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THE“

This is to certify that the

thesis entitled

Three-Dimensional Dynamic Motion of

the Shoulder Complex
presented by

Tamara Ann Reid

has been accepted towards fulfillment
of the requirements for

M. S . . Mechanics
degree in

 

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DATE DUE DATE DUE DATE DUE l

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MSU Is An Affirmative Action/Equal Opportunity Institution
chimera”!

 

 

 

 

 

 

THREE - DIMENSIONAL DYNAMIC MOTION OF THE SHOULDER
COMPLEX

By

Tamara Ann Reid

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

MASTER OF SCIENCE

Department of Material Science and Mechanics

1994

ABSTRACT

THREE-DIMENSIONAL DYNAMIC MOTION OF THE SHOULDER
COMPLEX

By

Tamara Ann Reid

The kinematics of the shoulder complex were studied by non-
invasive motion analysis and by developing a computer program which
calculates the three-dimensional rotations of the shoulder . Because of the
large range of motion at the shoulder, it was necessary to investigate and
address several singularities. The mathematics used in the computer
program created local coordinate systems on body segments and used
Euler angles in the form of a joint coordinate system as introduced by
Grood and Suntay (12) .

Six young men, who had no previous shoulder injury, performed a
series of arm movements while 60 Hertz positional data were collected
using a motion analysis system. The data were then read into the program
and three angles were calculated: the internal/external rotation of the
humerus, the rotation of the humerus in a transverse plane relative to the

thorax and the elevation angle.

DEDICA'HON

I would like to dedicate this piece of work to my parents who have
given me guidance and support (both morally and ﬁnancially) throughout
my entire life. Thank you for always being there for me.

To my husband, Neil, thank you for keeping me sane and for
believing in me throughout this entire ordeal - I love you.

ACKNOWLEDGMENTS

The author would like to express her sincerest gratitude to the
following people for their efforts, advice, and encouragement in the
completion of this thesis.

To my co-workers and friends for their help and support: Gordie
Alderink, Cheng Cao, Shawn Evans, Kathy Hillmer, Brock Horsley, David
Marchinda, Jim Patton, Leann Slicer and Patricia Soutas-Little

I would like to extend special thanks to Yasin Dhaher for spending
many hours with me both as a friend and as a colleague.

I would also like to thank Kim Lovasik for her everlasting friendship
and support.

To my graduate committee: Dr. Robert Hubbard and Dr Dahsin for
their friendship and for taking the time to review my work.

To my graduate advisor: Dr. Robert Soutas-Little we've spent much
time together over the last four years, I've learned a great deal from you
and would like to thank you for your guidance and friendship.

This is an accomplishment l am proud of and all of you helped make
it possible. Thank You.

TABLE OF CONTENTS

Basra
LIST OF TABLES ....................................................................... vi
LIST OF FIGURES ..................................................................... vii
INTRODUCTION ........................................................................ 1
LITERATURE REVIEW .............................................................. 9
EXPERIMENTAL METHODS ..................................................... 25
ANALYTICAL METHODS ........................................................... 34
Calculation of Segmental Coordinate System ...:....37
Elevation ................................................................. 46
Rotation in the Plane of Elevation .......................... 47
Internal/External Rotation of Humerus ................... 51
Complications ......................................................... 51
RESULTS ................................................................................... 54
DISCUSSION ............................................................................. 71
BIBLIOGRAPHY ......................................................................... 78

LIST OF TABLES

Iable ................................ Eagg
1. Anthropometric Data ............................................................... 15
2. Maximum Ranges of Motion ................................................... 61
3. Maximum Elevation vs. Plane of Rotation .............................. 68
4. Maximum Elevation vs. Internal/External Rotation ................. 69

5. Intersection Point on Elevation vs Internal/External Rotation .69

vi

LIST OF FIGURES

ﬁgure ......................................................................................... Rage
INIBQDILGIIQN:

1. Shoulder Articulations ............................................................ 2
2. Codmans Paradox ................................................................. 4
3. Globographic Representation ................................................ 6
4. Shoulder Angle Description ................................................... 7
LIIEBAILLBEBEMIEIM

5. Dempster's Linkage System .................................................. 11
6. Dempster's Planar Analysis ................................................... 12
7. Path of Instantaneous Center of Rotation ............................. 13
8. Planar Descriptors 01 Shoulder Motion .................................. 17
9. Motion of Humerus' In the Horizontal Plane ........................... 18
10. Non-Planar Motion ................................................................ 19
11. Cardan Angles.......-. .............................................................. 22
12. An et al. Experimental Setup ................................................ 23
EXEEBIMENIALMEIHQQS:

13. Calibration Structure ............................................................. 26
14. Frontal View of Targets ........................................................ 29
15. Sagittal View of Targets ........................................................ 30
16. Range of Rotation ................................. ° ................................ 3 2
ANALILIQALMEIHQQS:

17. Tracked Stick Figure ............................................................. 36
18. Segmental Axes System ...................................................... 38
19. Rotation Z X' Z” ................ . ................................................... 44
20. Spherical Angles ................................................................... 48
21. Elevation Angles ................................................................... 49
22. Conical Singularity Region ..................... 52

vii

23.
24.
25.
26.
27.
28.

29.
30.
31 .
32.
33.
34.

35.
36.
37.
38.

Range of Motion for Average Subject: Belaxedﬁgndmgn ...55
Range of Motion for Stocky Subject: Which ...... 56
Range of Motion for Average Subject: Winn ....57
Range of Motion for Stocky Subject: MW ....... 58
Range of Motion for Average Subject: WM ...59
Range of Motion for Stocky Subject: waiting ...... 60
Cross Plots for Average Subject: awning ........... 62
Cross Plots for Stocky Subject: Wilton .............. 63
Cross Plots for Average Subject: Winn ............ 64
Cross Plots for Stocky Subject: Internalﬁcndjtign ............... 65
Cross Plots for Average Subject: Enemaqundmgn ........... 66
Cross Plots for Stocky Subject: WM .............. 67
Humeral Rotation .................................................................. 72
Humeral Rotation .................................................................. 72
Intersection Point .................................................................. 76
Intersection Point .................................................................. 76

viii

 

INTRODUCTION

The shoulder complex has been stated as being the most difficult
system of joints in the human body to kinematically evaluate (7). The
reason is because it is a compilation of four articulations: acromioclavicular
articulation , the scapulothoracic articulation, the sternoclavicular
articulation and the glenohumeral joint (14, 5) (Figure 1). The sum of these
articulations creates joints allow different ranges of movement; each
articulation is not solely responsible for one type of motion, they all work
together. To understand the shoulder complex and to define it clearly, it is
necessary to elaborate on the four articulations. The acromioclaviculaumm
is the articulation between the acromial end of the clavicle and the
acromion of the scapula. It is held together by various ligaments which run
between the coracoid process of the scapula and the clavicle. This
Iigamentous connection gives the articulation a " joint" characteristic.
Sometimes, this region is considered as two joints, the acromioclavicular
and the coracoclavicular joints (5). The scapulgthgracjg articulation does
not ﬁt the typical hinge or ball and socket " joint" description either, but is a
point at which the scapula rotates on the thorax. Theﬂemgclavicular joint
is the articulation between the eternal end of the clavicle and the sternum.

This is described as a ”Saddle” type joint where the clavicle and sternum

 

2

Ventral or Anterior Aspect

acromioclavicular joint

/ _ sternoclavicular
clavrcle

 

 

Dorsal or Posterior Aspect

 

 

 

acromioclavicular joint
ﬂ glenohumeral joint
ii \f‘
'-
. i ‘i scapula
c; '1' F humerus

scapulothoracic

FigureI: Shoulder Articulations

3

are concave and convex surfaces, respectively, separated by a
intraarticular meniscus, and the right and left sternal ends of the clavicle
are connected by an interclavicular ligament. The glenghumeral joint is the
joint which many people refer to as the shoulder. This is a ball and socket
joint between the glenoid fossa of the scapula and the head of the
humerus. (7,16)

Since the shoulder is extremely complicated, several methods of -
analysis have been studied. These methods include mathematical models
which simulate the movement of the shoulder, cadaver experiments which
deal with only the scapula, clavicle and humerus (1, 2, 5), cinematographic
(19) and roentoeographic studies (13). Unfortunately, none of these are
dynamic movement studies; therefore they are very difﬁcult to apply to a
clinical patient. One objective of this thesis is to develop a protocol which
can be used easily and quickly for a clinical evaluation, such as a range of
motion test or for sports enhancements such as baseball pitching.

