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This is to certify that the

thesis entitled

A Model of Average Adult Male Human Skeletal and Leg
Muscle Geometry and Hamstring Length for
Automotive Seat Designers ~

presented by

Robert L. Boughner

has been accepted towards fulfillment
of the requirements for

Mechanics

in

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Master S degree in

 

 

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University

 

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TO AVOID FINES return on or before date due.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

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AUG 1 7 2002

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i MSU Is An Affirmative Action/Equal Opportunity Institution
i 6mm

 

A MODEL OF AVERAGE ADULT MALE HUMAN SKELETAL AND LEG MUSCLE
GEOMETRY AND HAMSTRING LENGTH FOR AUTOMOTIVE SEAT DESIGNERS

BY

Robert Lee Boughner

A THESIS

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

MASTER OF SCIENCE
Department of Metallurgy, Mechanics, and Material Science

1991

ABSTRACT

A MODEL 01“ AVERAGE ADULT MALE HUMAN SKELETAL AND LEG MUSCLE

GEOMETRY AND HAMSTRING LENGTH FOR AUTOMOTIVE SEAT DESIGNERS
by

Robert Lee Boughner

The need for comfortable, safe, and efficient use of
interior space in the modern automobile is creating a need
for anatomically and physiologically correct representations
of the human body.

This thesis describes the development of a detailed
geometric computer model representing the average adult
male. A skeletal model capable of assuming any human
posture functions as a framework to which models of other
tissues are referenced. An investigation into how muscles
might best be modeled leads to the use of ellipsoids to
represent entire muscle groups. A non-invasive method of
measuring hamstring length in vivo using sophisticated
optical tracking equipment is described. The hypothesis
that a limiting hamstring muscle length determines
permissible combinations of knee and hip angles is
investigated experimentally.

It is concluded that the methods selected for skeletal
and muscle modeling produce body contours useful in seat
design. It is also shown that a limiting hamstring muscle
length cauSes an interdependence of knee and hip angles in

certain postures.

Dedicated to my ever supportive Mother and Father.

iii

ACKNOWLEDGEMENTS

The author wishes to extend heartfelt thanks to the
following very special people:

My new wife, Susan, for her love, support, and
energetic help during the preparation of this thesis.

Dr. Robert Soutas-Little and Dr. George Mase for their
kindness and valuable advice.

Johnson Controls, Inc., for generously funding this
research.

Dr. Robert Hubbard, my advisor and friend, for his
trust, support, and humor.

iv

TABLE OF CONTENTS

Page

LIST OF TABLES .......................................... vii
LIST OF FIGURES ........................................ viii
1. BACKGROUND AND OBJECTIVES .............................. 1
2. SKELETAL MODEL ......................................... 7
2.1. Introduction .................................... 7

2.2. Methods ...................................... ...7
2.2.1. Computer System and Software ............. 7

2.2.2. Skull .................................... 7

2.2.3. Pelvis ................................... 8

2.2.4. Spine .................................... 8

2.2.5. Rib Cage ................................. 8

2.2.5. a. The lst Grahical Model. ...... .. .8

2.2.5. b. A 2nd Graphical Attempt .......... 10

2.2.5.c.1st Computer Generated Model ..... 13

2.2.5.d. 2nd Computer Generated Model ..... 16

2.2.5.e. 3rd Computer Generated Model ..... 22

2.2.5.f. The Problem of Rib Motion ........ 24

2.2.6. Long Bones .............................. 26

2.2.7. Hands and Feet .......................... 27

2.2 8. Positioning the Skeletal Model .......... 27

2.2.8.a. Lumbar Spine Positioning Program.27

2.2.8.b. Limb Positioning Program ......... 35

2.3 Results and Discussion .......................... 36

3. MUSCLE MODELING ....................................... 43
3.1 Introduction .................................... 43

3.2 Methods of Muscle Modeling ...................... 43
3.2.1. The Major MuScle Groups ................. 43

3.2.2. Alternate Depictions of Musculature ..... 48

3.3 Results and discussion .......................... 52

-4. MUSCLE LENGTH CONSTRAINT OF SKELETAL MOTION ........... 56
4.1 Introduction .................................... 56

4.2 Experimental Methods ........................... 57
4.2.1. Biomechanics Evaluatiuon Laboratory ..... 57

4.2.2. Data Gathering and Analysis ............. 59

4.2.2.a. Description of Exercises ......... 60

4.2.2.b. Calculation of Muscle Lengths....64

4.2.2.a. Calculation of Limb Angles ....... 68

4 2 2.d. Link Length Variations ........... 70

V

4.3 Experimental Results............................77
4.3.1. Experimental Results in Graphical Form..82

4.3.2. Error Estimation ........................ 96

4.3.3. Model Predictions Evaluated ............ 101

4.3.4. Discussion ............................. 102

5 . CONCLUSION ........................................... 108
APPENDICES

A. Spinal Joint Center Coordinates ................. 110

B. Lumbar Spinal Motion Program .................... 115

C. Limb Positioning Program ........................ 120

D. Linkage Equations ............................... 132

E. The Exercise Program ............................ 133

F. Error Estimates ................................. 147

BIBLIOGRAPHY ............................................ 150

vi

Table
Table
Table
Table
Table
Table
Table

Table

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LIST OF TABLES

page
Muscles Which Extend the Thigh ................. 44
Muscles Which Flex the Thigh ................... 45
Muscles Which Flex the Shank ................... 45
Muscles Which Erect the Spine .................. 46
Muscles Which Flex the Spine ................... 47
Subject Data ......................... . ......... 60
Nominal Link Lengths and Pelvic Constants ..... .77
Link Length Ratios by Subject .................. 82

vii

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

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11-14:
15:
16:
17:
18-23:
24:
25-26:
27:
28:
29:'

LIST OF FIGURES

page
The 2-D Drawing Template .................... 2
The 3-D H-Point Machine ..................... 2
An Earlier 2-D Model ..................... ...5
The 3-D Model Skull ......................... 9
The 3-D Model Pelvis ........................ 9

The First Graphically Depicted Rib Cage....11
An UMTRI Drawing ........................... 12
The First Geometric Rib Cage ............. ..14
The Basic X-section Shape of the Rib Cage..15
The Rib in Polar Coordinates ............... 17

Orthographic Projections of Ribs 1-4....18-21

Computer Rib Cage Model #2 ................ .23
Computer Rib Cage Model #3 ................. 23
'The Final Rib Cage Model .......... . ........ 25

Engineering Drawings of the Long Bones..28-33

The Model Skeletal Hand and Foot ......... ..34
The Assembled Skeletal Model ............ 37,38
An Alternate Skeletal Posture ..... . ........ 39

Poor Lumbar Curvature in a Seat Design.....4l

Depiction of Spinal Motion in the Model....42

viii

Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

Figure
Figure
Figure
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Figure
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Figure

Figure

Figure

Figure

30:
31:
32:
33:
34:
35:
36:
37-38:

39:
40:
41:
42:
43:
44-47:
48-59:
60-63:

64-67:

68:
69:

Muscle Groups as Straight Lines ............ 49
Alternative Muscle Modeling Techniques ..... 51
Views of the Model Leg with Muscles ........ 53
A Poor Muscle Modeling Result .............. 55
Hip Angle & Knee Angle Defined ............. 58
Creation of a Standing File .............. ..62
The Experimental Exercises ................. 63
Computer Representations of

Subject Targeting Geometry .............. 66,67
Vector Definitions ......................... 69

The Pelvis & Thigh as a Four Bar Linkage...71
Link Hip Angle And Laboratory Hip Angle....72
The Model Does the Laboratory Exercises....75

Hamstring Length Related to Joint Angles...76

Variations in Skeletal Link Lengths.....78-81
Unprocessed Experimental Data ........... 83-94
Experimental Lengths

versus Model Predictions ............... 97-100
Experimental Joint Angles

Compared to Theory .................... 102-105
The Linkage ............................... 128
Error Estimation .......................... 142

ix

1. BACKGROUND AND OBJECTIVES

The need for comfortable, safe, and efficient use of
interior space in the modern automobile is placing demands
on the scientific disciplines of anthropometry, ergonomics,
and biomechanics to provide better methods of human
accommodation in vehicles. Advances in the application of
computer technology to the design of automobiles provide new
potential for improved comfort and safety in tomorrow's car;
however, new representations of the human body are needed if
designers and engineers are to create optimal products.

For two decades, human accommodation in the automobile
interior has relied primarily upon two tools [1,2]:

1. "Oscar", the 2-dimensional drafting template shown in

Figure 1, and
2. the H-point machine, a 3-dimensional seat testing device

depicted in Figure 2.

These SAE (Society of Automotive Engineers) tools were
originally intended only as a means to assure consistent
positioning of the occupant in the vehicle; however, the SAE
2-D template is now often used improperly to represent human
geometry during seat design.

The SAE 3-D H-point machine is used to evaluate
prototype and production seats to measure the location of

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the H-point (the theoretical location of the center of

rotation of the hip joint) and seatback angle for comparison
with design values. This design approach is self-consistent
in that the seat properly accommodates the tools from which
it was designed - it does not necessarily follow that such a
seat will adequately or comfortably support a human being.

The 3-D H-point machine can only be used to evaluate
existing hardware. If a prototype seat fails to meet
specifications, it must be redesigned and another
constructed and tested. This often results in an expensive
cycle of design and redesign.

These SAE accommodation tools and associated design
practices assure that new automobile seat designs conform to
earlier standards, rather than to current knowledge of
ergonomics and biomechanics. These accommodation tools and
design practices will remain in use until the industry
adopts a new approach to seat development. For this to
happen, a new set of design tools compatible with current
knowledge and methods will be required.

It is imperative that future seat designs be based upon
what is anatomically and phySiologically correct for the
occupant. If a truly foresighted design procedure is to
become reality, design tools capable of adequately‘
representing people in the seated environment must be
developed.

Models which represent significant features of the

human body will do much to facilitate the incorporation of

4
biomechanics into the automotive design process. Such

models, capable of accurately representing the geometry,

permissible ranges of joint motion, and changes in position

of the human body will become powerful new design tools.

For seating, important body regions are the spinal
column with its complex motion capabilities, torso, and
head. Haas [3] has developed a two dimensional, side view
computer model which represents the average adult male's
torso geometry and spinal motion (Figure 3).

In this thesis, the torso model is further developed
with additions of a three dimensional rib cage, shoulder
complex, and limbs. The addition of muscles is explored
with attention to simple muscle shapes which result in a
realistic body configuration. The role played by muscle
(hamstring) length in retriction of possible body positions
is also addressed.

The specific objectives of this work have been to:

1. Construct a computer model of the average male adult
human skeleton;

2. Investigate how the body's muscle masses might best be
represented in such a model, with emphasis placed on
the musculature of the legs;

3. Investigate the role played by muscle lengths in the

limitation of relative motion between various adjacent

skeletal components, with emphasis placed on the muscles of

the posterior thigh.

(:1

 

 

 

 

 

 

 

FIGURE 3: AN EARLIER Z-D MODEL

6
The body of this thesis is organized into three separate

sections, one devoted to each of the primary objectives
stated above. Each section includes a description of
methods used along with presentation and discussion of

results.

2. THE SKELETAL MODEL

2.1. Introduction

The external contours of the human body are created
primarily by the skin being stretched over underlying
structures. The supporting tissues most important to
contour creation are the skeleton, muscle masses, and
superficial fat pads. The modeling approach used in this
study was based on the following assumption: if the
skeletal structures could be portrayed in an anatomically
correct fashion, then major muscle masses and fat deposits
could be simulated and positioned relative to the skeleton.
Then, through the use of a surface generating feature of the
CAD software, body contours could be represented.
2.2. Methods
2.2.1. Computer System and Software

The computer system used to develop this model of the
average size adult human male skeleton was the SUN SYSTEM
3/60 utilizing the SDRC IDEAS 3.8 and 4.0 GEOMOD [4] solid
modeling packages. These software packages permit graphical
representations of solid objects to be generated and

manipulated by the operator.'

2.2.2. 3-D Skull

The 3-D skull used in this model is that created by
Haas [3] from three-dimensional locations of various
landmarks representing the skull of the 50th percentile
male. This skull, which is based on work done by Hubbard

7

8
and McLeod [5] as a step in their development of what is now

the Hybrid III crash dummy head, is illustrated in Figure 4.
2.2.3. 3-D Pelvis

The pelvis for the model was created by Haas [3] using
data contained in a report by Reynolds, et al [6]. These
data for pelvic geometry have been recognized as the best
available information for the development of future crash
test dummies [7]. A wireframe depiction of this pelvis can
be seen in Figure 5.

