2.551 1.250 1.830 0.526 2.346
0.830 1.950 -0.013 2.500 1.260 1.790 0.538 2.295
0.830 1.910 -0.013 2.449 1.270 1.750 0.551 2.244

 

 

134

TABLE 59. Raw and Bookstein coordinates taken from the outer and inner curves of C31 321 claw 3.

TABLE 59 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.820 1.860 -0.026 2.385 1.270 1.700 0.551 2.179
0.800 1.830 -0.051 2.346 1.280 1.650 0.564 2.1 15
0.780 1.790 -0.077 2.295 1.280 1.610 0.564 2.064
0.770 1.750 -0.090 2.244 1.270 1.570 0.551 2.013
0.760 1.710 -0.103 2.192 1.270 1.530 0.551 1.962
0.750 1.670 -0.1 15 2.141 1.260 1.480 0.538 1.897
0.740 1.630 -0.128 2.090 1.270 1.450 0.551 1.859
0.720 1.570 -0.154 2.013 1.260 1.400 0.538 1.795
0.710 1.510 -0.167 1.936 1.260 1.350 0.538 1.731
0.700 1.460 -0. 179 1.872 1.260 1.320 0.538 1.692
0.690 1.420 -0. 192 1.821 1.260 1.270 0.538 1.628
0.690 1.350 -0. 192 1.731 1.270 1.230 0.551 1.577
0.680 1.290 -0.205 1.654 1.290 1.180 0.577 1.513
0.680 1.250 -0.205 1.603 1.310 1 . 120 0.603 1.436
0.680 1.210 -0.205 1.55] 1.320 1.080 0.615 1.385
0.670 1 . 170 -0.218 1.500 1.330 1.030 0.628 1.32]
0.650 1 . 150 —0.244 1.474 1.350 1.000 0.654 1.282
0.640 1.1 10 -0.256 1.423 1.370 0.960 0.679 1.231
0.620 1.060 -0.282 1.359 1.390 0.920 0.705 1.179
0.600 1.020 -0.308 1.308 1.410 0.880 0.731 1.128
0.590 0.970 -0.321 1.244 1.440 0.840 0.769 1.077
0.590 0.930 -0.321 1.192 1.450 0.790 0.782 1.013
0.610 0.870 -0.295 1.1 15 1.470 0.760 0.808 0.974
0.630 0.820 -0.269 1.051 1.490 0.730 0.833 0.936
0.640 0.770 -0.256 0.987 1.510 0.680 0.859 0.872
0.640 0.720 -0.256 0.923 1.520 0.640 0.872 0.821
0.670 0.660 -0.218 0.846 1.530 0.590 0.885 0.756
0.680 0.600 -0.205 0.769 1.530 0.550 0.885 0.705
0.700 0.540 -0. 179 0.692 1.530 0.510 0.885 0.654
0.700 0.490 -0.179 0.628 1.540 0.470 0.897 0.603
0.700 0.440 -0. 179 0.564 1.560 0.420 0.923 0.538
0.710 0.380 -0.167 0.487 1.560 0.380 0.923 0.487
0.730 0.330 -0.141 0.423 1.560 0.350 0.923 0.449
0.750 0.290 -0.1 15 0.372 1.570 0.310 0.936 0.397
0.770 0.250 -0.090 0.321 1.580 0.270 0.949 0.346

1.600 0.230 0.974 0.295

1.620 0.180 1.000 0.231

1.640 0.130 1.026 0.167

 

 

 

 

 

135

 

y = 3.3709112 + 5.436111 + 2.3259 (331321 Claw 3

R3=07629
4.500
:233 .4. Outer Curve—(BS)
8 ‘3'000 I Inner Curve (BS)
2 ' ‘_Poly. (Outer Curve (BS))
{5. 2.500 1 P1 In C BS
8 2.000 ~ -- _°.Y-( film“ )1,
if 1.500 « 3
1,000 - )1: 7.7248x‘ - 16.428x + 9.0653
0500 4 ' R3 = 0.7547
0.000 - ‘ 74* ~ : ~ +-~
-0.500 0.000 0.500 1.000 1.500

X Coordinates

FIGURE 63. Plotted Bookstein coordinates taken from the inner and outer curves of C3132] claw 3, with
trend lines and matching equations.