A problem occurs in the method of defining the shoulder movements.
The most popular method used by clinical individuals and sports
biomechanists is to define the motions in three separate planes such as
flexion/extension, abduction/adduction, and internal/external rotation.
However, this becomes extremely confusing when a movement falls
between two planes or when two or more movements are coupled. To
further complicate matters, the order of motion is important as we find out
by Codmans Paradox where an individual can perform two sets of
movements and end in the same ﬁnal position (Figure 2).

Rotation Set #1

 

 

Anterior View

 

Rotate about the humerus 1800

 

Rotation Set #2

 

 

b, 1800 Abduction

Side View

 

 

d. 1

Figure 2: Codman's Paradox

C. 1800 Flexion

EXAMPLE:
E' l B | l' S l :
a. Start with the arm in the anatomical neutral
position.
b. Rotate the arm 180° along the humerus axis, now

the palm is facing posteriorly.

W:

a. Start with the arm in the anatomical neutral
position.

b. Abduct the arm 180° in the frontal plane.

c. Flex the arm 180° in the sagittal plane.

After the second rotation set, the arm is at the side of the body with the
palm facing posteriorly, yet axial rotation of the humerus did not occur (17).
One solution to the angle definition problem was proposed by An et
al., at the Mayo Clinic (1 ). They chose to form an imaginary globe around
the humeral head of cadavers (Figure 3). This type of descriptorhas also
been termed globographic (7, 3, 5). An et al. (1) described the motion of
the shoulder by an elevation angle (the latitude lines on the globe), a
rotation in the elevation plane (the longitudinal lines) and internal/external
rotation about an axis down the humerus (Figure 4). This naming
convention eliminates the confusion of the separate plane description and

with these three angles, the position of the humerus is uniquely deﬁned.

 

 

 

 

 

8. Elevation Angle b. Rotation Plane Angle

Posterior Aspect

lntemal

 

0. Internal and External Rotation

Figure 4: Shoulder Angle Description

8
Overall, the object of this thesis is to study the kinematics of the
shoulder complex in viva. This data will be calculated and presented in a

similar fashion to the work presented by An et al..

LITERATURE REVIEW

Several methods of studying the shoulder complex have been used
over the last century. Individuals began the analysis of the shoulder by
studying the osteology, the musculature and the Iigamentous structures of
the shoulder complex (2, 5, 14). Dempster (5) and Inman (14) are known
for pioneering studies on the shoulder.

Inman et al. (14) published a thorough article including an anatomical
comparison analyzing the morphological changes of the scapula and
humerus between several other species. He also used roentgenography
and pin insertion to compile an analysis of the ranges of motion at the
shoulder. From this data, Inman et al. set up equations to calculate the
forces at the glenohumeral joint. To verify this data, he recorded the
changing action potentials (electromyography) often different muscles.
From their data collection on both cadavers and living subjects, Inman et
al. formed the conclusion that, contrary to the teaching of that time period,
the scapular and humeral motion are simultaneous, not successive. He
also stated that, for free and full elevation, a lateral rotation of the humerus
was necessary.

Dempster's study (5) broke the shoulder complex down into three
distinct joints and then discussed the functionality and ranges of motion of
each. He also discussed the role of associated ligaments and the

restraining ability they have on the shoulder complex. In the” Mechanisms
9

1 0
of Shoulder Movement”, Dempster separated the upper body into three

links, the claviclular, scapular and humeral. His deﬁnition of a link is a
straight line span between pivots at both ends of a bone. He treats the
body as a mechanism and creates open and closed chain system of links.
(Figure 5 ). From this method, Dempster looked at positions of the arm in
three different planes, the transverse, frontal and sagittal (Figure 6).
Internal and external rotation of the humerus were not examined. In this
study, all data were collected from cadavers. Dempster also introduced the
”joint sinus” which is described as the continuous boundary of a single
joint's extreme range. Other authors have taken this idea and expanded on
the notion (3, 8). .

A third article entitled ”Human Mechanics - Four Monographs
Abridged" is a compilation of work from Braune, Fischer, Amar and
Dempster (3). Some sections gave specific attention to the shoulder
complex. The shoulder was discussed relative to kinematics and
anthropometrlcs. These results were extracted from cadaveric data. In this
pamphlet, the entire human body was discussed and the goal was to use
the collected data to create a manakin which would adequately model a
human. One diagram which confirms the point that the shoulder motion is a
compilation of all four articulations, (acromioclavicular, sternoclavicular,
scapulothoracic and glenohumeral) is shown in Figure 7. This diagram,
produced from a cinefluorographic film, displays the path of the
instantaneous center of rotation for one motion, abduction.

The above authors (3) also mention the globographic representation
of kinematics of the shoulder and they note that " Simple globographic

presentations used by others are inadequate for this joint due to lack of

11

 

Various upper-limb postures with arm and forearm links, shoulder-girdle links, and
siernocosiol link (shown in two Interpretations).

Figure: 5 Dempster's Linkage System

12

 

 

 

 

-Different positions of the upper limb and of the shoulder and arm links, In the
plane defined by the scapula at rest. B—Positions of the limb and links in horizontal move-
ment at shoulder height. C—Extreme positions of the upper limb; stippled cone represents
the range of total clavicular motion. In each sketch, the line of dashes shows the elbow

position.

Figure 6: Dempster's Planar Analysis

13

as
I ‘~

_______ ‘~~-‘~" “3:3. ,>.
T“\\\ ‘I':‘.‘:\/
‘ ' ‘5 ‘
‘3?)1‘173'
/
. 'QI

Path of instantaneous Center of Rotation During Shoulder Abduction

Figure 7: Path of Instantaneous Center of Rotation

I

14

consistency in the locus of the center of rotation. However, they do
represent gross values and have some value.".

Only for completeness of this thesis, the anthropometric data are
presented in the form of tables. This data is shown in Table 1 (3).

The globographic method of describing the motion at the
glenohumeral joint is not a new concept. Shino and Pfuhl (3) used this type
of analysis in the early 1900's. Since then several biomechanists have
adopted this method of analysis. Although this method does not have the
capabilities of isolating the motion of each joint in the shoulder complex, it
does allow for the tracking of relative motions between the thoracic cage
and the humerus in a living subject. The simplicity of this descriptor is
obvious when we look at what those in the clinical field are using to
describe the motion at the shoulder.

The common clinical descriptions allow for little deviation and include
flexion, extension, abduction, adduction and internal or external rotation
(15). If the subject is not in one of these planes performing this exact
motion, the system becomes complex and the descriptors become
muddled and confusing. First, the planar definitions or common clinical
descriptors will be discussed.

In 1959, the American Academy of Orthopedic Surgeons appointed
a committee to study Joint Motion. This study was published as the Joint
. WM (15), and is the guideline for
describing the motion which occurs at certain joints. It is necessary to
understand the present method for description of joint motion in order to
fully comprehend the simplicity of the globographic model and the three
angles discussed in this thesis. During the time frame in which this
committee assembled these guidelines, it should be noted that a

15

Table 1: Anthropometric Data

 

 

Joint and Type Median Muscular Thin Rotund
of Movement. (mill) (ntll) In=l0l 10"”

WRIST: 0 It 0 ‘I' ‘l +
Flexion 94. 60 I 5.2 91.9 ; 9.4 95. 6: ; 9.0 77. 7: ;I4.0
EXLCHIIOH IOZeo - no 9 970 o ’ 90 o '00. 0 - no 3 °6e D .|70 D
I96.6° 1I2.2 I68. 9° 1I4.5. I95. 6° 1I4.I I66. 5° t26.7
Abdomen 254: :40. 2 27. I: E 7. 6 23. a: E 7. 9 27. 5: I. 0. 0
Adduction 46.3 - 5.I 47.4 - 6.4 47.I - 6.7 46.I - 6.4
7I.4° tI3.6 74. 5° in. 4 75. 9° 3 9.0 73.6 tIz.9

roasmw: o + . o * 0 *
:supmauon I00.6° :22. I II3. 3; ;I5. 3 I23. 00 :20. 0 I I4. so +49. 2
Pronution 74.0 -I7. 0 69. I -I4. II 75. 0 -I6. 0 a9. 0 -37. 9
I74.6° 126. 0 I62. 4° tIB. 6 I98. 0° 122. 9 203. 0° ‘42. 3