2.2.4. The Spine

The spine was represented by Haas [3] as a series of
small spheres located at the centers of the intervertebral
joints (Figure 3). The spatial coordinates of the joint
centers are listed in Appendix A.

2.2.5. 3-Dimensional Rib Cage
2.2.5.a. The First Attempt at a Graphical Model of the Rib
Cage

No known previous attempts had been made to adequately
model the human rib cage geometry; thus, no data describing
its geometric details were available. The approach taken
during this work was to first develop a detailed 3-
dimensional rib cage and shoulder geometry which appeared
accurate when compared to anatomical references and
specimens. This geometry was then modified as required to

bring it into compliance with known anthropometric

dimensions.

10
In the first attempt to geometrically represent the rib

cage, photographs of horizontal sections of human cadavers
[8] were used to generate 3-D coordinates for the ribs and
costal cartilages. The three principal directions were
specified as x = anterior; y = left lateral; and z =
craniad. The origin of each section was placed
approximately at the center of vertebral joint rotation, as
depicted by Panjabi and White [9]. The X and Y coordinates
at each vertebral level obtained for the ribs, costal
cartilages, and sternum were plotted against a straight
vertical axis to obtain the orthographic projection and
other views of the rib cage shown in Figure 6. It was
thought that the "kinks" in the ribs were due to the lack of
spinal curvature in the plot, and the drawings were
repeated, this time using the spinal curvature depicted in
the drawings from UMTRI [7] (Figure 7). Unfortunately, this
second series of plots were less desirable than the first,
being even more grossly distorted. It was concluded that
apparently, in spite of elaborate processing of the cadaver
[8], it had been fixed in a posture with an unnaturally flat
spinal position, and was therefore inappropriate for the
study at hand.
2.2.5.b. A Second Attempt at a Graphical Rib Cage Depiction
After examination of several skeletal rib cages in the
Gross Anathmy Laboratory at Michigan State University and
anatomy texts [10,11,12], it was concluded that the rib cage

might be modeled by using two basic assumptions:

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13

1. When viewed from above, the shape of the human rib cage
can be approximated by a six-sided polygon, with each
rib having the same basic proportions but altering in
scale;

2. When viewed from the side, the ribs appear as straight
lines, with each rib descending anteriorly and downward
at a constant slope. (Ribs 1 thru 8 descend at an
angle of approximately 25 degrees, while Ribs 9 thru 12
descend at successively steeper angles).

Using these two conclusions and the rules of orthographic

projection, the highly simplified and symmetric drawings

shown in Figure 8 were produced. It was conjectured that by
using this approach (with more numerous points) a reasonable
model could be produced.

2.2.5.e. The First Computer Generated Rib Cage Model
The best data points available for the rib cage of the

50th percentile male were those located on the thoracic

spinal column and sternum contained in the UMTRI study

[7](Figure 7). This study used a coordinate system with the

origin located halfway between the centers of the hip

joints, with the three principal directions specified as x =
anterior, y = left lateral, and z = upward. It was decided
to use a basic cross-sectional shape of the rib cage to
generate the Y coordinates. The basic shape was assumed to
be that shown in Figure 9. By relating the vertebral-
sternal distance at the level of each rib in the UMTRI

drawings to 25 points on the basic rib shape using the polar

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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FIGURE 9: THE BASIC X-SECTION SHAPE OF THE RIB CAGE

16
coordinate system (with the origin at the center of the

vertebral bodies) shown in Figure 10, it was possible to
create a 3-D depiction of each rib. A straight line
connecting the centers of T1 and T12 was used to define the
vertical axis.

In this model, it was assumed that all the ribs
descended at a slope of dz/dx = -25 degrees, with no slope
in the y direction.‘ Because this model depicted the ribs as
vertical-sided, concentric structures, it was deemed
unsuitable for representing the first four ribs, which in
actuality have non—vertical sides.
2.2.5.d. The Second Computer Generated Rib Cage Model

To more accurately represent the sloping sides of ribs
one through four, trigonometric and orthogonal projections
were used to graphically determine the coordinates for these
ribs. The known geometry in the Side and Auxillary Views
(Figures 11-14) was used to create the Top View, from which
the missing Y coordinate could be measured. Ribs 5 through
12 were depicted as in the first computerized model.

Although the best attempt yet, this model had several
flaws, the worst of which was the lack of proper slope in
the floating ribs (ribs 10,11,12). This defect was due to
the fact that these floating ribs are very short, and most
of their travel occurs in the Y direction when viewed from
above. Since all the slope in the model was dependent upon

changes in the X coordinate, these ribs appeared as

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FIGURE 12: ORTHOGRAPBIC PROJECTION OF RIB TWO

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22
horizontal "stubs" (Figure 15), and not at all like the

actual ribs which angle downward.

2.2.5.e. The Third Computer Generated Rib Cage Model
Upon determination of the shortcomings in the second

model, corrective changes were incorporated into the third,

as follows:

1. The ribs were assumed to articulate with the vertebral
column at the level of the disk spaces, instead of at
the midpoint of the vertebral bodies as had been the
case in the previous models;

2. A variable slope, dz/dy, was included for that portion of
rib travel which is dependent primarily upon changes in
the Y coordinate (points 23-25 in Figure 10); this
slope varies with each rib, progressing from 0 degrees
at the fourth rib to ~40 degrees at the twelveth rib;

3. The slope dz/dx, included for that portion of rib travel
depending primarily upon change in the X coordinate
(points 1-22 in Figure 10), varies from -25 degrees at
the 5th rib to -32 degrees for the 12th rib. (This had
been a constant -25 degrees in the previous models).

This model rib cage, shown in Figure 16, needed only the

following minor corrections before it was incorporated into

the full-body model:

1. Smoothing of the transition between the dz/dy and dz/dx
slopes;

2. Inclusion of the costal cartilages;

 

COMPUTER RIB CAGE MODEL #2

FIGURE 15:

     

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FRONT VIEW

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COMPUTER MODEL
OBLIQUE VIEW

COMPUTER RIB CAGE MODEL “3

'FIGURE 16:

24

3. Scaling in all three directions to force the model to

comply with known rib cage dimensions; and

4. More anatomically accurate depictions of the sternum,

clavicles, and scapulae. (The improved representations

of these structures were developed using the methods

described in Section 2.2.6. Figure 17 shows the final

configuration of the rib cage model.
2.2.5.f. The Problems of Depicting Rib Motion

A literature search [13,14,15,16,17] has shown that the

problems of incorporating respiratory movements into the rib

cage model are varied and complex. They include:

1. Upper ribs move as "pump handles" (fixed at the posterior

end, with relatively large motions at the anterior

end), while the lower ribs move primarily as "bucket

handles" (both ends stationary with the bulk of motion

occurring in the center portion via rotation about an
imaginary axis between the rib ends). The middle ribs
move by a mixture of these two motions.

2. The upper ribs are relatively less mobile than the lower

ones due to the stabilizing influences of the clavicles

and sternum.

3. The amount of flexion in the thoracic spine is open to
debate [3].

4. Children, women, and men all expand the rib cage

differently during normal respiratory motions. Men
tend to be abdominal breathers, while women usually

expand their upper rib cage to a greater degree.

 

 

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FIGURE 17:

26
5. The relative contributions to thoracic movement of spinal

flexibility and respiratory motion are of greatly
differing magnitudes - the larger motions of breathing
will overshadow any rib motion due to spinal motion.

Because thoracic motions are not well quantified and are

small compared to other body movements (Haas [3] represented

changes in position of the rib cage relative to the pelvis
using lumbar motions only), it was decided to model the
thoracic spine as a rigid structure, and to ignore
respiratory motions in this model.

2.2.6. The Limb Bones
The long bones of the arms and legs were modeled in the

following manner:

1. Study of cadavers in the Gross Anatomy Laboratory at
Michigan State University, anatomical preparations,
anatomy texts [10,11,12], and live human subjects was
undertaken to determine the overall configuration of
the bones, with emphasis on the location of structures
critical to muscle attachment;

2. Decisions were made as to how the bones could best be
represented with simple geometric shapes (cylinders,
spheres, etc.) while maintaining critical anatomic
relationships and proportions;

3. Engineering drawings, using the simple shapes determined
above, were prepared for each bone. A characteristic
length (usually overall bone length) known from the

UMTRI drawings [7] was used as a reference, against

27
which all other dimensions of interest were scaled.

These engineering drawings are shown in Figures 18-23.
2.2.7. Hands and Feet

The skeletal hands and feet were modeled using
cylinders and cones to represent the bones. Basic
proportions were determined through study of skeletal
preparations and live subjects. The overall dimensions were
set to represent a glove size of eight, and a shoe size of
nine (Figure 24).

2.2.8. Positioning the Skeletal Model

For a computerized human model to be truly useful, it
must be capable of assuming any posture attainable by the
person it represents. Computer programs written in the I-
DEAL language [4] enable the operator to place this model
skeleton in any desired position, using as inputs:

1. TLC (Total Lumbar Curvature),
2. Coordinates for the heels and hands, and
3. Splay angles for the arms and legs.

Once the torso and limbs have been positioned,
information vital to designers of automobile interiors, such
as hamstring lengths, magnitudes of the knee joint angles,
distance between the elbows, and distance between the knees
in the selected posture can be provided as output. Further
discussion of these computer programs follows.
2.2.8.a. Lumbar Spinal Motion in the Skeletal Model

Using the basic conclusion of Haas [3] (that it is

acceptable to evenly distribute total lumbar curvature

28

 

 

 

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35
between the joints of the lumbar spine) in conjunction with

the assumption of a rigid thoracic spine from section
2.2.5.f., a computer program was written to facilitate
positioning the model spinal column. This program uses the
desired amount of total lumbar curvature (TLC) as input.
Spinal flexion (bending forward) is negative TLC, spinal
extension (bending rearward) is positive TLC. The program
first rotates all model components above the T12-L1
interspace about the T12-L1 joint center by one sixth the
desired TLC. During the next iteration, these components
plus the sphere representing the T12-L1 joint center are
rotated about the L1-L2 joint center. The process continues
for a total of six iterations. Appendix B contains the
entire text of this program, written in the I-DEAS language
[4].
2.2.8.b. The Limb Positioning Program
The basic algorithm of the program, repeated four times
to position all four limbs, is as follows:
1. Variables required for the mathematical manipulations are
named and initialized;
2. The Law of Cosines is used to determine the 3—D
coordinates of the knee joint or elbow in question;
3. The distal ends of the long bones are translated to their
chosen locations, and then rotated into their final
position;

4. The appropriate foot or hand is translated to its new

position;

36
5. Distances and angles of interest are calculated.

Appendix C contains the complete text of the Limb
Positioning Program, written in the I-DEAS language [4].
2.3. Rssults and Discussion for Skeleton

The model skull, pelvis, thorax, limb bones, hands and
feet, together with a series of spheres representing the
centers of the spinal joints, were assembled in the basic
driving posture depicted in the UMTRI [7] drawings. The
model skeleton of the average size adult human male shown in
Figures 25 and 26 was thus created.

This geometric computer model of the human skeleton,
hereafter referred to as BONEMAN, is capable of performing
the tasks for which it was designed. It can simulate any
posture attainable by a live human. Figure 27 shows two
views of BONEMAN in a typical driving posture, with the left
elbow resting on the window ledge, right hand operating a
console mounted shift lever, and the left leg splayed
outward in a relaxed manner.

Although based on relatively simple geometric shapes,
BONEMAN is easily recognizable for what it is, and
represents the morphology of the human skeleton well enough
to serve as a framework to which models of other organs may
be referenced.

The SAE 2-dimensional drafting template currently used
by seat designers forces the occupant to assume a forward
slumped posture and a flat lumbar spine. Because the

comfort of a seat depends greatly on the variety of postures

37

 

FULL SKELETALIMODEL - SIDE VIEW

FIGURE 25:

38

 

FIGURE 26: FULL SKELETAL MODEL - OBLIQUE VIEW

 

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FIGURE 27: AN ALTERNATE SKELETAL POSTURE

40
that can be adopted and the frequency and ease with which

they can be altered [18], this fixed lumbar curvature not
only results in lower back fatigue and discomfort during
long road trips, but also forces the occupant‘s shoulders to
press against the seat back in an unnatural manner (Figure
28). Even when attempts are made to incorporate proper
lumbar support into new designs, problems may remain. One
study of driver discomfort [19] concluded that although
firm, convex lumbar supports were initially rated as very
desirable by test subjects, seats so equipped were judged
extremely uncomfortable at the conclusion of a three hour
driving simulation. Often, the lack of tools which
adequately represent the various curvatures assumed by the
human spine during changes of position results in a "cut and
try" method of seat development in which prototype seats are
built and subjectively tested for comfort. Clearly, a more
efficient method of occupant depiction is needed by seat
designers.