136

APPENDIX V

LIST OF PAIRS OF CORRELATED VARIABLES

 

Positively Correlated Variable Pairs

 

centroid X coordinate

EBookstein L3 X coordinate

 

beta

{Bookstein L3 X coordinate

 

centroid Y coordinate

:Bookstein L3 Y coordinate

 

centroid size

EBookstein L3 Y coordinate

 

distance from L2 to L3

gBookstein L3 Y coordinate

 

distance from L1 to L3

:Bookstein L3 Y coordinate

 

distance from L3 to L4

 

EBookstein L3 Y coordinate

 

[alpha

iBookstein L3 Y coordinate

 

[alpha/beta ratio

EBookstein L3 Y coordinate

 

outer curve C coefficient

EBookstein L3 Y coordinate

 

distance from L1 to L4

iBookstein L4 X coordinate

 

centroid X coordinate

Ebeta

 

centroid Y coordinate

{centroid size

 

distance from L2 to L3

Ecentroid Y coordinate

 

distance from L1 to L3

Scentroid Y coordinate

 

distance from L3 to L4

zcentroid Y coordinate

A

 

centroid Y coordinate

{algha

 

centroid Y coordinate

Ealpha/beta ratio

 

centroid Y coordinate

iouter curve B coefficient

 

centroid Y coordinate

:outer curve C coefficient

 

distance from L2 to L3

 

distance from L1 to L3

Ecentroid Size
Ecentroid Size

 

distance from L3 to L4

 

Ecentroid Size

 

 

Ialpha Ecentroid Size
afipha/beta ratio icentroid Size

 

outer curve C coefficient

Ecentroid Size

 

distance from L1 to L3

Edistance from L2 to L3

 

distance from L3 to L4

idistance from L2 to L3

 

 

[alpha

 

alpha/beta ratio

1distance from L2 to L3
Edistance from L2 to L3

 

outer curve C coefficient

idistance from L2 to L3

 

distance from L1 to L3

idistance from L3 to L4

 

outer curve C coefficient

idistance from L1 to L3

 

 

Ialpha
Ialpha/beta ratio

Edistance from L3 to L4
Edistance from L3 to L4

 

outer curve C coefficient

Edistance from L3 to L4

 

 

alpha/beta ratio

idistance from L1 to L4

TABLE 60. List of pairs of positively correlated morphometric variables.

137

 

TABLE 60 (cont’d)

 

 

 

alpha/beta ratio {alpha
outer curve C coefficient Ealpha
aspect ratio Ebeta

 

outer curve coefficient A

:outer curve coefficient B

 

outer curve coefficient C

:outer curve coefficient B

 

 

inner curve coefficient A

Einner curve coefficient C

 

 

Negatively Correlated Variable Pairs

 

 

 

 

Bookstein L3 X coordinate Ealpha
Bookstein L3 X coordinate Ealpha/beta ratio
Bookstein L3 Y coordinate Ebeta

Bookstein L3 Y coordinate Egamma

 

Bookstein L3 Y coordinate

Easpect ratio

 

Bookstein L4 X coordinate

Edistance from L2 to L4

 

Bookstein L4 Y coordinate

Edistance from L1 to L4

 

Bookstein L4 Y coordinate

Tdistance from L2 to L4

 

centroid X coordinate

Ealpha

 

 

 

centroid X coordinate Ealpha/beta ratio
centroid Y coordinate fieta
centroid Y coordinate Egamma

 

centroid Y coordinate

:aspect ratio

 

centroid size

igamma

 

centroid size

Easpect ratio

 

distance from L2 to L3

Ebeta

 

distance from L2 to L3

{gamma

 

distance from L2 to L3

gaspect ratio

 

distance from L1 to L3

:gamma

 

distance from L1 to L3

faspect ratio

 

distance from L3 to L4

:gamma

 

distance from L3 to L4

Easpect ratio

 

 

 

 

 

[alpha ibeta
lalpha gaspect ratio
beta Ealpha/beta ratio
amma iouter curve C coefficient

 

 

aspect ratio

Ealpha/beta ratio

 

laspect ratio

:outer curve C coefficient

 

inner curve coefficient A

Einner curve coefficient B

 

 

inner curve coefficient B

:inner curve coefficient C

 

TABLE 61. List of pairs of negatively correlated morphometric variables.

138

 

 

APPENDD( VI

PRINCIPAL COMPONENT DATA WITHIN EACH CLUSTER OF EACH CLAW
PHENOGRAM

Claw 1
l
A B C
0.332 0.332 0.067
Component 1.519 1.519 -0
-1.871

'pal Component

0.]
0.3

A B E

1.024 1.02 - . . -0.