ELBOW: + ~ . + ‘
Ftexiorr I4I.0° - 9. 0 I40. 3° - 7. 6 I44. 6° -IO. 2 I43. 2° - a. 6

SHOULDER: o ‘ . o 0 o * o +
Flexion I93.zo ; 9. 6 I90. 2 ; 9. 9 I86. 0 +.I I. 7 I34. 00 -IZ. 2
Extension 63.0 -I4. 3 58. I° - 9. I 67. 0° -I I. I 54. 5 .I4. II
256.2° in. 7 24a. 3° 1m. 3 253. 0° in. 3 230. 5° 123. 9
Abduction I32.I: :46. 5 I35. 0: 90.4 I42. 5° 99.0 I27. 5: :42. 3
Adduction 50.8 - 6.4 44. 3- J 6.7 53. 5° - 6.9 43,6 ; 5.2
Iaz.9° till I79. 3° -I2.e I96.0° 123.3 I7I.I° .I6.z
Medial Rotation 95.7: 325. 4 95. 2° E20. 9 97. 0° :43. 0 I00. I: 124. 6
Lateriei Rotation 30.7 -I3. I 33. 0° -I3. 7 39. 5° -I0. I 32.5 - a. 5
I26.4° in 4 I20.z° tza.5 I36.5° tI6.7 I32.6° tI5.6

16

globographic description of motion was proposed, but did not receive
sufficient support. At the present time, biomechanists and clinicians are
consolidating their research, methods and information in a call for
standardization (4).

The following are some of the definitions given for shoulder motion
with all references being relative to the anatomical neutral position:
l. W
Figure 8A-Ahdu91innjn1AddumiQn

Abduction is the upward motion of the arm away from the side of the
body in the coronal plane, from 0° to 180°. Adduction is the opposite
motion of the arm toward the midline of the body, or beyond it in a upward
plane.
Figure8B.» u. '_ o z.” o u. . 0, -' ._ or (I. :2 A. .. 0 an or

Forward flexion is the forward upward motion of the arm in the
anterior sagittal plane of the body from 0° to 180°. The opposite motion to
the zero position may be termed depression of the arm. Backward
extension is the upward motion of the arm in the posterior sagittal plane of
the body from zero degrees to approximately 60 degrees.
II. BMW
Figure 80 HQLIZinaLElﬁxiQn

Horizontal flexion is the motion of the arm in the horizontal plane
anterior to the coronal (frontal) plane across the body. This motion is
measured from zero degrees to approximately 130-135°.
Horizontal extension is the horizontal motion posterior to the coronal plane
of the body. Figure 9 gives a description of the motion when the arm is in
the horizontal plane (transverse plane). Descriptors become confusing
when the arm is over the head, abducted and extended (Figure 10 ), the

17

180

  

  

   

NEUTRAL

 

 

 
   

 

‘t

O
90

Figure 8: Planar Descriptors of Shoulder Motion

18

TERMINOLOGY lDENTlFYlNG UPWARD MOTION
OF THE ARM IN VARIOUS HORIZONTAL POSITIONS

F
G... .13
Em

A00 .2:

‘

 

45' 135’

I Neutral abduction

POSITION

- Abduction In 45’ of horizontal flexion

8 Forward flexion

" Neutral adduct Ion

' Bockwa rd extension

A

B

C ,

D ' Adduction in I35. of horizontal flexion
E

F

G

" Abduction In 45' of horizontal extension

Figure 9: Motion of Humerus in the Horizontal Plane

19

 

 

Sagittal View

Anterior (.— ' Overhead View

Figure 10: Non-Planar Motion

20
humerus is not longer in one defined plane.

The globographic system is useful, because as presented by Engin
and Chen (8) and An et al. (1 ), this simplifies three dimensional data into
two components, latitude and longitude. Combining this with the internal or
external rotation of the humerus, the motion of the humerus relative to the
thorax is uniquely defined.

Cinematographic (19), X-ray, roentgenographic, goniometry (7)
multisegmented mathematical models (11), mechanism models (11), sonic
digitizing (7) are among some of the other methods used to try to better
understand the shoulder complex. Few individuals have analyzed dynamic
motion of the shoulder complex. The in vivo methods reviewed have
restrictions on the motion. The advantage to the type of analysis proposed
in this thesis is that the subject is free to move in a natural sense, and
because this form of motion analysis is non invasive, these are the true
recordings of the subject; in other words, is no artifact is introduced
because of pain caused by a brace or pin insertion.

Several other scientists have investigated the kinematics of the
shoulder complex. Engin (7), in one of his experiments collected resistive
force, moment and torque data on living subjects. Engin developed an
exoskeletal device(ESD)) and a global force applicator (GFA). The
exoskeleton device is a. measuring instrument which is ﬁtted to the arm on
bony landmarks and allows freedom of motion between the arm and torso.
The GFA moved the arm through a certain range of motion applying a
speciﬁc amount of force while the subject sat in a restraint system.

Engen (10) used three mirrors and a 35mm camera to compare the
motion of an anatomical arm to a motorized arm. He had the subject

perform tasks such as hair grooming, writing, page turning and table to

21

mouth feeding. He used time clocks to calculate the velocity and
acceleration of points on the arm.

Engin and Chen (8) used sonic emitters to track the motion of the
humerus relative to a fixed torso. They used 10 subjects in the age range
between 18 and 32. Three sonic emitters on each body segment were
used to create a joint coordinate system on the humerus and the torso.
During data collection, the torso was immobilized while the subject moved
the arm in a maximum range. The data was then displayed in a
globographic representation. Once again, the body was not free to move in
a natural sense because of the thorax immobilization.

Hogfors et al. (13) performed an experiment in which the arm and
torso were uninhibited by any sort of brace or mechanism but the
movement was limited by the size of film. His group inserted radiation
dense implants into the shoulder region and monitored the motion by
roentgenstereophogrammetry. Four tantalum balls were inserted into each
of the following three spots: proximal humerus, lateral acromion and lateral
clavicle. He had the subjects perform ”spiral arm lifts” with 1 and 2kg
weights. He then calculated the motion by using the Z, Y', X" order of Euler
angles (Figure 11). This data analysis does not limit the motion of the
subject, however it is not feasible to insert radiation dense balls into every
subject.

Lastly, An et al. (1) using a magnetic tracking system studied three-
dimensional glenohumeral joint motion in cadavers during arm elevation.
He used a Z X' 2" order of Euler angles to evaluate the tracked data and
the globographic representation of the data. He noted that there would be
singularities in the analysis if the elevation of the arm reached 0° or 180°

and only evaluated cadaveric data so these singularities could be

22

 

 

Figure 11 : Cardan Angles

23

 

 

 

 

 

 

Figure 12: An et al. Experimental Setup

24

avoided (Figure 12). An et al. (1 ), held the humerus at either a maximum
internal rotation or a maximum external rotation, and were able to monitor
the rotation of the humerus. ‘

Methodology for a clinical analysisof shoulder motions has not been
the subject of many investigations by the biomechanics community. The
articles reviewed above are not concerned with identifying basic shoulder
function and dysfunction. The objectives have been to anatomically identify
the mechanisms in the shoulder. Much cadaveric data has been collected
but it has been primarily used to created lifelike models. The in viva
kinematic data which has been collected in other studies has drawbacks
when applied to the clinical setting, such as being invasive, limited by size
of X-ray film or requiring one body segment to remain fixed.

EXPERIMENTAL METHODS

Before testing began, a calibration space was defined as a 1.5 m
cube, beginning 70 centimeters from the floor. The square space was
marked with four calibration stands (one on each corner). Each calibration
structure consisted of four targets which when placed in the square
arrangement created a box deﬁned by 16 targets (Figure 13). For
calibration, the largest targets (approximately 36mm in diameter) were
used on the calibration structure. The targets were spherical and were
covered in retro-reflective tape manufactured by 3M. The reflectivity of the
tape is from 600 to 1600 times brighter than a white surface and has the
highest amount of luminance at a 35° entrance angle (the angle between
the light ray and the normal to the surface). The tape allows for a range of
up to 60° for an entrance angle (18). Since the targets were spherical and
there were four cameras with light sources, this entrance angle
requirement was easily met. Once the calibration stands were in position,
the four 60 Hz NEC shuttered video cameras were placed around the
calibration space so they would provide optimum viewing of the subject. A
light source was mounted approximately five centimeters to the left of the
center of the camera lens. This light served as the lumination source for

the targets and the threshold of these lights was adjustable on the

25

 

26

200 cm

I60 cm

110cm

70 cm

 

 

 

 

ISO Cm I

Figure 13: Calibration Structure

27

video processor (VP320 by Motion Analysis) to compensate for variations
in light intensities.