Because of its ability to represent any degree of
spinal curvature (Figure 29), BONEMAN will give designers a
tool with which they may create seats with anatomically

desirable lumbar contours.

41

Point of Contact Between I,
Seat and Shoulder

    

Erect Surface Contour

SAE 2-D Seating Template Contour

FIGURE 28: POOR LUMBAR CURVATURE IN A.SEAT DESIGN

42

 

 

(1)

20 Degrees of Lumbar Flexion

(2)

Straight Lumbar Spine

(3)

20 Degrees of Lumbar Extension

FIGURE 29: DEPICTION OF SPINAL MOTION IN THE MODEL

3 . MUSCLE MODELING
3.1. Introduction

The complex shape of the human body is, in part, the
result of contours generated by hundreds of muscles. The
computer model should represent the musculature with
geometric simplicity, yet with sufficient fidelity to
provide body contours which are useful in representing body
interactions with seat contact surfaces. The objective of
this section was to explore how the body's muscle masses
might best be geometrically represented.

3 . 2 . Methods
3.2.1. The Major Muscle Groups

Once the skeletal components of the model have been
positioned in a desired posture, the locations of the boney
origins and insertions of the various muscles of interest
may be determined. If an accurate representation of body
contours is to be developed, models of important muscle
groups must be created and positioned relative to the boney
structures.

Study of cadavers, anatomical preparations, anatomy
texts [10,11,12] and live human subjects was again
undertaken to develop an understanding of how the various
muscle groups could best be portrayed in the computer model.
Tables 1 through 5 list major muscle groups which determine
the gross conformation of the human body. The locations,
origins, insertions, and functions of individual muscles are

43

44
Table 1. Muscles Which Extend the Thigh

Muscle Origin Insertion

QUADRACEPS GROUP

Vastus Medialis Linea Aspera of Patellar Tendon
Femur

Vastus Lateralis Greater Trochanter Patellar Tendon
of Femur

Vastus Intermedius Anterior Surface Patellar Tendon

of Femoral Shaft

Rectus Femoris Anterior Inferior Patellar Tendon
Illiac Spine (AIIS)

OTHERS

Sartorius Anterior Superior Medial Surface
Illiac Spine (ASIS) of Proximal

Tibia

MOST REPRESENTATIVE ORIGIN: Between A518 and AIIS
MOST REPRESENTATIVE INSERTION: Patellar Tendon
Note: Patella is to be modeled as an extension of the

proximal tibia due to the relatively constant distance
between the patella and the tibial crest.

45
Table 2. Muscles Which Flex the Thigh

Muscle Origin Insertion

HAMSTRINGS GROUP

Biceps Femoris, Linea Aspera Head of Fibula

Short Head of Femur

Biceps Femoris, Ischial Tuberosity Head of Fibula

Long Head

SemiMembranosus Ischial Tuberosity Medial Condyle
of Tibia

SemiTendinosus Ischial Tuberosity Proximal, Medial

Side of Tibia

MOST REPRESENTATIVE ORIGIN: Ischial Tuberosity

MOST REPRESENTATIVE INSERTION: Proximal Tibia / Fibula,
Midpoint in Lateral View.

Table 3. Muscles Which Flex the Shank

Muscle Origin Insertion

Gastrocnemius Femoral Condyles Calcaneus
(both heads)

Soleus Proximal Fibula Calcaneus
(Lateral Surface)

RATIONALE FOR MODELING: Since the gastrocnemius is the most
powerful of this muscle group, its
origin and insertion are used.

\

46

Table 4. Muscles Which Erect the Spine
(Sacrospinalis or Erector Spinae Complex)

Muscle Origin Insertion

LONGITUDINAL GROUP (Splits at L5)

 

 

Iliocostalis Illiac Crest and Angles of Ribs
sacrospinal and Transverse
aponeurosis of Processes of
Ribs 3—12. C4-C7.

Longissimus Sacrospinal Angles of Ribs
Aponeurosis and 1-7, Transverse
Transverse Process Process of C1-T12
C1-L2. and Mastoid of

Temporal Bone.

Spinalis Spines of T11-L2, Spines of
and C5-T2. T2-T4 and C2-C4.

TRANSVERSOSPINAL GROUP *

SemiSpinalis Cover 4-6 Vertebral Segments

Multifidi Cover 3 Vertebral Segments

Rotatores Cover 1 Vertebral Segment

* This group should be ignored in the modeling process, due
to the extremely short length of the muscles, and angles of
action at large angles to the plane of the 2-D model.

POSTVERTEBRAL MUSCLES Of the NECK

 

Obliquus Capitus Atlas Axis

Superior

Obliquus Capitus Axis Atlas

Inferior

Rectus Capitis Axis Occipital Bone

Posterior Major

Rectus Capitis Atlas . Occipital Bone
Posterior Minor

RATIONALE FOR MODELING THE ERECTOR SPINAE: This muscle
group includes members which originate on the illiac crest
and insert all along the spinal column, plus others which
originate at various levels along the vertebral column and
insert as high as the occipital bone of the skull. It is
therefore best modeled as originating at the iliac crest and
inserting on the skull, with attachments (pulleys?) to the
vertebral column at intervals in between.

47
Table 5. Muscles Which Flex the Spine

Muscle Origin Insertion

Iliacus * Iliac Fossa Lesser Trochanter

Psoas Major * Ll-LS Bodies Lesser Trochanter

Psoas Minor ** T12—L1 Bodies Illiopectineal
eminence

* These muscles should not be considered in the model as
their prime function is to flex the thigh.

** This muscle should not be included in the model because
of its small moment arm.

PREVERTEBRAL MUSCLES Of the NECK

Rectus Capitis Atlas Occipital Bone
Anterior
Rectus Capitis Atlas Occipital Bone
Lateralis
Longus Capitis Transverse Occipital Bone

Process C2-C6

Longus Colli Transverse C1-C6
Process of C3-T3

MOST REPRESENTATIVE ORIGIN: C2
MOST REPRESENTATIVE INSERTION: Occipital Bone

ABDOMINAL MUSCLES WHICH SERVE TO FLEX THE SPINE

Rectus Abdominus Xiphoid Process Pubic Symphysis
and Pubic Crest

External Abdominal Lower 8 ribs Anterior Illiac

Oblique ' Crest

Internal Abdominal Illiac Crest and Last 4 Ribs,

Oblique Inguinal Ligament Linea Alba, and
Pubis

RATIONALE FOR MODELING: Since the rectus abdominus is the

chief antagonist of the erector spinae group, its origin and
insertion should be used.

48

summarized. Graphical representations of the summarized

information are shown in Figure 30.

The following question was asked: Could adequate body
contours be generated by the computer if the various leg
muscles were modeled in groups? This approach would
simplify the modeling and save in development time, computer
processing time, and required computer memory.

3.2.2. Alternative Methods of Muscle Depiction
The SDRC IDEAS 3.8 GEOMOD [4] solid modeling software

used in development of the skeletal model allowed a choice

of two methods for depicting the muscle groups.

The first method was to represent the muscle groups as
ellipsoids. Advantages of this method were:

1. Ease of construction.

2. Relatively low required computer memory.

3. A constant volume assumption could be used to predict
muscle dimensions following a change in length. It was
shown before 1700 AhD. by numerous investigators [20]
that muscle volume changes very little during
contraction.

The main disadvantage of this method is that only

approximate muscle contours can be developed.

49

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The second available method for modeling the muscle

bellies was using a "skinning" technique, in which a series
of cross-sectional templates is developed. Spaced at
appropriate intervals along an imaginary axis, these
templates would then be "covered" by a computer generated
skin representing the muscle surface. The shapes thus
created could be as detailed as desired, but at the expense
of difficult, time-consuming construction and high use of
computer memory and time. Figure 31 graphically depicts
these two modeling methods. Representation of the muscle
groups as ellipsoids was the method chosen for use in the
model.

Most researchers investigating joint and muscle forces
have assumed that muscles act along straight lines from
origin to insertion, as such straight line models are
sensitive to both segment position and orientation [21].
Other investigators [22], comparing the accuracy of such
straight line models to that of models based on muscle belly
centroids, concluded "the numerical data for the particular
muscles examined showed a relatively small variation from
straight lines...". Therefore, each muscle group in this
model is represented by a single ellipsoid, its major axis
extending from a representative muscle origin to a
representative muscle insertion.

Two assumptions were made:

1. Total muscle volume = (4/3)(PI)(R1)(R2)(R3)would remain

constant, (where R1 = one half the muscle length, R2 =

51

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52
one half the muscle width, and R3 = one half the muscle

thickness) and,

2. Since seat designers will be most interested in a side
view of the model, muscle width (that muscle dimension
parallel to the Y axis) should also remain constant.
This second assumption is incorrect in a strict
biological sense, and may be replaced by a more
representative relationship between muscle width and
thickness in future versions of the model if deemed
necessary by users.

3.3. Muscle Modeling Results and Discussion
As evidenced by Figure 32, muscle modeling with

ellipsoids does produce contours easily recognizable as

those of the human leg; also, the problem of representing
individuals with differing degrees of muscularity is easily

handled by simply changing the selected muscle volumes. A

muscle volume adjustment was included in the program to

facilitate such changes; however, no attempt was made in
this study to represent any particular level of muscular
development.

Another advantage with this modeling approach is that
since muscle volume and width are held constant, anytime a
muscle shortens, it also gets thicker, or bulges, in a
realistic manner.

The uSe of ellipsoids (with major axes running between
muscle origins and insertions) to model major muscle groups

usually generates body contours which look realistic;

 

VIEWS OF THE MODEL LEG WITH MUSCLIS

FIGURE 32:

54
however, it should be noted that contours thus generated may

become distorted in extreme body postures. Because actual
tendons of origin and insertion may be forced to bend around
boney structures during changes in posture, the relative
positions of muscle bellies and skeletal structures change;
since a straight line connecting the origin and insertion of
a muscle group cannot simulate such tendon deformation [21],
modeling results in extreme postures may be compromised.

Figure 33.a is a hidden line plot generated for a
posture of extreme hip and knee joint flexion. It can be
readily seen that true anatomical relationships are lost in
this plot. The use of ellipsoids to represent muscle groups
results in the apparent burrowing of the Achille's tendon
through the tibia, as well as the passage of the quadraceps
muscle group through the distal femur.

Figure 33.b is the same posture as that in Figure 33.a,
but with manually simulated curvature in the quadraceps
tendon of insertion and the tendon of origin of the
gastrocnemius muscle. Clearly, more accurate representation
of the anatomy is generated; however, the automation of this
tendon curvature would be prohibitive in terms of increased
programming complexity and running time. It must therefore
be remembered by users of this model that body contours

generated in extreme postures may not be satisfactory for

seat design purposes.

55

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4.1MUSCLE LENGTH CONSTRAINT OF SKELETAL MOTION
4.1. Introduction

To be useful in the seating design environment, the
geometric model of the human body developed here must be
representative both in the configuration of its segments and
in the range of motion it permits between segments. In
order to assess the acceptability of a selected posture, a
method of predicting allowable combinations of joint angles
must be found.

The following hypothesis was proposed: Muscle lengths
impose limits upon what postures may be assumed by adults,
and, within any given individual, regardless of posture,
muscle length will not exceed a certain upper limit. The
findings of a study by Stokes and Abery [23] are consistent
with the hypothesis that the range of hip flexion permitted
by the hamstring muscles influences lumbar spine curvature
during sitting. Tension in the hamstring muscles
necessitates rotation of the pelvis to maintain comfort
[19,23]. Thus, if a limiting muscle length condition could
be shown to exist for the hamstrings, the mechanism which
makes the positions of the upper leg, lower leg, pelvis, and
lumbar spine interdependent could be accurately modeled.

A decrease in hamstring length necessitates a more
upright seated posture, e.g. people with shortened
hamstrings‘find it awkward to sit in low slung, reclining
seats. If the validity of such a limiting hamstring length
could be demonstrated experimentally, the computer programs

56

57
used to position the geometric model could utilize hamstring

muscle length as a criterion to orient the model's pelvis,

legs, and lumbar spine, and to judge the appropriateness of

any selected posture. Similar methods might also be used to
determine acceptable combinations of ankle and knee angles
as limited by gastrocnemius length, and to establish the
relationship between TLC and pelvic tilt as limited by the
length of the lumbar musculature.

The objectives of this investigation of limiting
hamstring length were to experimentally determine:

1. what combinations of measured knee and hip angles (Figure
34) are permissible within a given individual;

2. whether or not the range of these permissible angular
combinations is limited to a single body posture;

3. if the observed limitations in possible combinations of
hip and knee angles are due to a limiting length of the
hamstrings; and

4. if a simple four bar linkage might serve as a
satisfactory model of the limiting motions of the
pelvis, femur, hamstrings, and lower leg.