Component 1.01 1.01 . - . -0.
1. - . -1.1

-0.1

 

TABLE 62. Principal component data within each cluster in the phenogram of claw 1.

139

Claw 2
l
A B C D
-0.37 0.948 ~0.37 0.591
-0.8. -1.473 -0.8- -0.61 1

pa] Component 0.948
-1.473

A B E F
-0.34 -1.622 1.- 1.

-O.56l -0.305 1.11 1.11
ipal Component 0.

A B
-0.082 -1.02
-0.233 -0.
ipal Component

'ncipal Component

5
D E P
0.217 01 -0.1 -1.63
0.731 0.082 0.08 -1.463
'ncipal Component 0.01 0.705
1.44
0.21
0.731

 

TABLE 63. Principal component data within each cluster in the phenogram of claw 2.

140

Claw3
l

A B C D E F I .1

1.11 1.11 -0.99. 1.11 0.01 1.01 . -2.002 1.01
1.3 —0.8 0.21 -0. -0.32 0.01 . 0. 0.019
'ncipal 1.3 1. 0.328 0.418 -0.328
mponent -0.993 -0.553 -2.002
0.21 0.
0.418
-0.553

A B G H
-O.381 -0.381 .. 4.103 0.973
0.26 0.298 . .- -2.24 -0.33

'ncipal 0.267
mponent

A B G H

1.163 1.16. -0.43 -0.57

0.603 2.4 . -0 -0.565
0.603

G H
-0. -1.381
-0.41 -1.24

 

-0.

TABLE 64. Principal component data within each cluster in the phenogram of claw 3.

141

TABLE 64 (cont’d)

5
A B C D E F G H I
-0.2- -0.2. 0.547 -O -0.615 -1.41 -0.745 2.013 -0.745
0.743 -0.318 0.705 -0.31 -1.318 -0.615 -0.21 0.8 -0.21

0.743 0.74- -1.318 2.013
0.54 0.
0.

 

Claw 4

ipal Component

USICI’

'ncipal Component

USICI‘

Principal Component

uster
'ncipal Component

-0.

5
er B C D
-0.71 0.261 1.93 1.93
0.04 0.21 1 0.3 0.-
-1.3 -0.7

'ncipal Component

 

TABLE 65. Principal component data within each cluster in the phenogram of claw 4.

142

APPENDIX VH

 

 

 

 

 

 

 

UNKNOWN ARTICULATION
Specimen Pes Claw Centrond Location Centroid
X Y Size
KU49399 Unknown UNKl 0.396 1.167 3.994
Unknown UNK2 0.733 1.308 4.435
YPM2554 Unknown UNK3 0.558 0.74 2.842
YPM2436 Unknown UNK4 0.718 0.343 1.665

 

 

 

 

 

 

 

MORPHOMETRIC DATA FOR THE FOUR PTERANODONT CLAWS OF

TABLE 66. Claw centroid locations and sizes of the four claws of unknown articulations.

 

 

 

 

 

 

 

. Distances between Landmarks (Bookstein)
Specimen Pes Claw
L1-L2 L2-L3 Ll-L3 L3-L4 Ll-L4 L2-L4
KU49399 Unknown UNK] 1 4.647 4.556 4.464 0.512 0.512
Unknown UNK2 1 5.059 5.224 4.921 0.61 0.458
YPM2554 Unknown UNK3 1 3.127 3.2 3.277 0.523 0.523
YPM2436 Unknown UNK4 1 1.525 2.003 1.795 0.541 0.485

 

 

 

 

 

 

 

 

 

 

 

TABLE 67. Distances between the Bookstein landmarks of each claw of unknown articulation.

 

 

 

 

 

 

 

. An os(degrees)
Specimen Pes Claw
a B v
KU49399 Unknown UNK] 88.952 78.623 12.425
Unknown UNK2 75.036 93.954 1 1.01
YPM2554 Unknown UNK3 76.799 85.061 18.14
YPM2436 Unknown UNK4 47.891 102.995 29.114

 

 

 

 

 

 

 

TABLE 68. Angle calculations (in degrees) between Bookstein landmarks 1, 2, and 3 of each claw of
unknown articulation.

 

 

 

 

 

 

 

Specimen Pes Claw Aspect Ratio Ratio of a to B
KU49399 Unknown UNK] 0.22 1.131

Unknown UNK2 0.198 0.799
YPM2554 Unknown UNK3 0.321 0.903
YPM2436 Unknown UN K4 0.673 0.465

 

 

 

 

 

143

TABLE 69. Aspect ratios and ratios of a to B of each claw with unknown articulation.