Once the calibration space was set and the cameras were in
position, data were collected for six seconds on marker positions in the
calibration space. Data from the four cameras were sent through the
VP320 which synchronized the four cameras. The dimensions of the
calibration space were manually entered into the computer and then data
were digitized in pixel space by the VP320.in real time. With the pixel
coordinates and with the manually inputted laboratory coordinates of each
target, transformation matricies were formed. This set of matrices allowed
the data to be converted from lab space to pixel space by the method of
direct linear transformation. The transpose of these matrices allowed the
conversion from pixel space to lab space. These matrices were then stored
in an environment ﬁle and were applied to the test data. The six seconds of
digitized data then became the video file. _

The accuracy was measured by a ”norm of residuals". This was a
number which related, for each camera, the least square solution of the
transformation. For the shoulder evalution calibratiion, the norm of
residuals were .31 -.40 for the ﬁrst day and .27-.59 for the second day. The
residuals computed on day two were not as tight as day one, but due to
multiple tests and time constraints on the subjects, this test space was
used. These values were well below the system's value for the maximum
norm of residuals and no tracking problems were encountered due to the
larger span of residuals.

The subjects were six male high schoOl baseball pitchers who had
no previous shoulder injuries or surgeries. An informed consent was sent to

each of them, along with a consent form allowing photographic pictures

28

and video taping. All subjects brought their signed consent forms with them
to the laboratory. All lab testing was done under # IR889-559 approval.
Prior to testing these anthropometric measurements were recorded for

each subject:
1) Weight
2) Height
3) Hand Length from top of the wrist to the tip of the middle
ﬁnger
4) Arm length from acromion process to the wrist joint
5) Shoulder breadth (which was measured as the width
between the left and right acromion processes)

These measurements were not used in this study, but were obtained for
future studies and reference.

After these measurements were obtained, each person was
targetted. The spherical targets used were approximately 24 mm in
diameter and were covered with the 3M retro-reflective tape, the same tape

used in the calibration. Targets were placed on the following locations:
1) Medial Elbow Epicondyle
2) Lateral Elbow Epicondyle
3) Humeral Head
4) Sternal Notch
5) First Thoracic Vertabrae
6) Eighth Thoracic Vertebrae
7) Xyphoid Process '
8) Medial Wrist
9) Lateral Wrist

The last three targets were not used in calculations, but were placed on the
subjects to aid in tracking (Figure 14 and Figure 15).

The subjects were given a brief explaination along with a
demonstration on what types of motions were desired. The subject initially
began with their body erect and in the anatomical neutral position. While in

the neutral position, a six second standing file was shot. All subjects began

29

 

 

3 Anterior Aspect

1) Medial Elbow Epicondyle

2) Lateral Elbow Epicondyle

3) Humeral Head

4) Sternal notch

5) First Thoracic Vertabrae

6) Seventh Thoracic Vertebrae
7) Xyphoid Process

8) Medial wrist

9) Lateral Wrist

Figure 14: Frontal View of Targets

3O

 

Figure 15: Sagittal View of Targets

31

each trial in the anatomically neutral position and after a cue was given,
they moved into one of the three positions: arm internally rotated, externally
rotated or in a relaxed position and then they began their range of motion
movement. The subjects were asked to hold their arm in the desired
position as ”best able" throughout the trial. The relaxed position began with
the arm In the neurtal position and then on the cue, they internally rotated
their arm until the thumb was pointing anteriorly. They then began the
movement allowing their arm to rotate comfortably in order to achieve the
maximum range of motion at the shoulder.

Each subject had a series often trials:
1 neutral
3 internally rotated
3 externally rotated
3 in relaxed position

Each trial was 10 seconds in duration. The path which the individual
followed in order to obtain maximum range of rotation at the glenohumeral

joint is described in the following paragraph.

RANGE OF ROTATION:

After the subject first rotated the humerus to one of the three speciﬁed
conditions (internal,external or relaxed) (Figure 16a), the movement of the
arm began posteriorly ( Figure 16b). The subject ﬁrst extended his arm
posterior to the thorax then while moving posteriorly and elevating the arm
he brought it as close to the midline of the thorax as possible (Figure 16c).
The subject then raised the arm superiorly behind the back and eventually
over his head. (Figure 16d ) The arm was lowered down and across the
front of the body (Figure 169 & f), then back to the starting region

(Figure 169). The subject was asked to continue for ten seconds.

32

Side View of Left Arm

 

 

 

 

 

 

Anterior View

 

 

 

 

, g. 1

Figure 16: Range of Rotation

 

 

33
Most subjects achieved two full rotations. The object of this movement was
to obtain the largest range of motion at the glenohumeral joint.
All subjects were photographed with a polaroid camera while in the
anatomically neutral position. Subjects were also photographed with a
35mm camera at random positions while performing the series of tests. All

trials of each subject were also videotaped using a Sony camcorder.

ANALYTICAL METHODS

After the data were collected, the raw video files were ﬁrst viewed
and frames of merged targets were identified. After identification, a mask
operator in the ev3d software was used to separate the merged targets,
one pixel at a time. The mask operator acted like an editor for the motion
ﬁles; this allowed the user to delete an entire target or just a few pixels.
Each camera's data was analyzed individually.

Separating the merged targets slightly decreased the accuracy of
identifying the centroid of the target, although it was felt that having a
fragment of an actual target was better then joining over a merged area
where the target position would have been eliminated completely. A
merged target occurs when the view from a camera identifies two targets
as having centroid locations which are extremely close. The targets appear
to come together and form one large target. This commonly happened with
the elbow targets.

After the files were masked, they were tracked using the ev3d
software by Motion Analysis. This system tracks all four cameras
simultaneously in three dimensions and was described in detail in the
Experimental Methods section. If a target was obscured and the target
could not be identified in two cameras, the computer could not triangulate
on the target and therefore, could not determine its location. Thus, the

34

35
trajectory of that target was incomplete and interpolating in the trajectory
path could not be avoided. The interpolation fit a cubic spline between the
tracked trajectory segments. Great care was taken to assure the best
possible ﬁt and any inconsistent trials were discarded.

The kinematic data was smoothed by digital ﬁltering which was done
before the angles were calculated from the tracked data. A tracked ﬁle
appears in Figure 17.

Data were mapped into a position format where one time was given
and all target positions were listed below that time. The data were then run
through the shoulder angle program developed for this thesis. This
program gave the position of the humerus relative to the thorax by using
the previously described system: an elevation angle, a plane of rotation
and internal/external rotation of the humerus.

A local coordinate system was developed on each segment by using
the three targets placed on that segment. Two of the targets on the body
segment always identified an anatomical axis, while all three identiﬁed an
anatomical plane. On the thorax, the two vertebral targets defined the

Superior/inferior anatomical axis and the sternal notch target , along with
the two vertebral targets defined a sagittal plane. The two vertebral targets
were used to form the anatomical axis instead of the sternal notch and the
base of the sternum targets because a universal targeting scheme was
desired. On some individuals, particularly females, the sternum region
might be a difﬁcult and a sensitive area to target.

On the humerus, the lateral elbow epicondyle target and the
humeral head target formed the anatomical axis while the medial elbow
epicondyle target formed a frontal plane when the body was in the
anatomical position.

36

iiiiiii°iiiiiiiiiiiiiiliii?

r'

 

3'7" ' ' 55

“iii? 333399333999999992/
W/WWWWWWWW”

FFFFF

~+$ﬁ§X>. \\hiii;£é£//////K/'

ﬂﬂﬂﬂﬂﬂﬂﬂ

 

2'44 2'50 2'55 2'52 2'50 274 2'00 3'04 3'I0 3'13 3'22

KERRHRHRRHﬁﬁﬁﬂﬁﬁhppppppffpi

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37 343 349 379 3'05 391
France

Figure 17: Tracked Stick Figure

37

The local coordinate system was formed on the thorax by identifying
a vector from the eighth thoracic vertebrae to the first thoracic vertebrae as
the 21 axis of the thorax. A vector (Gt) was then formed from the first
thoracic vertebrae to the sternal notch. The superior Zt axis was crossed
(vector cross multiplication) into the other axis formed between the sternal
notch and the ﬁrst vertebrae to obtain the Yt axis which was defined as
always pointing to the left:

zxe=x
After each axis was created on each segment, each axis was made into a

unit vector. This was done by taking each component of the vector and
dividing it by the magnitude of that vector.