4.2. Experimental Methods

4.2.1. Biomechanics Evaluation Laboratory
All experimental data were collected at the

Biomechanics Evaluation Laboratory (BEL) of Michigan State

University. Basic data acquisition systems of the

'laboratory include three-dimensional motion analysis. All

data were collected on a SUN 4/260C workstation. This SUN

58

 

(I) - n19 ANGLE

(2) - KNEE ANGLE

FIGURE 34: RIP ANGLE AND KNEE ANGLE DEFINED

59
was networked with the A.E. Case Center for Computer-Aided

Design in the College of Engineering.

Motion of a body segment was measured by placing retro-
reflective spherical targets on anatomical landmarks. A
four camera 60 Hz Motion Analysis, Inc. system tracked the
trajectories of the targets in space, yielding three-
dimensional position data. A video processor identified
targets using the light reflected to the cameras. The
camera apertures were closed to increase target light
intensity relative to ambient light. The video processor
digitized target data in pixel space from all four cameras
in real time, and then transferred digital position data to
the SUN workstation. Direct Linear Transformation routines
from "EV3D" software were used to obtain three-dimensional
target coordinates. Every tenth frame of collected data was
analyzed.

4.2.2. Data Gathering and Analysis

Because the muscle origins and insertions of interest
are located on the boney skeleton, for any single skeletal
geometry, there can exist only one corresponding muscle
length. Therefore, it should be valid to study the skeletal
geometry in the limiting postures, which in turn would imply
the muscle length. This is not to imply that there can only
be one muscle circumference per skeletal posture. For
example, one can easily change the circumference of the
biceps muscle in the upper arm by contracting it while

maintaining a constant elbow angle.

60
4.2.2.a. Description of Exercises

To experimentally examine the maximum muscle length
hypothesis, four human subjects, whose physical
characteristics are listed in Table 6., were targeted with
adhesive reflective spheres in the following locations:

1. The highest point on the right illiac crest
The highest point on the left illiac crest

2
3. The spine of the first sacral vertebra

4. Right greater trochanter
5. Right lateral femoral epicondyle
6. Right fibular head

7. Anterior surface, proximal right tibia, approximately one
third the distance from knee to ankle
8. Anterior surface, distal right tibia, approximately two
thirds the distance between the knee and ankle.
Two of the subjects each had an additional target, number 9,
placed on the posterior midline of their right calf to
facilitate tracking rotation of the lower leg about the
tibial axis.
Table 6. Subject Data

Height(mm) 'Weight(Kgm) Age(years)

Subject 1: 287 82 47
Subject 2: 268 73 22
Subject 3: 264 75 44

Subject 4: 283 77 43

61
A "standing file" was created for each subject with the

subject standing erect, his right foot supported on a chair
at a height which produced approximately 90 degrees of hip
flexion (Figure 35). Following palpation and compression,
an estimate of the depth of soft tissue covering the right
ischial tuberosity was made. An additional target, number
10, was then placed on the buttock surface over the right
ischial tuberosity, and approximately 3 seconds worth of
data was collected while the test subject remained as
motionless as possible. The marker on the right ischeal
tuberosity was then removed. The spatial relationship
between the fixed pelvic markers (1,2, and 3) and the right
ischial tuberosity was thus determined, making it possible
to estimate the spatial position of the tuberosity whenever
the locations of the other three pelvic markers are known.

The volunteers performed two exercises which caused
them to reach their individual limits of hamstring stretch,
while simultaneous determinations of upper leg, lower leg,
and pelvis positions were conducted. The first experimental
exercise was designed to increase hamstring tension through
hip flexion, while the second exercise created hamstring
stretch by opening the knee angle. Muscle length would then
be estimated from these position studies.

The two experimental exercises were performed as
follows (Figure 36):
Exercise I: The test subject began by standing erect. He

slumped forward at the waist, keeping his knees

62

 

 

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64
straight, until hamstring tension prevented further

motion. The knees were then allowed to slowly bend

(the subject maintaining hamstring tension by

additional, simultaneous bending at the waist) until

the subject reached a "sitting on the heels" posture.
Exercise II: After completing Exercise I, the subject

straightened the knees as far as possible without

moving his head. After a short pause, the subject

maintained hamstring tension for as long as possible

while slowly returning to the erect posture.
These exercises were preceeded by a period of suitable
warmup stretching motions of the hamstrings and lower back
muscles to increase repeatability of the test runs. Each of
the four test subjects performed the sequence of exercises
three times, thus creating twelve sets of experimental
results.
4.2.2.b. Calculation of Muscle Lengths

The long head of the biceps femoris muscle was deemed
to be most representative of the hamstring muscle group
(Table 2), and its length, defined as the straight line
distance between its origin on the right ischial tuberosity
and insertion on the right fibular head, was used to
estimate the length of the entire right hamstring muscle
group.

The distance between the right hamstring origin and
insertion (ischeal tuberosity and fibular head,

respectively) was calculated as follows. Using the 3-D

65
spatial relationship between the right ischeal tuberosity

and the other three pelvic markers (1,2,and 3) established
in the standing file in conjunction with the known
coordinates of pelvic markers 1,2, and 3 during the
exercises, the spatial coordinates of the ischeal tuberosity
could be computed. Because the right fibular head was
targeted, its spatial coordinates were tracked. The
trigonometric distance between these two known points
(ischial tuberosity and fibular head) represented the
hamstring muscle length.

A three dimensional computer representation of each
subject's skeletal geometry was constructed by utilizing the
spatial coordinates of the skeletal markers developed in the
standing files (Figures 37 & 38). The I-DEAS software then
was used to manipulate these representations, by using the
known coordinates of the live subject's skeletal markers to
position the corresponding markers on the representations,
through motions duplicating those performed by the live test
subjects. In Figures 37 and 38, target locations shown as
circles were positioned in computer space using the
corresponding subject target coordinates. The locations
shown as squares were then calculated using known spatial
relationships from the standing files. The software also
simultaneously calculated the distance between the estimated

location of the ischial tuberosity and the coordinates of

the fibular head.

66

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68
4.2.2.c. Calculation of Limb Angles

Angular relationships between various skeletal

components were tracked as follows (Refer to Figure 39):

1. Vector A was defined as originating at the target located
on the distal right tibia and extending to the target
on the proximal right tibia, thus representing the
spatial orientation of the lower right leg;

2. Vector B was defined as originating at the right greater
trochanter and extending to the right femoral
epicondyle, thus representing the spatial orientation
of the right thigh;

3. Vector C was defined as originating at the upper midline
of the sacrum and extending to a point midway between
the high points of the right and left illiac crests,
thus creating the ability to track pelvic tilt in the
sagittal plane.

It should be noted here that the skeletal tracking was done

in a relative sense only - the exact position of the bones

in space was unknown due to possible uncertainty in
placement of the targets relative to boney landmarks.

Because the locations of the targets on the test
volunteers defined the tails and tips of these vectors, both
ends of all three vectors were tracked during the
experiment, making construction of the vectors possible for
each frame of data.

Hip Angle for the live subjects was defined as the

angle between Vectors C and B, while Knee Angle was defined

69

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70
as that angle which existed between Vectors B and A. The

magnitudes of these angles were determined using dot
products.

Graphs of Knee Angle versus Time, Hip Angle versus
Time, Hip Angle versus Knee Angle, and Muscle Length versus
Time were plotted for every tenth frame of data. The
resulting graphs were examined to determine if similar
limiting muscle lengths and angular relationships existed
for both exercises, both within each subject and between
subjects.
4.2.2.d. Link Length Variations

Examination of the experimental data revealed that the
apparent distances between targets mounted on the same boney
structure varied considerably. To eliminate this
complication, a nominal length for each skeletal segment
(femur, tibia, and pelvis) in each subject was determined
using the data in the standing files (each segment length
was calculated in the first ten frames of standing file
data, and the results averaged).

The tibial, femoral, and pelvic segments may be thought
of as three links in a four bar linkage, with the hamstring
muscles representing the fourth link (Figure 40). Equations
predicting the relative relationships of the four links are
readily available [24]. As is depicted in Figure 41, the
definition of Hip Angle in the linkage equations differs

from that used in the laboratory. It was thus necessary to

71

'D
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5.

_ Pelvis
Slack Hamstrings

”No Tension Situation"
Linkage Equations Do Not Apply

613

T
aut Hamstrin
9s Pelvis

"Limiting Tension Situation"
Linkage Equations Do Apply as Long
as Limiting Tension is Maintained

FIGURE 40: THE PELVIS AND TRIGR.AS.A FOUR BAR LINKAGE

72

 

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73
convert the Laboratory Hip Angle to equivalent Linkage Hip

Angles by using the following relationship:
LABORATORY HIP ANGLE + PELVIC CONSTANT = LINKAGE HIP ANGLE,

where the Pelvic Constant is the angle between Vector C and
Vector D, which extends from the right greater trochanter
(the greater trochanter of the femur is commonly used in the
automotive seating design industry to estimate the location
of the hip joint center) to the right ischial tuberosity.
The value of the pelvic constant is thus specific to each of
the test subjects.

The nominal skeletal segment lengths were utilized
along with the experimentally determined knee angles and the
converted hip angles as input to a four bar linkage equation
(Appendix D) which was used in an iterative manner to
predict the length of the fourth segment, that representing
the hamstring muscle length. The corrected hamstring lengths
thus calculated were plotted against time.

In an attempt to determine the ability of the geometric
model developed in the previous sections of this thesis to
predict trends in the hamstring lengths of live humans, a
computer program (Contained in Appendix E) was written which
would cause the model to duplicate the experimental
exercises performed by the human volunteers. Because this
program uées pelvic, hip, and knee angles as input, it was
possible to use the known angular data from the human

experimental subjects as input, thereby causing the computer

74
model to recreate the motions of the live test subjects

(Figure 42).

The model's hamstring length (the straight line
distance between the model's ischial tuberosity and fibular
head) was calculated for each posture of interest, so that
trends in the model's hamstring length could be compared to
those generated in the human trials. Using the models
dimensions in the linkage equations, a composite plot was
created which shows what combinations of knee angle and hip
angle are possible for a variety of hamstring lengths
(Figure 43).

The twelve corrected muscle length versus time graphs
were examined to determine what data points corresponded to
an approximately constant muscle length. The corresponding
data points from the knee angle versus hip angle plots were
superimposed on the composite plots in an attempt to gage
the correlation between theoretically acceptable angular
combinations and those actually observed in the laboratory.

In summary, three different types of hamstring lengths
were computed for each set of human subject motion data:

1. Hamstring length for each frame of subject body position
data based on target positions on the pelvis and lower
leg (hereafter referred to as Muscle Length),

2. Hamstring length for each frame of data based on hip
angle, knee angle, and average lengths of the pelvic,
femoral, and tibial links, (hereafter referred to as

Corrected Muscle Length), and

 

8 THE LABORATORY EXERCISES

THE MODEL DOE

FIGURE 42:

76

Knee Angle
(Degrees)
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FIGURE 43: HAMSTRING LENGTH RELATED TO JOINT ANGLES

77
3. Hamstring lengths in the model which correspond to the

pelvic and knee angles measured in each frame of
subject body position data (hereafter referred to as
Model Muscle Length).
4.3. Muscle Length Results and Discussion
Nominal link lengths and pelvic constants (both defined
in Section 4.2.2.), determined using target data from the
standing files (Section 4.2.2.) via dot products, were as

follows: (Also See Figures 44 through 47).

Table 7: Nominal Link Lengths(mm) and Pelvic Constants(deg)

Tibia Femur Pelvis Pelvic constant
Subject 1: 53.7 369.3 218.0 68
Subject 2: 48.2 407.4 145.5 59
Subject 3: 47.0 350.7 124.2 73
Subject 4: 87.6 363.4 142.1 79

The fact that the pelvic links were relatively much
longer when compared to their corresponding femoral links in
the test subjects than they were in either the geometric
model or the UMTRI drawings (Table 8), supports the
supposition that the method of estimating the depth of soft
tissue over the ischial tuberosity probably included some
errors. In retrospect, some soft tissue thickness was

likely included during the determination of pelvic segment

lengths.

 

 

 

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FIGURE 47: VARIATIONS IN SKELETAL LINK LENGTHS, SUBJECT 4

82
Table 8. Link Length Ratios by Subject

Tibia/Femur Ratio Pelvis/Femur Ratio
Subject 1: .146 .590
Subject 2: .118 .357
Subject 3: .134 .354
Subject 4: .241 .391
Model: .198 .178
UMTRI: .119 .224

4.3.1. Experimental Results in Graphical Form

The Knee Angle versus Time, Hip Angle versus Time, Knee
Angle versus Hip Angle, and Muscle Length versus Time graphs
prepared from the raw laboratory data are presented in
Figures 48 through 59.