 

Curvature Equation Coefficients

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Curve Inner Curve
Specimen Pes Claw x2 X X0 R2 x2 x x0 R2

Coeff. Coeff. Coeff. Value Coeff. Coeff. Coeff. Value

(A) (B) (C) (A) (B) (C)
KU49399 Unknown UNK] 24.814 20.535 5.804 0.51 2.215 —5.851 4.716 0.829
Unknown UNK2 -0.931 2.908 2.876 0.928“ -8.348 19.477 -6.933 0.521
YPM2554 Unknown UNK3 -2.771 4.188 1.492 0.991' -0.501 —3.169 5.12 0.884
YPM2436 Unknown UNK4 -0.48 1.54 0.325 0.998“ -2.888 9.447 -6.254 0.598

 

TABLE 70. Coefficients from polynomial (Y = AX2+BX+CXO) equations of outside and inside curves of
the four claws with unknown articulations (with their R2 values), derived from Bookstein coordinates.

144

 

 

TABLE 71. Raw and Bookstein coordinates taken from the outer and inner curves of KU49399, unknown

claw 1.

 

KU49399 UNKl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
1 . 190 1.590 -0.028 4.417 1.270 1.600 0.194 4.444
1.170 1.570 -0.083 4.361 1.270 1.560 0.194 4.333
1.160 1.530 -0.1 1 1 4.250 1.290 1.520 0.250 4.222
1.160 1.490 -0.1 1 1 4.139 1.290 1.500 0.250 4.167
1 . 160 1.450 -0.1 1 1 4.028 1.290 1.450 0.250 4.028
1 . 160 1.420 -0.1 1 1 3.944 1.300 1.400 0.278 3.889
1.150 1.400 -0.139 3.889 1.300 1.330 0.278 3.694
1.140 1.350 -0.167 3.750 1.310 1.280 0.306 3.556
1.130 1.310 -0.194 3.639 1.310 1.220 0.306 3.389
1.120 1.270 -0.222 3.528 1.290 1.140 0.250 3.167
1.120 1.230 -0.222 3.417 1.290 1.090 0.250 3.028
1.1 10 1.190 -0.250 3.306 1.290 1.070 0.250 2.972
1.110 1.150 -0.250 3.194 1.300 1.030 0.278 2.861
1.110 1.110 -0.250 3.083 1.290 1.010 0.250 2.806
1 . 100 1.060 -0.278 2.944 1.290 0.940 0.250 2.611
1 . 100 1.020 -0.278 2.833 1.300 0.910 0.278 2.528
1 . 100 0.980 -0.278 2.722 1.310 0.860 0.306 2.389
1.100 0.930 -0.278 2.583 1.330 0.820 0.361 2.278
1.100 0.900 -0.278 2.500 1.350 0.780 0.417 2.167
1 . 100 0.850 -0.278 2.361 1.360 0.750 0.444 2.083
1.080 0.810 -0.333 2.250 1.380 0.720 0.500 2.000
1.070 0.770 -0.361 2.139 1.400 0.690 0.556 1.917
1.060 0.730 -0.389 2.028 1.430 0.660 0.639 1.833
1.060 0.700 -0.389 1.944 1.460 0.630 0.722 1.750
1.060 0.660 -0.389 1.833 1.480 0.600 0.778 1.667
1.060 0.610 -0.389 1.694 1.520 0.560 0.889 1.556
1.070 0.570 -0.361 1.583 1.570 0.510 1.028 1.417
1.090 0.530 -0.306 1.472 1.610 0.480 1.139 1.333
1.080 0.500 -0.333 1.389 1.640 0.440 1.222 1.222
1.070 0.470 -0.361 1.306 1.660 0.390 1.278 1.083
1.080 0.430 -0.333 1.194 1.680 0.340 1.333 0.944
1.080 0.390 -0.333 1.083 1.700 0.300 1.389 0.833
1.1 10 0.350 -0.250 0.972 1.710 0.250 1.417 0.694
1 . 120 0.320 -0.222 0.889 1.720 0.200 1.444 0.556
1.110 0.270 -0.250 0.750 1.700 0.150 1.389 0.417
1 . 100 0.230 -0.278 0.639
1.1 10 0.190 -0.250 0.528
1.120 0.150 -0.222 0.417

 

 

 

 

 

145

 

 

 

y = 24.814112 + 20.35311 + 5.8039 KU49399 UNK1
R2 = 0.5101
6.000 -- ,-
O

5.000 _ Outer Curve (BS)
m I Inner Curve (BS)
13 4.000 7 —Poly. (Outer Curve (BS))
1:
E 3000 , —Poly. (Inger Curve (BS))
13
> 2.000 1. -

1 I y = 2.2148\" - 5.851.15x + 4.7156
1.000 ~ ( R“ = 0.8294
0.000 4 ~ ~
-1 .000 0.000 1.000 2.000

X Coordinates

FIGURE 64. Plotted Bookstein coordinates taken from the inner and outer curves of KU49399 unknown
claw 1, with trend lines and matching equations.