 

Magnitude: M=)12 1'}? +22

A

Unit Vector: U =

_x_ _y_ .2.
M’M’M

Thus, Yt was made into a unit vector where Y, is the vector in terms of
individual components and |Y,| is the magnitude :

The third axis was obtained by crossing the Yt into the 21 to obtain the Xt
axis. The Xt axis pointed anterior (Figure 18 ).

38

 

Juli x his

Figure 18: Segmental Axes System

39
KXZ=XI

.. X‘
X' "IX—.l

Zt was also made a unit vector:

t
L: l' l' ,

Since the targets that identified the thoracic Z axis were along the
thoracic vertebrae, a natural kyphotic curvature existed between the
location of the ﬁrst thoracic vertebrae and the eighth thoracic vertebrae.
This caused an initial tilt in the thoracic coordinate system which ranged
from 8 to 20 degrees relative to the vertical of the laboratory space. When
the arm is in the starting position (at the side of the body) the Z axis of the
arm and the Z axis of the thorax are both in a vertical position and because
these two axes are close to parallel, the cross-product used to define the
ﬂoating axis is sensitive to small angle errors.

This initial tilt caused the position of the floating axis to be pointed
medially and posteriorly for the time period the arm was at the side of the
body. The vectors that form the floating axis were chosen under the
assumption that, when crossed while the body was in the neutral
position, the ﬂoating axis would be pointing anteriorly. Thus, the zero
degrees of rotation in the elevated plane was chosen to be In line with the
X axis of the thoracic cage.

40
In some cases, the Z axes crossed over each other and changed
the position of the floating axis by approximately 180° , causing a
discontinuity in the data. Once the thoracic coordinate system was aligned
with the laboratory coordinate system, this problem was solved.
AdjustmentchaLScace:
To remedy the initial tilt due to the curvature of the back, the
orientation of the thoracic coordinate system was recorded for the ﬁrst

frame of data and a transformation matrix was identified as:

[B]=i ii

 

 

which are the three components of each unit vector of the thoracic
coordinate system relative to the lab coordinate system.

Next, the transpose of this matrix was identified as:

41
lxx’iyx,izx
[B]T = 1,0,1ij
1' i i

xz’ yz’ zz_

 

 

The transpose matrix of a rotation matrix is the inverse of the matrix.
This is a unique characteristic only true to an orthogonal rotation matrices.

For the initial frame, the thoracic rotational matrix was multiplied by
its transpose matrix. Visually, the matrix [B] is the amount the initial
thoracic coordinate system is rotated relative to the laboratory coordinate
system and when multiplied by the transpose, the coordinate system is
rotated back that initial amount, aligning the thoracic coordinate system

with the laboratory system.

[1]=[B]T[B]

"1,0,0“
[1]: 0,1,0
_o,o,1_

This action results In the identity matrix, which means the thoracic

 

 

coordinate system and the laboratory coordinate system are aligned.
For each of the following frames, this same transformation matrix

was used to rotate the thoracic coordinate system back this initial amount.

The data was only normalized to standing data. A new transformation

matrix was not computed for each frame, and if the thorax was rotated

42

medially of laterally during the course of the actual arm movement it was
incorporated into the data analysis.

The local coordinate system was formed on the humerus by deﬁning
the segmental Zh axis to be pointing superiorly when in the neutral position
from the lateral elbow epicondyles toward the humeral head.

A vector was then formed from the lateral elbow epicondyle to the
medial elbow epicondyle on the left side (Gh). On the right side, these
same two targets were used to form this vector, but it was deﬁned in the
opposite direction. Then, the epicondyle vector was crossed into the Zn

axis to define the anterior/posterior axis of the humerus.
G, x Z, = X h
This was then made into a unit vector:
X
X, = —"
IXII

The Zh axis was crossed into the Xh axis to obtain the Yh axis or

medial/lateral axis and it was made into a unit vector (Figure 18 ).

490942

11.

Y: = 1m

43

Lastly, Zh vector was also made into a unit vector:

—_ZL
Zh‘lzi

Using Euler's angles with a Z X' Z" rotation and the method
described by Grood and Suntay(12), joint coordinate systems were formed
on each body segment and the three angles were computed.

The Euler angles represent three ordered rotational transformations.
Euler angles may be formed in the following fashion. The first rotation

which deﬁnes the rotation in the elevated plane is a rotation about the Zt

axis:
cos¢ sine O
—sin¢ cost) 0
0 0 l

The second rotation defines the angle of elevation which is the rotation
about the X' axis and is denoted as Euler's line of nodes or the floating axis
as described by Grood and Suntay.

1 O O
0 case sine
O - sine case

The third rotation is a rotation about the new 2" axis which is Zn (2 of the
humerus)and defines internal/external rotation about the humerus (Figure
19).

44

Z, Z'

 

 

X‘I’X'

 

 

Figure 19: Rotation Z X' Z"

45

easy! simv 0
-sin\|r cosw O
O 0 1

Obtaining the Euler angles in the above fashion requires that the three

matricies be multiplied together and the angles be teased from this large
and usually complex matrix. By using the analysis method of Grood and
Suntay (12), the exact same angles can be obtained by using simple dot
products. Thus the angles (i). 9 and \I’ can also be obtained as follows:

2, = 2, where él is the axis of rotation in the elevated plane

23' = 2,, where 5 3 is the axis which internal and external
rotation of the humertrs occurs

 

 

,. e x

e2 = 1 on the left side
|e1xe:|

.. é‘ xé‘

e2 = 3 1 on the rightside
|e3xe1|

where 82 is the floating axis or the line of nodes which is
perpendicular to both 4 and 33 and is the axis of elevation.

These three unit vectors, 31.32.33, form a non-orthogonal joint
coordinate system. It should also be noted that the switch of the cross
product order from the left side to the right side was done to maintain the
condition that the floating axis begin pointing anterior to the thorax. If this
condition is met, then a sign consistency can be maintained between the
right and left sides. '

As put by Cole et al.(4), the method used by Grood and Suntay
eliminates the sequence dependency by predefining the axes of rotation.

46

However a sequence effect is still imposed in the manner that one must

decide upon the fixed body axes.

Q | I I. I I | I I. ,
** Note: from this point on, all vectors referenced in the text are unit

VBC‘IOTS.

Elevation:

The elevation angle (Figure 20) was calculated by :
elevang = arccos (2, 'Z) for angles greater than 10°
for angles less than 10°

elevang = theta

Theta was used to calculate the elevation angle for small values
because using the arccos of Zt dotted with Zh is more likely to produce
errors as the angle approaches zero. Looking at the cosine value for
different angles, it can be seen that at the smaller angles, the sensitivity of
the calculation is decreased, meaning that a slight difference in the cosine
can make a large difference in the angle. For example between 0 and 15
degrees, the cosine ranges from 1 to .9659 which is only a difference of
.0341 where the same 15 degree range taken from 70 to 85 degrees has a
cosine range from .3420 to .0871, a difference of .2549. Thus to avoid
some of the possible error in this region, the other two shperical angles,
alpha and beta were found and using the relationship that
co§ 0t+co§ l3+co§ 6:1 the angle theta, which is the angle of elevation, was

calculated.

47
The elevation angle did not reach 180° with any of the subjects so
possible problems at the upper end did not have to be addressed.
Spherical angle calculations:
alpha = acos (22 02,.)
beta = acas (é2 - Z3.)
theta =41. O -— alpha 2 - beta 2

 

Conceptually, this is the angle between the humerus and the
superior axis of the thorax. Due to the nature of the cosine calculation and
the usage of the square root to determine the elevation angle, sign
identification is lost. Thus the elevation angle will always be positive and
will only range between 0° and 180°; if the angle exceeds this range, the
larger, or smaller value will not be displayed. Since we are looking at a
globographic representation, this calculation is acceptable (Figure 21). The
latitude lines on one side of the globe should be equal to those on the other

side.