Using the graphs in Figure 54 as being representative,
we see that the following events occurred during a typical
pair of exercises. The subject began Exercise One just
before data recording began; thus, the hip angle begins at a
value smaller than that observed during normal stance at the
end of the trial. The hip angle decreased rapidly at the
start of Exercise One due to bending at the waist. It
continued to do so until hamstring stretch prevented furthur
bending at about 1.5 seconds. The hip angle then remained
constant until 3 seconds as the subject discovered he could
bend no further at the waist. At 3 seconds, the knees began
to bend. The decreasing knee angle relieved hamstring

tension, thus allowing the hip angle to again begin

83

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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0 Time in seconds 10 0 Time in seconds 10

Note: Angles in degrees, Length in millimeters

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-—-—.. ..-- ...... -..—.....- __ T __ _ ._ _ -.. __ - -
“‘“’ “*‘“"*— “ " H _ ___ - _ _-____

0 HIP ANGLE 90 0 Time in seconds 10

FIGURE 48: UNPROCESSED EXPERIMENTAL DATA, SUBJECT 1, TRIAL 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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FIGURE 49: UNPROCESSED EXPERIMENTAL DATA, SUBJECT 1, TRIAL 2

 

 

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FIGURE 50: UNPROCESSED EXPERIMENTAL DATA, SUBJECT 1, TRIAL 3

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FIGURE 53: UNFROCESSED EXPERIMENTAL DATA, SUBJECT 2, TRIAL 3

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FIGURE 54: UNPROCESSED EXPERIMENTAL DATA, SUBJECT 3, TRIAL 1

 

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FIGURE 59: UNPROCESSED EXPERIMENTAL DATA, SUBJECT 4, TRIAL 3

 

95
decreasing as the subject bent forward at the waist while

attempting to maintain a constant hamstring tension. Both
knee and hip angle continued to decrease simultaneously
until minima were reached at approximately 4 seconds, when
Exercise Two was begun. Between 4 and 5 seconds, the knees
straightened while hip angle remained approximately
constant, again producing a limiting tension in the
hamstrings. The subject now was forced, due to this
hamstring tension, to increase hip angle as he straightened
his knees, reaching the straight knee position at just under
6 seconds. At this time, the subject made a small effort to
again decrease his hip angle, but, finding he was close to
his limit, quickly stood up and arched his back, thereby
overshooting his standing posture. This overshoot caused
the hip angle to reach its maximum value approximately 9
seconds into the test, after which it slowly decreased to
its value in normal stance.

The Knee Angle versus Hip Angle graph, beginning at the
upper right and moving left, shows that the hip angle
decreased independently of knee angle during the early parts
of the trial. Hip angle and knee angle then become coupled,
as is evidenced by the change from a horizontal line to the
section with an almost linear slope. The two vertical
portions of the graph indicate that knee angle was
independent of hip angle during the middle of the trial.

The two angles again became coupled for a time, after which

hip angle varies independently until trial's end.

96
The Muscle Length versus Time graph shows that the

muscle length computed from target locations did, indeed,
reach a maximum during each exercise, the second maximum
being slightly longer than the first.

The Corrected Muscle Length versus Time graphs,
prepared from the data after correction for apparent
variations in segment lengths, are presented in Figures 60.a
through 63.a.

4.3.2. Error Estimation

Since the angular data generated by the live test
subjects was used to drive BONEMAN, any error in the angle
calculations would directly affect the accuracy of the
model's performance. Because the vectors used to measure
the desired angles were based upon the target locations, the
most likely source of angular error would be inaccurate
position estimates for the targets. A technique for
estimating the largest likely error for the knee and hip
angles is presented in Appendix F. The result of such error
analysis is that the largest probable error in Hip Angle and
Knee Angle are 1.9 degrees and 2.5 degrees, respectively.

Examination of the Corrected Hamstring Lengths
presented in Figures 60.a through 63.a shows that each
subject reached two local maxima in muscle length during
each trial. The first maximum occurred due to hamstring
stretch created by pelvic tilt during Exercise One; the
second resulted from hamstring stretch caused by knee

extension during Exercise Two. This suggests that there

97

     

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

600 tug ""1 _”u ” 600
L .. L - -._ -._- _
E E .__- _“_ ._,
N Trial N
G One G “" '*-'--- -~— -—-
T _-l_ ....... ___ _ _ T —_—. -._»...2 ....... .i
H ..- H ..- ._._ .. --
0 Time in seconds 10 0 Time in seconds 10
600 ._fl -1-..-: g. 600 ““'*““"“""" "'
_____ V- ......
L L
E E """" "
N Trial N *‘“'""‘"“““‘”'““* ““_‘
G ‘ Two G
T ..... ... ' T
H -_ .. .. ._ H
0 Time in seconds 10 0 Time in seconds 10
600 . “...-.. ...-u- —-.--.. .-.... . 600 Vi; --—-—-:-.__,I ;1 .. ...-...;
L L .---
E E ___ 1
N Trial N "’
G Three G “‘ ‘ “
T __________ __“ ___-_ __ T ._._. .._. ._._. . .1
H _____ ~_____ ____ .__ H --.. ._._. .._... l .-
0 Time in seconds 10 0 Time in seconds 10
(a) Corrected Muscle Lengths (b) Model Muscle Lengths

Note: Muscle lengths are in millimeters
FIGURE 60: CORRECTED VRS. MODELIMUSCLE LENGTHS, SUBJECT 1

600 _;m.;m_:. ”--th win 600 QQL:

Trial
One

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Trial
Two

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0 Time in seconds 10 0 Time in seconds 10

 

600 . f' '.; 7iQI " 600i ' "m"

 

 

Trial
Three

 

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no. —0 m on--- - - - h - _ -.o—_v _-.- - -
—.—-— ——-. - - .- _—- _ -_- .--.—
——- -._— --—- ._- ..-. .. —.- -
-

 

 

 

0 Time in seconds 10 0 Time in seconds 10

(a) Corrected Muscle Lengths (b) Model Muscle Lengths
Note: Muscle lengths are in millimeters
FIGURE 31: CORRECTED VRS. MODEL MUSCLE LENGTHS, SUBJECT 2

99

600 m.u_.wm..u,r q_“ _ 600 .;rlm :::~ -:
L kggWM;(w\\ , L n

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N '”""' ' “ \“4_ Trial N ”

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600 '"“”"' 600

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-‘.—.. -.

 

0 Time in seconds 10 0 Time in seconds 10

—.—-- ... ...._—- ..--.0

60° :; if”‘:t:“'ii ' 60° _. I. . (”:1;

/f ‘5/1. *\
.. I -- .. .-.. .- . .-. Trial

-“m.nu_..mm. .u . Three

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0 Time in seconds 10 0 Time in seconds 10

(a) Corrected Muscle Lengths (b) Model Muscle Lengths
Note: Muscle lengths are in millimeters
FIGURE 62: CORRECTED VRS. MODEL MUSCLE LENGTHS, SUBJECT 3

cm .W. . W. . 100
600_ mu I”. h, 600 . m .u. .m-“ r

 

Trial

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Trial
TWO

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0—0‘

0 Time in seconds 10 0 Time in seconds 10

(a) Corrected Muscle Lengths (b) Model Muscle Lengths
Note: Muscle lengths are in millimeters
FIGURE 63: CORRECTED VRS. MODEL MMSCLE LENGTHS, SUBJECT 4

 

101
was, indeed, a limiting muscle length reached by each of the

test subjects. In most instances, the second local maximum
was higher than the first, making it clear that this
limiting muscle length is not strictly constant within a
given individual, but one that can change not only between
exercises, but also during the same exercise. This
observation is consistent with Atha and Wheatly [25] who
found that repeated performance of a similar test improved
the range of hip flexion.
4.3.3. Model Predictions Evaluated

Comparison of Corrected Muscle Length data generated by
the live subjects with the corresponding Model Muscle Length
predictions (Figures 60.b through 63.b) shows that in the
majority of exercises, the trends in muscle length of the
live subjects are closely followed by the computer
predictions. The local maxima and minima, inflection points
and overall shape of the curves generated by the test
subjects are reflected in the curves generated by the model.
The conclusion is that, given adequate angular input, the
model will qualitatively duplicate what actually happens to
muscle length in live subjects. It will not, however,
because of differences between subject and model link
lengths, predict actual muscle length. This shortcoming
will not prevent the model from performing its primary duty,
which is the generation of lifelike body contours.

Figures 64 through 67 are composed of apropriate

sections of the composite plot described in Section 4.2.2.,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K
N
E
E
TRIAL l
A
N
G
L
E
50 Note: All
angles in
180 degrees.
K
N
E
E -
W
A
N
G
L
E
50
180
K
N
E
E
TRIAL 3
A
N
G
L
E
0 HIP ANGLE 50

FIGURE 64: EXPERIMENTAL.RNGLES COMEARED TO TBEORI, SUBJECT 1

BJL'WDZ.’ 513327:

    

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TRIAL 1

525;: All
angles in
degrees.

TRIAL 2

TRIAL 3

FIGURE 65: EXPERIMENTAL ANGLES COMPARED TO THEORX, SUBJECT 2

 

 

 

 

 

 

 

   

180

K

N

E

E

TRIAL 1

A

N

G

L

E

50 Note: All
angles in

180 degrees.
K

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TRIAL 2

A

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L

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HIP ANGLE 50

180 'I VI:

   

 

 

 

 

 

 

 

....-- .._ . EBB-2.2
A ' - . -. .
L .. -. ..
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0 HIP ANGLE 50

FIGURE 65: EXPERIMENTAL ANGLES COMPARED TO THEORI, SUBJECT 3

151m

 

 

 

 

 

 

 

 

0 HIP ANGLE 50 Note: All
angles in
degrees.

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FIGURE 67: EXPERIMENTAL ANGLES COMPARED TO THEORY, SUBJECT 4

106
upon which have been superimposed those portions of the live

subjects' Knee Angle versus Hip Angle graphs which
correspond to the times during which approximately constant
muscle lengths were observed. Since each trial consisted of
two exercises, and one period of "constant" muscle length
occured during each exercise, two segments of interest were
generated during each of the twelve trials. It can be seen
that there is a consistent tendency for the superimposed
portions to parallel the lines of the composite plot,
leading to the conclusion that the combinations of Knee
Angle and Hip Angle observed in the laboratory were, indeed,
the result of a limiting constant length of the hamstring
musculature. Because of this, it should be possible to use
such a composite plot to determine permissible angular
combinations for any given hamstring length, or conversely,
to predict what muscle lengths will allow a given
combination of knee and hip angles. Thus, this composite
plot does much to explain the limits on human flexibility.
4.3.4. Discussion

Knowledge of the relationship between Knee Angle, Hip
Angle, and Hamstring length will allow designers to work in
the following ways to predict the adequacy of a new seat
design before expensive prototypes are built. If the
product is intended for a certain target market, i.e.,
purchasers of luxury cars, compact cars, or sports cars,
consideration of factors such as age and physical condition

of the typical person purchasing that class of vehicle may

107
be used to predict the range of hamstring stretch and joint

angle combinations likely to be found desirable by the
buyer. If the goal is to accomodate as many people as
possible, the model could be used to predict whether or not
the new seat would be comfortable for a large segment of the
population. Considerable variation in the range of
hamstring-limited hip flexion, unrelated to sex, age, work,
or leisure activities [18] exists in the healthy adult
population. Consistent use of the model in this manner

should contribute to a more complete understanding of such

variations in hip flexibility.

5. CONCLUSION

The three specific goals of this work have been
accomplished.

A skeletal model (BONEMAN) has been developed which
incorporates torso mobility as developed by Haas [3] and
adds legs, shoulders, and arms which can be positioned to
represent all body postures of an average adult male. Thus,
BONEMAN will be useful in the representation of driving
postures.

Addition of muscles to BONEMAN has been studied, and
the use of ellipsoids to model muscle groups will, when
properly used in conjunction with the skeletal model,
produce computer simulated body contours useful to designers
of automobile seats.

The role played by the hamstring muscle group in the
limitation and interdependence of knee angle and hip angle
has been described in this thesis. Because the
straightening or reversal of lumbar lordosis during sitting
is also related to hamstring tightness [18], with tight
hamstrings limiting the amount of lordosis attainable for a
specified knee angle, an immediate goal for future research
should be the determination of the relationship which exists
between TLC and hamstring length.

The level of constraint placed by other muscle groups
upon joint ranges of motion throughout the body, such as
gastrocnemius length limiting combinations of knee and ankle

108

109
angles, or the lumbar muscles and fascia influencing lumbar

curvature, should be explored in future work.