 

 

TABLE 72. Raw and Bookstein coordinates taken from the outer and inner curves of KU49399, unknown

claw 2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

KU49399 UNK2

Outer Raw Outer Bookstein Inner Raw Inner Bookstein

X Y X Y X Y X Y
0.970 2.140 1.047 4.977 1 . 190 2.080 1.558 4.837
0.940 2.1 10 0.977 4.907 1.200 2.030 1.581 4.721
0.920 2.080 0.930 4.837 1.200 1.990 1.581 4.628
0.900 2.050 0.884 4.767 1.200 1.910 1.581 4.442
0.890 2.020 0.860 4.698 1 . 180 1.880 1.535 4.372
0.870 1.990 0.814 4.628 1 . 180 1.850 1.535 4.302
0.870 1.960 0.814 4.558 1.170 1.810 1.512 4.209
0.850 1.940 0.767 4.512 1.180 1.770 1.535 4.1 16
0.830 1.900 0.721 4.419 1.180 1.730 1.535 4.023
0.810 1.880 0.674 4.372 1.180 1.710 1.535 3.977
0.790 1.850 0.628 4.302 1.170 1.680 1.512 3.907
0.790 1.830 0.628 4.256 1.150 1.650 1.465 3.837
0.760 1.790 0.558 4.163 1 . 140 1.620 1.442 3.767
0.740 1.750 0.512 4.070 1 . 140 1.580 1.442 3.674
0.720 1.730 0.465 4.023 1 . 150 1.540 1.465 3.581
0.710 1.690 0.442 3.930 1 . 160 1.500 1.488 3.488
0.700 1.670 0.419 3.884 1.170 1.460 1.512 3.395
0.680 1.630 0.372 3.791 1.180 1.420 1.535 3.302
0.660 1.590 0.326 3.698 1.180 1.380 1.535 3.209
0.650 1.540 0.302 3.581 1.170 1.350 1.512 3.140
0.630 1.510 0.256 3.512 1.170 1.310 1.512 3.047

 

 

 

 

 

 

 

 

146

 

TABLE 72 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

147

0.610 1.480 0.209 3.442 1.170 1.280 1.512 2.977
0.600 1.450 0.186 3.372 1.170 1.250 1.512 2.907
0.580 1.410 0.140 3.279 1.180 1.210 1.535 2.814
0.570 1.360 0.116 3.163 1.180 1.180 1.535 2.744
0.550 1.320 0.070 3.070 1.180 1.140 1.535 2.651
0.520 1.290 0.000 3.000 1.190 1.100 1.558 2.558
0.490 1.250 -0.070 2.907 1.190 1.060 1.558 2.465
0.480 1.210 -0.093 2.814 1.180 1.020 1.535 2.372
0.470 1.170 -0.116 2.721 1.180 0.980 1.535 2.279
0.450 1.120 -0.163 2.605 1.190 0.950 1.558 2.209
0.440 1.080 -0.186 2.512 1.190 0.910 1.558 2.116
0.430 1.040 -0.209 2.419 1.190 0.860 1.558 2.000
0.420 1.000 -0.233 2.326 1.210 0.830 1.605 1.930
0.400 0.940 -0.279 2.186 1.230 0.790 1.651 1.837
0.390 0.920 -0.302 2.140 1.240 0.740 1.674 1.721
0.370 0.880 -0.349 2.047 1.260 0.700 1.721 1.628
0.360 0.840 —0.372 1.953 1.270 0.650 1.744 1.512
0.340 0.800 -0.419 1.860 1.270 0.610 1.744 1.419
0.320 0.760 -0.465 1.767 1.290 0.560 I .791 1.302
0.310 0.710 -0.488 1.65] 1.300 0.500 1.814 1.163
0.280 0.670 -0.558 1.558 1.300 0.460 1.814 1.070
0.270 0.610 -0.581 1.419 1.300 0.410 1.814 0.953
0.270 0.560 -0.581 1.302
0.270 0.520 -0.58] 1.209
0.270 0.470 -0.581 1.093
0.260 0.410 -0.605 0.953
0.270 0.370 -0.581 0.860
0.270 0.310 -0.581 0.721
0.280 0.260 -0.558 0.605
0.280 0.210 -0.558 0.488
0.300 0.160 -0.512 0.372
0.320 0.120 -0.465 0.279
0.330 0.070 -0.442 0. 163
0.360 0.030 —0.372 0.070