B I I. . II I .
The plane of rotation was calculated by either:
rotplane = arccos (32 0 X,)

rotplane = arcsin (52 9 Y.)

This angle can be obtained by computing the angle between one of
the segmental axes, Xt, of the thoracic coordinate system and the ﬂoating
axis. By deﬁnition, the result of a cross product between two vectors

produces a third vector perpendicular to the other two. Since the floating

48

7-h

 

 

Figure 20: Spherical Angles

49

 

 

 

20° 0°

Elevation is measured by latitude lines

 

 

 

00 20°

Figure 21: Elevation Angles

50

axis (62) is a cross product between Zt and 2h, 62 is always perpendicular
to both Zt and Zn and is in the thoracic XY plane. As described in the
previous section, the rotation plane is the position of the arm as defined by
the longitudinal lines on a globe centered around the glenohumeral joint.
When the ﬂoating axis is computed, it is in laboratory coordinates.
The rotation angle in the elevated plane can be calculated from laboratory
coordinates, but for ease of writing the computer algorithm the floating axis

was transformed into the thoracic coordinate system.

[5.1 =1016.1

in,i ,in

xy

[D]: 5.5,},

iu,z

 

 

_ a ’ in _
where [D] is comprised of the axes of the thoracic coordinate system

in the form of unit vectors:
X, =i i 1'

xx’ xy’ xz
Y =lyx,lyy,lyz
Z,=Iu,rzy,zu

After the transformation, the X,Y and Z axes of the thoracic coordinate
system are used as references to identify the position of the ﬂoating axis.
This position is then tracked from one frame to the next. When the ﬂoating

axis is within 30 degrees of the zero degree angle, the arcsin calculation is

51

used to achieve a smooth curve through zero and to define the sign

change of the angle.
lntemaliExtemaLBctaticnmmatlumems:

The internal/external rotation of the humerus was calculated in the
following manner:
inte = acos(éz ' XI.)

inte = asin(éz ° Yr.)

As stated before, by the nature of the cross product, the floating axis is
perpendicular to Zh and Zt and is therefore in the XY plane of the humeral
coordinate system and in the XY plane of the thoracic coordinate system.
This calculation was done in the same fashion as the rotation in the
elevated plane except, the floating axis was left in the laboratory coordinate
system.

The arcsin calculation was used to monitor a sign change and to

produce a smooth curve through the zero angle.

6 I. I. ,
In both the rotation in the elevated plane and the internal/external
rotation of the humerus, the direction of the floating axis was identiﬁed.
Since the shoulder has a high range of motion, tracking of the floating axis
was necessary. By slight movements in the neutral position, the floating
axis can jump from quadrant to quadrant (Figure 22) which produces
discontinuities. The problem occurs when the arm is at the side and forms

a conical region where a slight adjustment of position causes the

52

with small movement of arm

y \ Various positions of humerus axis

 

, V9
' "

b a

 

Floating axis in the transverse
plane of the thorax

9:)
J ,

Figure _22: Conical Singularity Region

 

 

 

53

Z axis of the humerus and the Z axis of the thorax to cross. Since the
floating axis is the cross product between these two axes, this causes a
switch of axis direction, and maintaining the same cross product order
causes the floating axis to jump to a different quadrant.

An index system was developed to identify the quadrant in which the
floating axis was pointing and thus it any ”jumping” of the floating axis
occured, it was immediately identified. Then from this planar analysis, an
index was assigned to the position of the ﬂoating axis, it's previous position
is compared to its present position and then, the desired computation is
performed.

It also should be noted that at the point where the Z axis of the
humerus and the Z axis of the thoracic cage become parallel, the floating
axis can no longer be defined. As these two axes approach this position,
the accuracy of the cross product decreases. The data showed small gaps
when this occurred, and points around the gap were scattered. The points
around the gap were eliminated in a subjective fashion and thus created a
larger gap, but cleaner data. Typically this happened at the initial starting
position and in the externally rotated condition.

RESULTS

A collection of data obtained from the left arm of six different subjects
Is presented in this section. Data were processed for each trial and
individual angles were plotted for each motion: elevation, the rotation in the
elevated plane ( rotation plane) and the internal/external rotation of the
humerus. Representitive plots for the average subject and for a stocky
subject are presented. The ﬁve thinner built subjects all had similar trends
and ranges of motion, while the heavier, stocky subject had similar trends
in the data but the ranges of motion were less. Because of this, the two
sets of data are presented throughout this section. Data in the form of the
individual angles, for the relaxed condition are presented in Figures 23 and
24. Data for the Internally rotated humerus are presented in Figures 25
and 26. Data for the externally rotated condition are presented in Figures
27 and 28. h

The overall ranges of motion for the three conditions based on
different humeral rotations are comparable. None of the three different
rotations showed a large change in motion when compared with the other
two. A summary of the maximum ranges of motion for each humeral
rotation condition are presented as follows in Table 2.

54

55

 

BB Relaxed: elevation

I75 'l

5‘5

I25‘

 

 

Elevation: Degrees
o a 8 a 8

 

0 2 4 6 8 IO
Time: Seconds

 

 

 

BB Relaxed: rotation plane

Rotation Plane:
Degrees

 

lime: Seconds

 

 

 

 

BB Relaxed: Internal/external rotation of
humerus

25 1
0 5 . v —4. 2 4
_50 4 V 0 IO
-75 .

Time: Seconds

Int/Ext Rotation:
Degrees
r15
01

 

 

 

 

Figure 23: Range of Motion for Average Subject: Wm

56

 

SW Relaxed: elevation

I75 I
ISO:
l25‘
ICD 1’

75 ‘1

25 .
0 2 4 6 8 IO
'l'lme: Seconds

 

Elevation: Degrees

 

 

 

 

SW Relaxed: rotation plane

 

 

 

 

125
.. 19g
3 50
g i 2g - . . .
c __ . . . .
.9 8’ '25 \2’ 4 6 0 10
:9 e 32
8 -l00

-125

-150

time: Seconds
SW Relaxed: Infernal/external rotation of
humerus
III)

-25

Int/Ext Rotation:
Degrees
8

-l25

 

time: Seconds

 

 

 

Figure 24: Range of Motion for Stocky Subject: W

57

 

 

 

 

 

 

 

 

 

 

 

 

 

88 Internal: elevation
I754
§ 150'
g» 125 .
e 100 ~
5 75 ~
5 so ~
5 25»
0 - 4
0 2 4 6 8 I0
Time: Seconds -
88 Internal: rotation plane
125
III)
a 3.8
2§ 25
n' 0 5 : c : ﬁ
= D-
o -25 4 6 v 10
5 5° 3%
3 -100
-125
-I50
Time: Seconds
88 Internal: Internal/external rotation of
humerus
ICD i
a £3
.9- <1
,5 73' 23 " . [\A I A;
3 g g 2 4 6 0 o
E D -75 l.
2:- -I00 1:
- -125 ll
-]50 ..
Time: Seconds

 

 

 

Figure 25: Range of Motion for Average Subject: lntemaLanaiticn

58

 

SW Internal: elevation

175 "

d

125 v

 

 

Elevation: Degrees
asaa

 

0 2 4 6 8 10
time: Seconds .