The area of deflection of body contours by surface
contact forces must be investigated if the model is ever to
predict body/seat interface contours. All this information
must also be applied to models of other sizes of people,
such as the small woman and large man.

The tasks completed in this thesis, i.e., the
representation of skeletal and muscle geometry, and the
description of the influence of hamstring muscle length on
body position, are important steps in the development of new

representations of humans for use in product design.

APPENDICES

APPENDIX A

Spinal Joint Center Coordinates

For the coordinates, CPI) indicates a cervical point. Each
interspace is represented by three numbers. The first
number is the X coordinate, the second number is the Y

coordinate, and the third number is the z coordinate.

ALL COORDINATES ARE IN MM

These are the coordinates for the Cl/SKULL interspace
(occipital condylar axis)

cp(1)=-213

CP(2)=0

cp(3)=612

These are the coordinates for the Cl/CZ interspace
cp(4)=-213

CP(5)=0

cp(6)=602

These are the coordinates for the C2/C3 interspace
cp(7)=-207

CP(8)=0

cp(9)=586

These are the coordinates for the C3/C4 interspace
cp(10)=-204

cp(11)=0

cp(12)=571

These are the coordinates for the C4/C5 interspace
cp(13)=-201

cp(14)=0

cp(15)=551 -
These are the coordinates for the C5/C6 interspace
cp(16)=-200

cp(l7)=0

cp(18)=532

These are the coordinates for the C6/C7 interspace
cp(19)=-203-

cp(20)=0

cp(21)=511

These are the coordinates for the C7/T1 interspace
cp(22)=-210

cp(23)=0 '

cp(24)=493

110

111

For the coordinates, tp() indicates a torso point. Each
interspace is represented by three numbers. The first
number is the X coordinate, the second number is the Y
coordinate, and the third number is the Z coordinate.

ALL COORDINATES ARE IN MM

These are the coordinates for the C7/T1 interspace
tp(l)=-210

tp(2)=0

tp(3)=493

These are the coordinates for the T1/T2
tp(4)=-218

tp(5)=0

tp(6)=476

These are the coordinates for the T2/T3
tp(7)=-226

tp(8)=0

tp(9)=459

These are the coordinates for the T3/T4
tp(lO)=-231

tp(11)=0

tp(12)=440

These are the coordinates for the T4/TS
tp(13)=-237

tp(14)=0

tp(15)=421

These are the coordinates for the TS/TG
tp(16)=-242

tp(17)=0

tp(18)é395

These are the coordinates for the T6/T7
tp(19)=—241

tp(20)=0

tp(21)=367

These are the coordinates for the T7/T8
tp(22)=-238

tp(23)=0

tp(24)=339

These are the coordinates.for the T8/T9
tp(25)=-232

tp(26)=0

tp(27)=311

These are the coordinates for the T9/T10
tp(28)=-225

tp(29)=0

tp(30)=281

112

These are the coordinates for the TIO/Tll
tp(3l)=-217

tp(32)=0

tp(33)=251

These are the coordinates for the Tll/T12
tp(34)=-207

tp(35)=0

tp(36)=219

These are the coordinates for the T12/L1 interspace
tp(37)=-194.1

tp(38)=0

tp(39)=189.2

For the spinous process points, sth) represents a spinous
process point. The first number is the X coordinate, the
second number is the Y coordinate, and the third number is

the z coordinate.

ALL COORDINATES ARE IN MM

These are the coordinates for T1
stp(1)=-270

stp(2)=0

stp(3)=462 .
These are the coordinates for T2
stp(4)=-277 ,
stp(5)=0

stp(6)=437

These are the coordinates for T3
stp(7)=-285

stp(8)=0

stp(9)=410

These are the coordinates for T4
stp(10)=-293

stp(11)=0

stp(12)=380

These are the coordinates for T5
Stp(13)=f297

stp(14)=0

stp(15)=352

These are the coordinates for T6
stp(16)=-300

stp(17)=0

stp(18)=325

These are the coordinates for T7
stp(l9)=-295

stp(20)=0

stp(21)=285

These are the
stp(22)=-284
stp(23)=0
stp(24)=253
These are the
stp(25)=-277
stp(26)=0
stp(27)=225
These are the
stp(28)=-265
stp(29)=0
stp(30)=192
These are the
stp(31)=-255
stp(32)=0
stp(33)=165
These are the
stp(34)=-246
stp(35)=0
stp(36)=146

113

coordinates

coordinates

coordinates

coordinates

coordinates

for

for

for

for

for

T8

T9

T10

T11

T12

114

For the coordinates, lpI) indicates a Lumbar point. Each
interspace is represented by three numbers. The first
number is the X coordinate, the second number is the Y
coordinate, and the third number is the z coordinate.

ALL COORDINATES ARE IN MM

These are the coordinates for the T12/Ll interspace
lp(1)=-194.1

19(2)=0

lp(3)=189.2

The coordinates for the Ll/L2 interspace
1pI4)=-l73.7

19(5)=0

lp(6)=160

The coordinates for the L2/L3 interspace
lp(7)=-152.9 -
lp(8)=0

lp(9)=130.3

The coordinates for the L3/L4 interspace
lp(10)=~130.0

lp(11)-0

lp(12)=98.7

The coordinates for the L4/L5 interspace
lp(13)=-110

lp(14)=0

lp(15)=69

The coordinates for the LS/Sl interspace
lp(16)=-89

lp(17)=0

lp(18)=39.

APPENDIX B

Lumbar Spinal Motion Program

This program produces the desired lumbar curvature in
the 50% male model, using total lumbar curvature as input.
Spinal flexion is negative, extension is positive.

Curvature is equally divided among the relevant spinal
joints.

: declare variables 8 read in total Iumbar curvature:

Iecho none

ldeclare angle(lI

linput"What is desired TLC?" angle
langle-angle/S

12

-l94.1 0 189.2
0 -angle 0

NXXRXRXNXXNXXXNXCOOOOOOOOOXXfiXXOOOXXXDfiOOO

N
(a)

115

XX

XOCOOCOOCOOXXXXNOOC'UXXXXXXXXXXNXXXXXOOOOOOCOOOXXX NOCC

—173.7 0 160
0 -angle 0

NXXXNXXXXXXXX

7:XXRCOO'UXX}:XXXNXXXXXXWXXOOOOOOOCOOXXXXXXOO

117

me

K
~152.9 0 130.3
0 -angle 0

rotate components about L3-L4:

~130.8 0 98.7
0 -angle 0

XXXXOOOOOOOOOOXXXXXXXXOOO'UwRXXR xxxxxxxxxxXCCQCOOCCCCXNX

118

..............................

EXXOOOxXXXXXXXXXXX

_119

0 -angle 0

ééfiA'éii ......................
/

APPENDIX C

Limb Positioning Program

This program positions the limbs of the 50% male model
in 37D space, using as inputs: a) the desired heel and hand
coordinates, and b) any desired splay angles for the

extremities. Hamstring length and knee angle are provided
as output.

XXXOOOOOXXXROXWXXXXXXXXXZXXXXXXXXXXOOOX

lecho none

OOOOOOOOOOOOOOOOOOOOOOOOOOOOO 0...... O

declare variables to move the right leg:

lDeclare RHeelIB)

lDeclare Rendpoint(3)

lDeclare RHipI3)

lDeclare Rlength(l)

lDeclare RInsertI3)

IDeclare Rstretch(1)

{Declare Rhng7I1)

lDeclare RSplayang(1)

lDeclare RellIl)

lDeclare RAnglIl)

lDeclare RAng3(1)

lDeclare RAngd(1)

[Declare RAngGIl)

lDeclare RKnee(3)

lDeclare Ra(1)

lDeclare Rb(1)

[Declare Rc(l)

lDeclare Rd(1)

lDeclare Re(l)

lDeclare-Rangle(1)

lDeclare Rhand(3)

IDeclare Rarmsplay(1)

Input for the rite side of the body

l1nput"Enter desired right hand coordinates” Rhand
lInput"Enter desired right heel point coordinates" RHeel
lInput"Enter desired right leg splay angle" Rsplayang
|Input"Enter desired right arm splay angle” Rarmsplay

Crunch the Numbers to locate the right knee :
( Other "crunch" sections below follow same logic ) :

Convert heel position to ankle joint position
lRHeel(1)-RHeel(l)-15.03

lRHeel(2)nR"eel(2)+.6

lR"eel(3)-Rfleel(3)+60.67

120

.121

: Initialize hip joint coordinates

° {Rhip(1)-0 .

lRHipI2)--81

IRHip(3)-0

. Determine distance between hip and ankle
: lRaaRhee1(1)-RHip(l)

: lRa-Ra*Ra

: le=Rhee1(2)—Rhip(2)

leaRb*Rb

ch-Rheel(3)-Rhip(3)

ch=Rc*Rc

lREll=sqrt(Ra+Rb+Rc)

If the specified heel is to far from the hip, abort the run
lIf (REll GT 870) then GOTO abort '
Use law of cosines to determine knee coordinates
lRAng3wasin((RHipI3)—Rheel(3))lRell)

: lRAngl-acos((-19229.6+(Rell*Rell))/(852.4*Re11))

: lRAng4=RAngl~RAng3

: IRAng6=asin((Rheel(2)-Rhip(2))lRell)

: lRAng7-90—RAn96

' lRKnee(1)-(426.24*cos(Rang4)*cosIRang6))+Rhip(1)
IRKnee(2)-(426.24*cos(Rangd)*sin(RangG))+Rhip(2)
lRKnee(3)-(426.24*sin(Rang4))+Rhip(3)

Locate the insertion of the hamstrings
IRd=Rknee(3)-Rheel(3)

lRangS=asin(Rd/439.8) ‘
lRInsert(l)nRheel(l)-((375*cos(RangS))fisin(Rang7))
IRe=(375*cos(RangS))
lRInsert(2)=RHee1(2)—(Re*cos(RAng7))
lRInsert(3)-RHeelI3)+(375*sin(RangS))

OXFIXO

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

58
R

706.95 ~119.0 -201.33
k

RHeel(1) RHeel(2) RHeel(3)

xxxxxxxxnnnxxxxzxxxxonnxxxmxxx20xxxxxxxxoxoxxxxxxx
\

Rhip(l) Rhip(2) Rhip(3)
k

122

404.1 -122.47 129.1
k
Rknee(l) Rknee(2) Rknee(3)

RHeel(l) RHeel(2) RHeel(3)
k

(RHee1(1)-302.85) (Rhee1(2)-3.47) (Rhee1(3)+330.43)
k

E RKnee(l) Rknee(2) Rknee(3)

706.95 -119.00 ~201.33
3 Rhee1(l) Rheel(2) Rhee1(3)
é5i59'éhg';ité ieé :

.57
=9
- k

Rhip(l) Rhip(2) Rhip(3)

k

: Rheel(1) Rhee1(2) Rhee1(3)
: k
: Rhip(l) Rhip(2) Rhip(3)
' r

. Rsplayang

: ab
h
. 58
3 P
- k

Rhip(l) Rhip(2) Rhip(3)

k

Rheel(1) Rhee1(2) Rheel(3)
k

RheelIl) Rheel(2) Rheel(3)
r

Rsplayang

xxxxxxxxxxxxxxx'xxxxxxxxzxxvonoxxxxxxxxxnnnxxxxxxx'xxnonxxx

Declare variables to move the left

lDeclare
{Declare
lDeclare
lDeclare
lDeclare
{Declare
IDeclare
lDeclare
{Declare
[Declare
lDeclare
lDeclare
lDeclare
{Declare
lDeclare
lDeclare
{Declare
IDeclare
IDeclare
lDeclare
IDeclare
IDeclare

leg:

Lheel(3)
Lendpoint(3)
Lhip(3)
Llength(1)
Linsert(3)
Lstretch(l)
Lang7(1)
LsplayangIl)
Lell(l) ‘
Langl(l)
Lang3(l)
Lang4(1)
Lan96(l)
Lknee(3)
La(1)

Lb(1)

Lc(l)

LdIl)

e(l)
Langle(l)
Lhand(3)
LarmsplayIl)

XXZXXXXXXXXXXXXXXXXXXCOOXNXXONXXXXXXXXXNXXXXXXXXXXXVGOC’

Input for the left side of the body

lInput"Enter desired left hand coordinates” Lhand
IInput"Enter desired left heel coordinates" Lheel
lInput"Enter desired left leg splay angle” Lsplayang
lInput"Enter desired left arm splay angle” Larmsplay

..........................................