 

y = 09306112 + 2.907811 + 2.8755 KU49399 UNK2

 

R2 = 0.9283
6.000
5-000 0 Outer Curve (BS)
g 4.000 . I Inner Curve (BS)
.5 —Poly. (Outer Curve (BS))
‘3 3000 .
8 ' —P0'Y- (InnsrCurve<BS>>
if 2.000 - .
v = -8.3481.\" + 19.477\ - (1.9331
1.000 . ' w -
R" = (1.5212
0.000 1 - ~ ~ ~ -
-1.000 0.000 1.000 2.000

X Coordinates

FIGURE 65. Plotted Bookstein coordinates taken from the inner and outer curves of KU49399 unknown
claw 2, with trend lines and matching equations.

148

TABLE 73. Raw and Bookstein coordinates taken from the outer and inner curves of YPM2554, unknown

claw 3.

 

YPM2554 UNK3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
1.010 1.590 0.577 3.058 1 . 100 1.580 0.750 3.038
0.990 1.570 0.538 3.019 1.1 10 1.540 0.769 2.962
0.980 1.530 0.519 2.942 1.110 1.500 0.769 2.885
0.960 1.510 0.481 2.904 1.1 10 1.470 0.769 2.827
0.960 1.480 0.481 2.846 1.1 10 1.430 0.769 2.750
0.950 1.450 0.462 2.788 1.100 1.380 0.750 2.654
0.950 1.420 0.462 2.731 1 . 100 1.340 0.750 2.577
0.930 1.400 0.423 2.692 1.090 1.290 0.73 ‘1 2.481
0.900 1.370 0.365 2.635 1.090 1.250 0.731 2.404
0.880 1.330 0.327 2.558 1.070 1.210 0.692 2.327
0.870 1.290 0.308 2.481 1.080 1 . 170 0.712 2.250
0.850 1.250 0.269 2.404 1.090 1 . 130 0.731 2.173
0.830 1.220 0.231 2.346 1.1 10 1.090 0.769 2.096
0.830 1.170 0.231 2.250 1 . 120 1.050 0.788 2.019
0.810 1.140 0.192 2.192 1.140 1.020 0.827 1.962
0.790 1.110 0.154 2.135 1.150 1.000 0.846 1.923
0.780 1.080 0.135 2.077 1.150 0.960 0.846 1.846
0.770 1.050 0.1 15 2.019 1 . 160 0.930 0.865 1.788
0.770 1.020 0.1 15 1.962 1 . 170 0.900 0.885 1.731
0.770 0.990 0.1 15 1.904 1.190 0.860 0.923 1.654
0.760 0.950 0.096 1.827 1.200 0.830 0.942 1.596
0.760 0.910 0.096 1.750 1.220 0.800 0.981 1.538
0.740 0.860 0.058 1.654 1.230 0.770 1.000 1.481
0.720 0.830 0.019 1.596 1.240 0.740 1.019 1.423
0.710 0.800 0.000 1.538 1.260 0.700 1.058 1.346
0.690 0.770 -0.038 1.481 1.270 0.670 1.077 1.288
0.700 0.720 -0.019 1.385 1.280 0.640 1.096 1.231
0.680 0.680 -0.058 1.308 1.280 0.600 1.096 1.154
0.660 0.640 -0.096 1.231 1.280 0.550 1.096 1.058
0.660 0.610 -0.096 1 . 173 1.270 0.510 1.077 0.981
0.650 0.570 -0.1 15 1.096 1.290 0.460 1.1 15 0.885
0.660 0.530 -0.096 1.019 1.300 0.440 1.135 0.846
0.650 0.480 -0.1 15 0.923 1.320 0.410 1 . 173 0.788
0.640 0.430 -0. 135 0.827 1.330 0.380 1.192 0.731
0.640 0.380 -0.135 0.731 1.330 0.340 1.192 0.654
0.630 0.340 -0.154 0.654 1.330 0.300 1.192 0.577
0.620 0.290 -0.173 0.558 1.310 0.250 1.154 0.481
0.600 0.260 -0.212 0.500
0.590 0.210 -0.231 0.404