 

 

 

 

SW internal: rotation plane

 

Rotation Plane

 

Trem: Seconds

 

 

 

 

SW internal: internal/external roatlon oi
humerus

int/Ext Rotation

 

Time: Seconds

 

 

 

Figure 26: Range of. Motion for Stocky Subject: Winn

59

 

88 External: elevation

 

 

 

§ 175 [

i50:

g. 125 ’

Q 100

C 75 ~

% so~

5 25

m o = : g 4
0 2 4 6 8 10

lime: Seconds

 

 

 

88 External: rotation plane

125

75
50

-25
-50
-75
400
-l25
450

Rotation Plane Degrees
O
b.
g
on
5 J

lime: Seconds

 

 

BB External: internal/external rotation at
humerus

 

10

Int/Ext rotation

 

' iime: Seconds

 

 

 

Figure 27: Range of Motion for Average Subject: W

60

 

 

 

 

 

 

 

 

 

 

SW External: elevation

§ 175 [
3:

i:'

O
In

Time: Seconds
SW External: rotation plane

to

3

8’

o

2

O

a:

r:

.0

3':

O

a:

Time: Seconds

 

 

 

SW External: internal/external rotation at
humerus

d
A A I
7 ﬁ“

 

int/Ext Rotation
lb
01

 

Time: Seconds

 

 

 

Figure 28: Range ot Motion tor Stocky Subject: W

61

Table 2
Maximum Ranges of Motion

 

 

 

Degrees Degrees Degrees
Elevation Rotation Plane Int/Ext Rotation
Relaxed, 131-153 108-207 97-186
jutemaL 121-151 98-193 133-201
Enema ' 125-145 105-150 95-150
' Based on three subjects

For the relaxed condition, the subject with the lowest amount of elevation
achieved the largest range of motion in the rotation plane and in the
internal/external rotation of the humerus and the subject achieving the
largest amount ot elevation had the lowest range of motion in the two
remaining angles. '

Along with the individual angles, three sets of cross plots for each
trial were then graphed:

1) rotation plane vs. elevation

2) internal/external rotation of the humerus vs. elevation

3) rotation plane vs. internal/external rotation of the humerus.
Figures 29 through 34 are representative trials with the subject BB having
the average trend and ranges of motion while SW showed consistently the
smallest overall ranges of motion. The data in Table 3 identiﬁes the ranges
of rotation in the elevated plane in which maximum elevation occurred. An
average position in the rotation plane for all subjects was computed and is
included in Table 3.

62

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BB Relaxed: rotation vs. elevation
g 150 "
5
3
m
-175 -i25 -75 -25 25 75 125 175
Rotation Plane: Degrees
BB Relaxed: int/ext rotation vs. elevation
g
5
-l75 -125 -75 -25 25 75 125 175
internal/External Rotation: Degrees
BB Relaxed: rotation plane vs. int/ext
.2
g 450 400 100 150
.‘s‘
Rotation Plane: Degrees

 

 

 

Figure 29: Cross Plots tor Average Subject: Belaxedﬁqnditign

 

 

 

 

 

 

 

 

 

 

 

SW Relaxed: rotation vs. elevation
8 150
2
g 100
8
E j 50
-175 -125 -75 -25 25 75 125 175
Rotation Plane: Degrees
SW Relaxed: Int/ext rotation vs. elevation
150
8
2
g 100
8
5
E
F _.,_b . v ,
-175 425 -75 -25 25 75 125 175
Internal/External Rotallon: Degrees
SW Relaxed: rotation plane vs. int/ext
i
8'
O
E
2
2
3
u-
E
5.
Relation Plane: Degrees

 

 

 

Figure 30: Cross Plots for Stocky Subject: Belaxedﬁgngiﬂqn

64

 

BB Internal: rotation vs. elevation

 

. .501
2

g .00

5

‘6

 

-175 -125 -75 -25 25 75 125 175

Rotation Plane: Degrees

 

 

 

 

 

 

 

 

 

 

 

BB Internal: int/ext rotation vs. elevation
1
z 5’1
E
5
3 50
T3
-175 -l25 -75 -25 25 75 125 175
int/Ext Rotation: Degrees
BB internal: roalalion plane vs. int/ext
i
'c'
g % :
:9 -150 -100
Q
s
Rotation Plane: Degrees

 

 

 

Figure 31: Cross Plots tor Average Subject: WM

65

 

SW internal: rotation vs. elevation

Elevation: Degrees
8

 

. _ 7—, ﬂ,

-175 -125 ~75 -25 25 75 125 175

Rotation Plane: Degrees

 

 

 

 

 

 

 

SW Internal: int/ext rotation vs. elevation
8
2
9
O
i:'
3
O
3
ii
-175 -125 75 125 175
Int/Ext Rotation: Degrees
1 SW internal: rotation plane vs. int/ext
rotation
150
g 100
§ 50
c
2 %. = : A —*——'
£450 -100 -50 _5 100 150
g
5 -
-150
Rotation Plane: Degrees

 

 

 

 

Figure 32: Cross Plots for Stocky Subject: Wm

66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BB External: rotation vs. elevation
S
s.
9
‘3
-175 -125 -75 -25 25 75 125 175
Rotation Plane: Degrees
BB External: int/ext rotation vs. elevation
é
a
-l75 -125 -75 -25 25 75 125 175
int/Ext Rotation: Degrees
BB External: rotation plane vs. int/ext
rotation
3.
i5
8 : c
5 -150 150
g
s
Rotation Plane: Degrees

 

 

 

Figure 33: Cross Plots tor Average Subject: W

67

 

SW External: rotation vs. elevation

8 150
g
S 100
g
5 50

 

-175 -125 -75 -25 25 75 125 175

Rotation Plane: Degrees

 

SW External: Int/ext rotation vs. elevation

Elevation: Degrees

 

 

-l 75 -125 -75 -25 25 75 125 175
Int/Ext Rotation: Degrees

 

 

 

 

SW External: rotation plane vs. 1nt/ext
rotation
150
100
50

 

-1(XJ
450

Rotation Plane: Degrees

int/Ext Rotation: Degrees

 

 

 

Figure 34: Cross Plots for Stocky Subject: ExtemaLandjﬁgn

68

Table 3
Maximum Elevation vs. Plane of Rotation

 

 

 

Degrees Degrees

Elevation Rotation Plane

Maximum - Menace Bangs Amos
Relaxed 153 142 38-75 57
ML 1 51 140 40-80 66
my 145 135 33-53 46
' Based on three subjects

The average elevation between conditons varied by 7 degrees and the
maximum elevation angle occurred in the relaxed humeral roatation. The
range of rotation was 11-20 degrees higher in the relaxed and internal
humeral positions than in the external.

Summarized data from the second cross plot, the elevation vs.
internal/external rotation of the humerus is presented in Table 4. The
average amount of humeral rotation varied 31 degrees between the three
different conditions. These graphs have some unique characteristics. One
of the characteristics is that, during posterior elevation for the first half of
the great circle completed by the prescribed motion and then during the
lowering of the arm in the front of the body during the second half of the
circle, there is a crossover point where the amount of humeral rotation is
the same. This intersection is present in all plots and the ranges of this
point are summarized in Table 5.

69

Table 4
Maximum Elevation vs. Internal/External Rotation

 

Degrees Degrees
Elevation Int/Ext Rotation

 

MaximumAiLQLaoa Bangs Avenue

 

Relaxed 153 142 20-72 41
LinemaL 151 140 10-50 35
EnemaL' 1 45 1 35 36-106 66
' Based on three subjects

Table 5

Intersection Point between Elevation and Humeral Rotation

 

 

Degrees Degrees

Elevation int/Ext Rotation

(Average) (Average)
Relaxed. 55 25
lntamaL 79 8
ExternaL‘ '46 56

 

' Based on three subjects

70
Notice the shift to the right of the intersection point, from the humeral
rotation in the internal condition at 8°, to the humeral rotation in the

external condition at 56°.

DISCUSSION

Little difference was observed in theranges of the angles between
the different humeral rotations. In the relaxed condition and the internal
condition, an initial internal rotation can be observed, but then as the arm
begins to move, it is forced to externally rotate ( Figure 35 8 36). This is a
natural motion, as one elevates the arm posteriorly and achieves a
maximum rotation plane, the humerus is forced to externally rotated in
order to continue the circular motion.

When comparing the cross plots obtained from these in vivo tests, to
the cadaver tests obtained by An et at. (1 ), it was found that the maximum
elevation range when the humerus was rotated in the external condition
occurred between 33 and 53 degrees in the rotation plane which is anterior
to zero degrees. The zero degree position occurs when the humeral Z axis
is in the YZ plane or the frontal plane of the thoracic cage. When the
humerus axis is in this position, the cross product between the Z axis of the
thorax and the Z axis of the humerus creates a ﬂoating axis which is
perpindicular to the frontal plane of the body. This is the 0° position as
defined for this study. Each subject did not begin at 0°, but rather in the

anatomically neutral position where the arm was for most subjects, slightly

7.1

int/Ext Rotation: Degrees

int/Ext Rotation: Degrees

72

BB Relaxed: Internal/external rotation of humerus

1m ..
75 ..

25 .1.

 

 

 

-25

-75
-100
-125
-150

 

Time: Seconds

Figure 35: Humeral Rotation

88 Internal: lntemal/external rotation ot humerus

1m ..