{Lfleel(1)~LHeel(l)-10

lLHeel(3)-LHeel(3)+60

thip(l)-O

thip(2)-81

thipIBI-O

lLa-Lheel(1)-Lhip(l)

lLa-La*La

ILb-Lheel(2)-Lhip(2)

ILbaLb*Lb

cheLheelI3)-Lhip(3)

chaLc*Lc -

ILell-sqrt(La+Lb+Lc)

IIf (Lell GT 900) then GOTO abort
lLang3-asin((Lhip(3)-Lheel(3))lLell)
lLanglaacosI(19217+(Lell*Le11))/(922.26*Lell))
lLangd-Langl-LangB
lLang6=asin((Lheel(2)-Lhip(2))/Lell)
lLang7890~LangG
lLknee(l)-(461*cos(Langd)*cosILangG))+Lhip(l)
lLkneeIZ)-(461*cos(Langd)*sin(LangG))+Lhip(2)
lLkneeIBI-(46l*sin(Langd))+Lhip(3)

1,24

lLdstneeI3I-Lheel(3)
lLangS-asin(Ld/439. 8)
lLinsert(l)-Lheel(l)- (375*cos(LangS))
le=(330*cos(LangS))
IIinsert(2)-Lhee1(2)-(e*cos(Lang7))
lLinsert(3)-Lheel(3)+(375*sin(LangS))

: mt
h
56
k

714 119.6 -206
k

Lheel(l) Lheel(Z) Lheel(3)

Lhip(l) Lhip(2) Lhip(3)
(Lhip(1)+440) 122.5 (Lhip(3)+138)

Lknee(l) Lknee(2) Lknee(3)

OOOOOOOOOOOOOOOOOOOOOOOOOOOOO

: Lheel(l) Lheel(Z) Lheel(3)
' k
(Lheel(l)—274) (Lheel(2)+3.5) (Lheel(3)+344)
k .

Lknee(l) Lknee(2) Lknee(3)

: 714 119.6 -206
' k
Lheel(l) Lheel(Z) Lheel(3)

xxxxxxxxxnnnxxxxxxxxXOOOXXXXZXXXXXXCOOXXXXXXXXXOOOZXXDEXX

.125

IGOTO stop2
Istop:
Iarm:

ab
h
. 55
3 P
- k

Lhip(l) Lhip(2) Lhip(3)

k .

Lheel(l) Lheel(2) Lheel(3)
k

Lhip(l) Lhip(2) Lhip(3)

r

—l*(Lsplayang)

ab

h

56

P

k

Lhip(l) Lhip(2) Lhip(3)

k

: Lheel(l) Lheel(2) Lheel(3)
: k '
: Lheel(l) Lheel(2) Lheel(3)
: r

: -1*(Lsplayang)

. {Declare Rshlder(3)
: lDeclare Rwrist(3)
- {Declare Relbow(3)
. lDeclare RfIl)
: {Declare Rg(1)
' IDeclare Rh(l)
lDeclare Ri(1)
lDeclare Rj(l)
ODeclare Rk(1)
{Declare R1(1)
CDeclare RAngldIl)
lDeclare RAngll(1)
IDeclare RAnngIl)

lDeclare RAnglG(l)
lDeclare Rfland(3)

..............................................

IRshlder(l)- -214
lehlder(2)-—l79
lehlderI3)-418

XXXOOCXZ‘XXX“XXXXXZXXXOOOXXXXXZXXXIXXXXXXXXXXXXXDExXOOOOOO

126

IRwrist(l)-Rhand(1)-63

IRwrist(2)=Rhand(2)

lRwrist(3)eRhand(3)-30

. IRE-Rwrist(1)-Rshlder(l)

: le=Rwrist(2)-Rshlder(2)

° ORh=Rwrist(3)—Rshlder(3)
lRl-sqrt(Rf*Rf+Rg*Rg+Rh*Rh)

“If (R1 GT 585 ) then GOTO abort
IRi=Rshlder(3)-Rwrist(3) ' °
IRangl4=asin(Ri/Rl)

ORj-296*296-293*293-R1*Rl

IRjaRj/(—2*293*Rl)

iRangll=acosIRj)

IRangl3=Rangll-Rangl4

IRang16=90
IRelbow(l)-Rwrist(1)-293*cos(Rangl3)*sin(RanglG)
IRelbow(2)-Rwrist(2)-293*cos(Ranng)*cos(RanglG)
IRelbow(3)-Rwrist(3)-293*sin(Ran913)

~214 —179 419

k

19 -l79 236

k

Relbow(1) Relbow(2) Relbow(3),

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

E 19 -179 236
o k .
. Relbow(l) Relbow(2) Relbow(3)
: mt
h

2

k

19 -179 236

k

Relbow(l) Relbow(2) Relbow(3)

..................................

XXXXOOOXXXXXXXXXXXXXXXOOOXXXSEXXZXxXXNOOOXXXXXXXXZWWXXXflXXX

.127

Relbow(l) Relbow(2) Relbow(3)

k

(Relbow(1)+237) (Relbow(2)-5) (Relbow(3)+l72)
k

. Rwrist(l) Rwrist(2) Rwrist(3)

i P
: h
° 2

:k ..

: Relbow(1) Relbow(2) Relbow(3)

k

(Relbow(1)+237) (Relbow(2)-5) (Relbow(3)+172)
k

; Rwrist(1) Rwrist(2) Rwrist(3)

256 -184 408
. k
: RwristIl) Rwrist(2) Rwrist(3)

. 12
3 P
' k

Rshlder(l) RshlderIZ) Rshlder(3)
k

Rwrist(l) Rwrist(2) Rwrist(3)

k

Rshlder(l) Rshlder(2) Rshlder(3)
r

-1*Rarmsplay

ab

h

. 3

' P
k

Rshlder(l) RshlderIZ) Rshlder(3)
k

Rwrist(1) Rwrist(2) Rwrist(3)

k

Rwrist(l) Rwrist(2) RwristIB)

r

—1*Rarmsplay

ab

h

2

' P

XXXXXXXXXXWflXXXXRxXXXWXXXXXXXXOCOXXXfiXXXOOOfiXXXNWRNXXXXflX

nrjrax:~7:x:=:ex1~7:x5:7:x:x7ex:sa=x:sacn<1rax:x:cx:n7ex:x7:xznacxzsatocfirim:x=K7=X=EF=X=~7cx

k

k

I

_128

3 Rshlder(l) Rshlder(2) RshlderIB)

; Rwrist(l) Rwrist(2) Rwrist(3)
: k
: Rwrist(1) Rwrist(2) Rwrist(3)

-1*Rarmsplay
/

au

Declare variables to move the left arm:

lDeclare
lDeclare
{Declare
lDeclare
IDeclare
{Declare
lDeclare
{Declare
{Declare
{Declare
{Declare
IDeclare
{Declare
IDeclare
lDeclare

Lshlder(3)
Lwrist(3)
Lelbow(3)
Lf(1)
L9(1)
Lh(1)
Li(1)

.LjIl)

Lk(1)
Ll(1)
Langl4(1)
LangllIl)
Langl3(1)
Lan916(1)
Lhand(3)

E'éééééfi the AGISéés to locate the left elbow:

;.ILshlder(l)--214

lLshlder(2)-l79

lLshlder(3)w418

lerist(l)-Lhand(l)-63

lerist(2)-Lhand(2)

leristI3)-Lhand(3)-30

lLf—Lwrist(l)-Lshlder(l)
iLg-Lwrist(2)-Lshlder(2)
ILh-Lwrist(3)-Lshlder(3)
lLl-sqrt(Lf*Lf+Lg*Lg+Lh?1h)

lIf ( Ll GT 585 ) then GOTO abort
lLi-LshlderI3)-Lwrist(3)

lLangld-asinILi/Ll)

ILj-296*296-293*293-L1*L1

lenLj/(-2*293*Ll)

lLangllnacos(Lj)

lLanng-Langll-Langl4

lLangl6-90
lLelbow(1)-Lwrist(l)-293*cos(Lang13)*sin(Lan916)
lLelbow(2)-Lwrist(2)-293*cos(Lanng)*cos(LanglG)
ILelbow(3)-Lwrist(3)-293*sin(Lan913)

‘ 129

3"OO\

13

k

-214 179 419
k .

19 179 23

k 0

Lelbow(1) Lelbow(2) Lelbow(3)

52

19 179 236

: k

: Lelbow(1) Lelbow(2) Lelbow(3)
: mt

: h
- 51

: k

: 19 179 236

- k

Lelbow(1) Lelbow(Z) Lelbow(3)

k .
Lelbow(1) Lelbow(Z) Lelbow(3)
k

(Lelbow(l)+237) (Lelbow(2)+5) (Lelbow(3)+172)
k

. Lwrist(1) Lwrist(Z) Lwrist(3)

= P
: h
: 51
: k
: Lelbow(1) Lelbow(2) Lelbow(3)

: k

: (Lelbow(1)+237) (Lelbow(2)+5) (Lelbow(3)+172)
: k

° Lwrist(1) Lwrist(Z) Lwrist(3)

XXOOOPSXXXXXXXXXXXXXXXXXOOOZ'XXXXXXRXXXxxxxnooxxxxxxxxxxxx

XXXXXXOOOXXNXXXXXXXZXXXXXXX XXXXXXXXXXNNXNSEXXNXXXOOOXXXXX

3 P
: k

130

ID

: k
: 256 184 408
: k

Lwrist(1) Lwrist(Z) Lwrist(3)

Splay the left arm:

13

P

k

Lshlder(1) Lshlder(2) Lshlder(3)
k

Lwrist(1) Lwrist(Z) Lwrist(3)

k

: Lshlder(1) Lshlder(2) Lshlder(3)

r

: Larmsplay
: ab
: h

52

: Lshlder(1) Lshlder(2) Lshlder(3)
: k

Lwrist(1) Lwrist(Z) Lwrist(3)
k

Lwrist(1) Lwrist(Z) Lwrist(3)
r

Larmsplay

ab

h

51

p
k

Lshlder(1) Lshlder(2) Lshlder(3)
k

Lwrist(1) LwristWZ) Lwrist(3)
k

Lwrist(1) LWrist(2) Lwrist(3)

: r
: Larmsplay
/

E Lhip(l) Lhip(2) Lhip(3)

mxxxxxxxxxxxxxxxxxxxx'xnnnzxxxxxxxxxxonnxxxxxxwxxwxnnnxxxxx

131
k

: Lknee(l) Lknee(2) Lknee(3)

k

Lheel(l) Lheel(2) Lheel(3)
ILangle-Z_LIST(1)

E'AéAéééé'iééééfi of the left hamstring:

21 60 -65

: k

: Linsert(l) Linsert(Z) Linsert(3)

: ILlength-Z_LIST(1)

° loutput"The left hamstring length is ”Llength” mm. "
ioutput"The left knee angle is "Langle”degrees”

3 Rhip(l) Rhip(2) Rhip(3)

k

RkneeIl) Rknee(2) Rknee(3)
: k

: RheelIl) Rheel(2) Rheel(3)
IRangle-z_ LIST(1)

\

. 21 -60 ~65

. k

: RinsertIl) RinsertIZ) RinsertIB)

. lRlength-z_ LIST(1)

: Ioutput"The right hamstring length is "Rlength"mm. "

{output"The right knee angle is "Rangle" degrees”
IWAIT 10

: au
lWait 30

/

: v

:rm

: 0 O 90

Iabort:

loutput"Location abort."
lEcho all

0 .6.
x

1 APPENDIX D

Linkage Equations

    

 

 

 

 

 

' x.
M ‘\

F a Femoral Link Length

T a Tibial Link Length

P a Pelvic Link Length

M - Hamstring Muscle Length

"A B Hip Angle

KA a Knee Angle

TA 6 Transmission Angle

The solution of this four bar linkage may be found
using the following formulas:

TA - arccosI(MZIPZ-Fz-T2+2FTcosKA)IZMP)

HA 2 2arctan((TsinKA-MsinTA)/(P-F+TcosKA-McosTA))

FIGURE 68: THE LINKAGE

132

APPENDIX E
The Exercise Program

This program uses angular information supplied by the user
to position a partial model of the 50th percentile human
male skeleton in a desired posture. Once this has been
accomplished, the program simulates and orients the major
muscle groups of the right leg.

During muscle fabrication, muscle volume and lateral
dimensions are assumed to remain constant. Muscle thickness
and length are allowed to vary as necessary. The
muscularity of the individual may be varied by changing the
magnitude of a multiplier of the nominal muscle volumes.

(As written, the program recreates the musculature of a
slight individual.)

This program supplies as output the final lengths of the
major muscle groups it has modeled.