 

 

 

149

 

y = 2.7714112 + 4.187611 + 1.492 YPM2554 UNK3

R2 = 0.9906

3.500

3.000 6 Outer Curve (BS)
33 2.500 I Inner Curve (BS)
2 2 000 . —Poly. (Outer Curve (BS))
-o .
8 1. 500 g—Poly. (Inner Cuere (BS))
U
>‘ 1.000 ,

\-' : -().5(1(,)9.\‘ - 3.16888 + 5.1 195
0.500 . ’ 1 .
R' = (1.8838
0.000 ~ - + ., - , *—-

-0.500 0.000 0.500 1.000 1.500

X Coordinates

FIGURE 66. Plotted Bookstein coordinates taken from the inner and outer curves of YPM2554 unknown
claw 3, with trend lines and matching equations.

150

TABLE 74. Raw and Bookstein coordinates taken from the outer and inner curves of YPM2436, unknown

claw 4.

 

YPM2436 UNK4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Outer Raw Outer Bookstein Inner Raw Inner Bookstein
X Y X Y X Y X Y
2.190 2.100 1.279 1.500 2.360 1.790 1.400 1.279
2.160 2.100 1.257 1.500 2.340 1.740 1.386 1.243
2.120 2.100 1.229 1.500 2.320 1.720 1.371 1.229
2.080 2.1 10 1.200 1.507 2.280 1.690 1.343 1.207
2.040 2.100 1.171 1.500 2.240 1.660 1.314 1.186
2.010 2.070 1.150 1.479 2.220 1.620 1.300 1.157
1.980 2.060 1.129 1.471 2.190 1.590 1.279 1.136
1.960 2.030 1.114 1.450 2.150 1.560 1.250 1.114
1.920 2.030 1.086 1.450 2.120 1.530 1.229 1.093
1.900 1.980 1.071 1.414 2.090 1.510 1.207 1.079
1.860 1.960 1.043 1.400 2.060 1 .470 1 .186 1.050
1.830 1.940 1.021 1.386 2.030 1.440 1.164 1.029
1.810 1.930 1.007 1.379 2.020 1.420 1.157 1.014
1.760 1.920 0.971 1.371 1.990 1.380 1.136 0.986
1.720 1.910 0.943 1.364 1.970 1.330 1.121 0.950
1.700 1.890 0.929 1.350 1.960 1.270 1.1 14 0.907
1.670 1.840 0.907 1.314 1.960 1.200 1.1 14 0.857
1.650 1.820 0.893 1.300 1.920 1 . 150 1.086 0.821
1.630 1.790 0.879 1.279 1.910 1.090 1.079 0.779
1.590 1.760 0.850 1.257 1.890 1.020 1.064 0.729
1.560 1.740 0.829 1.243 1.860 0.960 1.043 0.686
1.530 1.710 0.807 1.221 1.860 0.870 1.043 0.621
1.490 1.700 0.779 1.214 1.840 0.810 1.029 0.579
1.470 1.670 0.764 1.193 1.860 0.750 1.043 0.536
1.450 1.660 0.750 1.186 1.880 0.700 1.057 0.500
1.420 1.640 0.729 1.171 1.890 0.650 1.064 0.464
1.390 1.620 0.707 1 . 157 1.890 0.600 1.064 0.429
1.350 1.590 0.679 1 . 136 1.880 0.560 1.057 0.400
1.320 1.570 0.657 1.121 1.880 0.520 1.057 0.371
1.300 1.540 0.643 1 . 100 1.910 0.480 1.079 0.343
1.270 1.520 0.621 1.086 1.940 0.430 1 . 100 0.307
1.250 1.510 0.607 1.079 1.950 0.380 1.107 0.271
1.220 1.510 0.586 1.079 1.950 0.320 1.107 0.229
1 . 190 1.480 0.564 1.057 1.970 0.260 1.121 0.186
1 . 160 1.460 0.543 1.043 1.980 0.220 1.129 0.157
1 . 140 1.440 0.529 1.029
1.120 1.420 0.514 1.014
1.090 1.390 0.493 0.993
1.080 1.360 0.486 0.971
1.050 1.350 0.464 0.964

 

 

 

 

 

151

 