 

 

 

-25 2 4 6

.2: \ /

-150

§

Time: Seconds

Figure 36: Humeral Rotation

73

posterior to the zero position. An et al. (1) found that the maximum
elevation occurred at 25° anterior to the plane of the scapula when the
humerus was rotated in the external position. The zero position in this
study and the plane of the scapula are comparable, but are not necessarily
equal. No physical measurements were taken to identify the plane of the
scapula relative to the humerus and therefore, a physical verification
cannot be made. The trends of the data are similar, with the amount of
elevation being 20° higher and the rotation plane being 8°-28° larger in this
in vivo experiment.

The maximum elevation relative to 0° for the internally rotated
condition, occurred between 40° and 80° of rotation in the elevated plane
and in the relaxed condition, the maximum elevation occurred between 38°
and 75° of rotation in the elevated plane. As can be seen, the maximum
elevation was produced within the same ranges of rotation in the elevated
plane for all three positions of humeral rotation.

A second conclusion made by An et al. found that the maximum
elevation posterior to the plane of the scapula occurred when the humerus
was internally rotated. The data obtained in this research did not address
this issue in the testing protocol and therefore could not be compared with
the findings of An et al.. The primary objective was to obtain the largest
range of motion at the glenohumeral joint in the global measurement
system.

There are two major differences between the work done by An et al.
and the research performed for this thesis. One was that this study was
done in viva while An et al. used cadaveric specimens and they could
control the movements of the humerus. They were able to ensure that the
humerus maintained the desired rotation either internally or externally by

74

fixing the position of the humeral bone. During this study, the subjects were
not asked to wear any type of ”locking brace" to maintain an external or
internal rotation of the humerus, but were asked to maintain the desired
position as best able throughout the test. As can be seen from the graphs,
internal and external rotation of the humerus did occur.

A second difference was in the type of motions performed or induced
on the subjects. An et al. selected planes of rotation and then elevated the
humerus until it was restricted in the prescribed plane. They repeated this
motion for several different planes of rotation and for conditions with the
humerus internally rotated and externally rotated. For this research, an
emphasis was not placed on the subject achieving the maximum amount of
elevation in specific planes, but rather obtaining an overall maximum range
of motion in the globographic sense. Because of these differences both in
subjects and in motion formats some variation in the data are expected.

it was also felt that the relaxed condition would promote the largest
overall range of motion. When analyzing the data, it was found that the
relaxed condition did not consistently provide the maximum range of
motion for all three angles. The maximum ranges of motions were mixed
between all three conditions and all angles. No correlation could be
established that one type of humeral rotation continually provided the
maximum range of motion. It is felt that if the humerus was prevented from
rotating in the internal and external conditions, then the relaxed condition
would allow for the largest ranges of motion.

It should also be noted that the amoirnt of fat, muscle or type of
clothing worn during the testing procedure will affect the outcome of the
data. Individuals wearing restrictive clothing, or who have large deltiod and

trapezius muscle mass or are overweight may show a decrease in the

75

range of motion. Individuals which have muscles which are in pain may
also show a decrease in their range of motion. None of the subjects used
for this experiment were wearing any clothing on the thorax and none of
the subjects exhibited any problem or pain in the shoulder region.

Five of the six subjects tested in this research were of thin build
ranging in weight from 150 pounds at 5' 11" to 187 pounds at 6' 2" . The
sixth subject was of a stocky build and had a height of 5' 11" and a weight
of 199 pounds. This subject for all conditions showed the lowest range of
motion in the plane of rotation and the internal/external rotation of the ‘
humerus, but not necessarily in elevation.

The second cross plot of elevation vs. internal/external rotation of
the humerus has two unique characteristics. This plot has an overall shape
similar to that of a figure eight with the lower half of the eight varying in
size, followed by an intersection point (Figures 378 38)

This intersection point may suggest that for this humeral rotation,
there is an anatomical restriction on the amount of elevation which can be
obtained both anterior and posterior to the body. Also note, that, between
subjects and conditions, the lower half of the figure eight varies more in
size and shape than does the upper half.

For the last cross plot of the rotation plane vs. internal/external
rotation of the humerus, a rough linear relationship seems to exist between
these two movements. This would also identify a coupling between these
two motions.

These three cross plots have characteristics which, along with the

evaluation of the range of motion might be a useful paramater in identifying

Elevation: Degrees

-175 -125

Elevation: Degrees

76

BB External: int/ext rotation vs. elevation

 

 

125 175

 

Int/Ext Rotation: Degrees

Figure37: Intersection Point

SW External: int/ext rotation vs. elevation

 

 

 

-1 75 - l 25 -75 -25 25 75 125 l 75
Int/Ext Rotation: Degrees

Figure 38: Intersection Point

77

the function or dysfunction of the shoulder joint. For example, the area
under the curve along with the shape of the plot could be examined in the
may be able to indicate a problem.

As discussed in the results section, the point of intersection gradually
moves to the left as the condition changes from external to relaxed to
internal while the amount of elevation at which this point occurs increases.
This might also prove to be useful information in identifying shoulder

dysfunciton.

BIBLIOGRAPHY

BIBLIOGRAPHY

. An, K.N., Browne, A.O., Korinek, S., Tanaka,S., and Morrey, B.F. (1991)
Three-Dimensional Kinematics of Glenohumeral Elevation. Journal of
Orthopaedic Research 9:143-149.

. Bechtol, C. O. (1980) Biomechanics of the Shoulder. Clinical
Orthopaedics and Related Research 146 :37-41 .

. Braune, W., Fischer, O, Amar,.,J Dempster, W..T( 1963)1:|uman

WWWADC Tech Report 63-123
Wright-Patterson Airforce Base, Ohio, Wright Air Development Center.

. Cole G.K., Nigg, B.M., Ronsky, J.L. and Yeadon, M.R.(1993)
Application of the Joint Coordinate System to Three- Dimensional Joint
Attitude and Movement Representation: A Standardization Proposal.
Transactions of ASME 115: 344-349

. Dempster, W.T. (1965) Mechanisms of Shoulder Movement. Archives of
Physical Medicine and Rehabilitation 46:49-70.

. Dvir, Z. and Berme N. (1978) The Shoulder Complex in Elevation of the
Arm: a Mechanism Approach. Journal of Biomechanics 11 :21 9-225.

. Engin, A. E. (1980) On the Biomechanics of the Shoulder Complex.
Journal of Biomechanicst 3 :575-590.

. Engin, A.E. and Chen, SM. (1986) Statistical Data Base for the
Biomechanical Properties of the Human Shoulder Complex-z l:
Kinematics of the Shoulder Complex. Journal of Biomechanical
Engineering.1 08:21 5221

. Engin A.E. (1990mm; Mow,Ratcliffe and
Woo, Springer-Verlag. 405-439.

78

79

10. Engen, T.J. and Spencer, W.A. (1968) Method of Kinematic Study of
Normal Extremity Movements. Archives of Physical Medicine and
Rehabilitation 49:9-12.

11. Feltner, M. Dapena J. (1989) Three-Dimensional interactions in a
Two-Segment Kinetic Chain. Part I: General Model. International
Journal of Sport Biomechanics 5:403-419

12. Grood, ES. and Suntay,W.J. (1983) A Joint Coordinate System for
the Clinical Description of Three-Dimensional Motions: Application to
the Knee. Transactions of the ASME 105:136-144.

13. Hogfors, C., Peterson, 3., Sigholm G. and Herberst, P. (1991)
Biomechanical Model of the Human Shoulder Joint- II. The Shoulder
Rythm. Journal of Biomechanics 24 :699-709

14. Inman, V.T., Saunders, J.B., and Abott, L.C.(1944) Observations on
the Function of the Shoulder Joint. Journal of Bone Joint and Surgery
26A:1-30.

15. WW (1955) American
Acadamy of Orthopaedic Surgeons

16. Moore, Keith L. (1992) W Williams and
Wilkins, Baltimore, MD.

17. Miyazaki S. and lshida A. (1991) New Mathematical Deﬁnition and
Calculation of Axial Rotation of Anatomical Joints. Transactions of the
ASME 1 13:270-275

18. Product Bulletin for 3M High Gain 7610 and High Contrast 7615.
(1993) lndustral Optics/3M, St. Paul, Minnisota.

19. Sakurai, S., Ikegami, Y., Okamoto, A., Yabe, K. and Toyoshima, S. (
1993) A Three-Dimensional Cinematographic Analysis of Upper Limb
Movement During Fastball and Curveball Baseball Pitches. Journal of
Applied Biomechanics 9:47-65. ‘

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