: Regain straight lumbar spine if so desired.
iecho none

C

K o

C : IGOTO HERE

K : / ' '

K ° 0

K ' r

K ' h

K ° 6

K ° k

K : -23.22 0 214.25
K ' 0 25 0

K ' r

K ' h

K ° 23

K ' k

K : -23.22 0 214.25
K : 0 25 0

K ' r

K : h

K ° 53 ;
K : -23.22 0 214.25
K .:'-0 25 0

K ' r

K : h

K : 17

K ° k

K : -23.22 0 214.25
K ° 0 25 0

K ° r

K : h

K : 6

133

7:xxzxxxa:xxxxxxxwxxxxxxxxxxxxxnxxxxxxxxxxxxxxxxxxxxxxwxxxt.

-lI.15 0 156.4

0 25 0

23

~11.15 0 156.4

0 25 0

53

-11.15 0 156.4

0 25 O
r

h

17

k

-11.15 0 156.4

0 25 0
r

h

46

k

-11.15 0 156.4

0 25 O

rotate all segments around ankle to maintain balance

r

h

2

k

-97.8 -120.
0 -8 0

r

h

3

k

~97.8 -120.
0 -8 0

r

: h
5

k
—97.8 -120.
o be 0

r

h

49

k

-98.7 -120.
o —e o

r

h

46

k

-98.7 -120.

s3

‘1

-858

-858

-858

-858

-858

XXXXXXXXXXXXX”9:742XXXXXZXXXXRNXOXXXXXfiXflX XXXNXXXXKXXXXXXR

0 -8 0
r
h
17
k
-98.7 -120.7
0 -8 0
r
h
53
k
-98.7 -120.7
0 -8 0

r

h
23

k

-98.7 -120.7
0 -8 0

r

h

6

k

-98.7 -120.7
0 -8 0

rotate pelvis
IDeclare Delt
lInput"What i
r

h

6

k

-124 —81 5.95
0 Delta 0

r

h

23

k

-124 -81 5.95
0 Delta 0

r

h

53

k

-124 -81 5.95
0 Delta 0

r .

h

17

k

-124 -81 5.95
0 Delta 0

t

h

46

k

135

-858

-858

-858

-858

& torso about hips
a(l)
s pelvic rotation?” DeltaIl)

XXXXXXXXXXXXXXXKZXXXXXXXXXXXXXX 74XXXRXXXXXROXNXXXXXXXXXSEX'X

136

~124 ~81 5.95
0 Delta 0

r

h

48

k

~124 ~81 5.95
0 Delta 0

r

h

S

k

~124 ~81 5.95
0 Delta 0
rotate about ankles to keep balance
r

h

2

k

~97.8 ~120.7 ~858
0 (~Delta/4) 0

KW3H

—97.8 -120.7 ~858
o (~Delta/4) o

97.8 ~120.7 ~858
(~Delta/4) 0

8

97.8 ~120.7 ~858
(~Delta/4) 0

6

97.8 ~120.7 ~858
(~Delta/4) 0

7

97.8 ~120.7 ~858
i-Delta/4) 0

3

XUID’NOIWHD’HOIXh3HOIK-53'HOIWU‘3’H

97.8 ~120.7 ~858
(~Delta/4) 0

O I

xxxxxxxxwxxxnwxxxxxxxxxxxxxnxxxxxxxxxxxxxxxnxxxxxxxzxxxx

: mt
° h

137

r

h

23

k

~97.8 ~120.7 ~858
0 (-Delta/4)-0

X’QJ’H

~97.8 ~120.7 ~858

0 (~Delta/4) 0

Calculate knee and hip locations, using Law of Cosines
{Declare Alpha(l)

IDeclare BetaIl)

{Declare Gamma(1)

{Declare Knee(3)

{Declare Hip(3)

IInput"What is anterior tibial angle with floor?" Alpha
#Input"What is knee angle?" Beta

{echo none

CGamma~Beta~Alpha

lKneeI1)-(440.6*cos(Alpha))+(~97.8)

{Knee(2)-~120.7

IKnee(3)-(440.6*sin(Alpha))+(~858)
lHip(l)-Knee(1)~(436.94*cos(Gamma))

IHip(2)--81

lHipI3)-Knee(3)+(436.94*sin(Gamma))

rotate tibia to new position

97.8 ~97.7 ~858

O

X’NNr'Ul-‘I X’ND’TSO\

Knee(1) Knee(2) Knee(3)

translate head, torso to new positions
mt

X‘acn:flg hua:r

Hile) Hip(2) Hip(3)

: po

. mt

: mt

xxxxxxxnx7:xxx'xxzxxxxxxxxxxxxxxxxxxxxxxxxxzxwxxwxxxxxxxx7e

.138

Hip(1) HipIZ) Hip(3)

: mt

h
53
l

Hip(l) Hip(2) Hip(3)

IIip(l) Hip(2) Hip(3)

h
46
1

: p0'

Hip(l) Hip(2) Hip(3)

Hip(1) Hip(2) Hip(3)
translate pelvis to new position

Wig-HUI:

: mt

p

.me

xxxxxxxnxnxxx7:997:99xxxxxx7:997:61nxxxxxxxxxxxxoxzxxxzxzanxxx

139

4

k

Hip(1) Hip(2) Hip(3)

translate femur to new hip location

”5304:7103 I-‘(JZT

H19(1) HipIZI HipIBI
rotate femur to new position

h

3

k

Hi9(1) Hip(2) Hip(3)
l

po

h

3

l

k

Knee(1) Knee(2) Knee(3)
I HERE:

: measure final hamstring length

/
1

po
1
po
h
5
l
po
h
2
1
d .
IOutput"Final hamstring length is "2_List(7)"mm."
/

: Create hamstring muscles

OOutput"Creating hamstring muscle bellies."
Establish dimensions of biceps femoris
lDeclare Bicep(3)

lBicep(1)-(Z_List(7)/2)

IDeclare Haszl)

Iflamz(l)-(7200/Bicep(l))

lBicep(2)-42

lBicep(3)-Hamz(1)

/

3
.._...
O c
4 i
1 B
2 8
I P
D. e 0
e 0 C
C .1 0
.1 0 b
B S S \I
9 9 I e I
I n n 1 t 1
l i i I a I
l\ r r S D. l D.
0D. t .r. p e S e
e S S e C n C
0 Oc om m c x i o a 1
mm P.661hc i tamar a i A 9U B t ma r t 7 B O
nOCSIIIISSKOB/shnscclh b1d/TC966PCk.d/S Y/nS/tothkILPhZI

.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .. .0 .0 .0 .0 .. .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 00

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKCKKKKKKKKKKK

XXXDEXXXXXXXXXXXXXXXXOXXXXXXXXXXXXXXXXOKZXXXXXXXX3X5XRXW7€O

'om

141

pivot biceps

P

h

57

L

po

h

2

l

L

po

h

57

1

L

po

h

5

1

measure final quadriceps length
/

1

me

po

L

po

h

5

5

po

h

2

3

d

lOutput"Final quadriceps length is "Z_List(7)"mm."
lOutput"Creating quadriceps bellies."
Establish dimensions of quadriceps
IDeclare Quad(3)
lQuadIl)-(Z_List(7)/2)
{Declare Quadz(l)
IQuadz(1)-II8950*1.0)/Quad(1))
lQuad(2)-60

lQuad(3)-Quadz(l)

/

nm

c
8P
1.0
16

16

11
sh

sc

k

0 0 0

3 Quad(l) Quad(Z) Quad(3)

_142

s
d
a 0
0 u
s a o q o a
P P e I a
.n i s u h H a.
r u
d s d t
ow w a a n a o
tumar u a A On m. .w ma m t 8 m. o .w. 8 o o 8
/so.nsccla. vld/Tc97aPck.d/s Y/ns/tomh5kILPh23PPh5LPh23LPh5

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKCKKKKKKKKKKKCKKKKKKKKKKKK

XXXXXXXXXXRXXXXXXXXXXXXXXXXXXXXXCXXXRZXXXXXXXXXXXCXXXXXX

0. 0. 0. 0. 0. 0. 0. 00

143

0

ensure final gastroc-Achille length

usurpar\amm3prw
O om

undergo.»

IOutput"Calf length is "z_List(7)"mm.”
lOutput"Creating gastrocnemius muscle belly."
Establish dimensions of gastrocemius muscle.
iDeclare GastrocI3)
lGastrocI1I-(Z_List(7)/4)
lGastrocI1I-IGastroc(1I*1.1I

lDeclare Gast(1)
lGast(1)-((8740*0.65)/Gastroc(l))
iGastroc(2)-57

{Gastroc(3)-Gast(l)

/

nm

:om
:C

8P

1.0

16

16

11

sh

sc

k

0 0 0
Gastroc(1) Gastroc(Z) Gastroc(3)
/

sto
calfmuscle
nm

sa

or

c

l

: calfmuscle

: gastrocnemius

144

n
0
d
n
e
T
s
e
8 l
u 1
m H...
e S c
n u A
c .1
o 0 m a.
0 r e n
t 0 n i
0 s c t
a I O a
\I g \I r. e
1 1.. t r
I e I 8 C
c t c a u
o a O 9 t
r 1 r u
t s t t P
S n 8 o t
x a o a a v u
A in G t ma r t 9 G o i 9 o o 9 o 0 mm
1d/TC97 aPck . d/S Y/ns/tothkILPh33P PhSI... Ph33LPh51L Ph41l/no C

KKKKKKKKKKKKKKKKKKKKKCKKKKKKKKKKKCKKKKKKKKKKKKKKKKKKKKKKK

M5

n
O
M
e m
t
d
s n
p e
e T
1
1.. S
o1 I
h e
c n
A .1
6 e h
1 8 s 0 t C
e e a O A
0 1 1... n 0 1
6 1 1 O 3 S 0 t
2 .1 .1 d 1 n 3 0
oh h n x . o a 1 v
v.3 4 tcmar c e A 20 t ma r t 0 O i 0 o
c1N1/8an8ccla tId/Tcg7aPckOd/s Y/ns/Tomh6kOLPh41PPh6LPh4

so so 0o so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so oo so so so 0o so so so so so so so so so so so so so so

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKCKKKKKKKKKKKCKKKKKKK

macawxxxxxxwxxwxxxxxzxxxxxxxxxxxxxxnnxxxxzxxxzxz

146

IHERE:
Create gluteal musculature
OOutput"Creating gluteal musculature."
/

nm

om

c

3P

103.0

16

16

11

sh

sc

k

0 0 O

.73 .80 1.0
/

sto

butt

nm

sa

or

c

1

butt

gluteals
1
d

' dr

IOutput"PhewII"
lecho all
/

APPENDIX F

Sources of Error

Figure 69 illustrates that the angular error which may

be introduced due to a target positioning error is:

1. proportional to the distance between the actual
target location and its apparent location,

2. proportional to the sine of the angle between the
actual link and the apparent link, and will
therefore be greatest when angle "a" equals ninety
degrees,

3. inversely proportional to the actual link length.
Using the assumption that random errors due to all
causes in the determination of target positions during this

experiment were likely to be of similar frequency and
magnitudes in all directions, while noting that the largest
link length error observed in the standing files was less
than 3.0 mm. (the largest deviation from the mean link value
was 2.8mm., occurring in the femoral link of Subject 3 at
approximately 0.75 seconds), it may be concluded that the
largest likely distance between the actual and apparent
locations of any target is 3.0 mm.

Because the shortest nominal pelvic, femoral, and
tibial link lengths for the test volunteers were 124mm,
351mm, and 88mm., respectively, the maximum probable angular

error introduced by the tibial link = arctan (3/88) = 1.96
147

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148

I2)

 

II II II II II

/
.1

Angular Error

Actual Link Length

Apparent Link Length

Distance Between Actual and Apparent Target Locations
Actual Target Location

Apparent Target Location

FIGURE 69:. ERROR ESTIMATION

 

 

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main-I252. a ,
I

_149
degrees. The maximum probable angular error introduced by
the femoral link = arctan (3/351) = 0.49 degrees.
Similarly, the maximum angular error probably introduced by
the pelvic link = arctan (3/124) = 1.38 degrees. We now
conclude that the maximum probable Hip Angle Error = (1.38 +
0.49) = 1.87 degrees. Likewise, the maximum probable Knee
Angle Error = (1.96 + 0.49) = 2.45 degrees. The small
magnitude of these probable errors suggests that the angular
data gathered in the laboratory can be used with confidence
to estimate the length of the subjects hamstrings.

The apparent change in bone lengths encountered during
this experiment is the cumulative result of many unavoidable
errors, namely:

1. Human error in the layout of the calibrated space
resulting in errors in all position estimates made by the
computer;

2. Human error in the positioning of the targets over
the various anatomical landmarks resulting in a degradation
in the ability to accurately determine the spatial locations
of body parts;

3. The error inherent in using only reflected light to
locate the exact center of targets also created errors in

position reporting.

WW"-
Lu

 

 

 

BIBLIOGRAPHY

 

 

1.

9.

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