TABLE 74 (cont’d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.020 1.320 0.443 0.943
1.000 1.290 0.429 0.921
0.980 1.260 0.414 0.900
0.960 1.230 0.400 0.879
0.950 1.210 0.393 0.864
0.920 1.180 0.371 0.843
0.900 1.150 0.357 0.821
0.890 ] . 120 0.350 0.800
0.830 1 . 100 0.307 0.786
0.820 1.070 0.300 0.764
0.790 1.040 0.279 0.743
0.780 1.000 0.271 0.714
0.770 0.960 0.264 0.686
0.720 0.910 0.229 0.650
0.710 0.880 0.221 0.629
0.690 0.860 0.207 0.614
0.660 0.830 0.186 0.593
0.640 0.790 0.171 0.564
0.620 0.770 0.157 0.550
0.610 0.740 0.150 0.529
0.590 0.710 0.136 0.507
0.570 0.690 0.121 0.493
0.540 0.650 0.100 0.464
0.530 0.610 0.093 0.436
0.510 0.590 0.079 0.421
0.480 0.570 0.057 0.407
0.450 0.540 0.036 0.386
0.430 0.500 0.021 0.357
0.400 0.470 0.000 0.336
0.370 0.410 -0.021 0.293

 

 

152

y = 04799113 + 1.539911 + 0.325 YPM2436 UNK4

 

R2 = 0.9976
1.600 1
1.400 1
3 1.200 0 Outer Curve(BS)
g 1.000 1‘ I Inner Curve (BS)
:2 0.800 !—Poly. (Inner Curve (BS))
8 0.600 . —Poly. (Outer Cu:ve (BS)) ‘
>‘ 0.400 4 1 -
\r‘ = —2.887‘)\~ + 9.4473); - 6.2537
0.200 - ' 1
R” = (1.5976
0.000 . - < - f
0.000 0.500 1.000 1.500

X Coordinates

FIGURE 67. Plotted Bookstein coordinates taken from the inner and outer curves of YPM2436 unknown
claw 4, with trend lines and matching equations.

153

APPENDIX VIII
TAN GENTAL CLAW PHENOGRAMS

Figures 68 and 69 are claw phenograms calculated without regard to homologous
articulation. They are provided here as tangential ideas.

Ptaunadan longiccps claw l——-1 A -_
Pteranodon langicqps claw 4——-—-' N

rus marmus claw 8. D

Palacanus canspicillqhas claw 31:|B_J£F
ma 1
5.521%... ru '61::

Pelee-anus claw 4:};—
Croc Ius acums claw 2 R

All My??? claw
:{ator Mississippicns I

[Po ecanus melaw 2—— HH
Crocodyhgd porosus claw 1

J
I decanus claw } K ]M
M
1.1..me yam... ‘1" br.

guinis c X.
Pave cmtarus

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4
444
w:

 

 

 

 

odor: ongic c w
us ca: w

Eudocimusmbcrclaw

 

_.—1.nwwwu
U
O

O
u—n
N
W
:5

FIGURE 68. Phenogram of all claws regardless of articulation, without the four pteranodont claws of
unknown articulation. Clusters are labeled with capital letters.

154

 

[(043933 inborn claw l H
zsclaw 4 "

Pin
KU43933 wn claw % A
Olor columbianus claw :l—L
Olor columbianus claw‘ 1

 

 

 

 

 

 

 

 

 

nis claw
Olor colP' ianus c
Pteranodon ongieqn

Larus marinas claw 3 LL
Polocanus claw" J

Pavo onstarus claw l

Pavo cristarus claw J

Pavo cnsranu claw3 Q

Pinguim's claw I!
ocimus rubar claw. 7
ocimus rubar claw I!

Croc 'lus acutus claw 3 jlj I
1:413:14: mba'gm

 

 

 

 

 

 

 

 

 

 

 

   
  

 

Alligator misssissippisns claw 3
{4160 claw l
wn claw V

Polocama co oicillanrs claw
Pteranodon orificaps
Polocanus comic: lotus claw 3

Palocanus claw l
lus wporosus claw

Alligaro wippions ”“213: l Z
WWIPJO tetanus mgflwg (KR

Pavo cristam: claw "

Alligator missisippians claw 3

Pramnodon longicops claw 41
Praranodon longicops claw 1 JJ

man'nusclaw .

I 1 l
0 1 2

 

 

 

 

‘—

 

 

 

w—
I‘—

he

FIGURE 69. Phenogram of all claws regardless of articulation, with the four pteranodont claws of
unknown articulation. Clusters are labeled with capital letters.

155

 

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