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LIBRARY
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University

 

 

 

This is to certify that the
thesis entitled
MECHANICAL WORK: AN ANALYSIS OF ITS APPLICATION

TO THE STUDY OF HUMAN PERFORMANCE

presented by

Raymond Robert Brodeur

has been accepted towards fulfillment
of the requirements for

. . . i i
M S degree 1n Eng neer ng

 

 

@{flm

Major professor

 

Date May 20, 1988

 

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HECHANICAL.NORK: AN ANALYSIS OF ITS APPLICATION
TO THE STUDY OF HUMAN PERFORMANCE

By

Raymond Robert Brodeur

A THESIS

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

MASTER OF SCIENCE

Department of Metallurgy, Mechanics and Material Science

1988

ABSTRACT

MECHANICAL WORK: AN ANALYSIS OF ITS APPLICATION

TO THE STUDY OF’HUMAN PERFORMANCE

By

Raymond Robert Brodeur

The purpose of this thesis was to investigate the methods
for calculating mechanical work as they apply to the study of
human efficiency. In the study of human efficiency there is
no agreed-upon method for determining the mechanical work done
by the body. A model for calculating the total work done by
all muscle moments of the body for any given event was
developed and compared analytically to previous methods.
Methods which use the change in segmental energy to calculate
mechanical work were shown to be inadequate for calculating
muscle moment work. The results show significant differences
between the muscle moment model and energy methods for
calculating total body work.

In addition, the work done on each body segment and the
work done by the joint muscle moment of each joint on the left
side of the body were investigated for the stance phase of
running. The results of the segmental work and the joint work

were similar to the results of other studies.

ACKNOWLEDGMENTS

The author wishes to express his appreciation to the
following people and institutions for making the completion of
his Master of Science degree possible:

To my major professor, Dr. Robert W. Soutas-Little, for his
patience, help and invaluable guidance in this project.

To Dr. V. Dianne Ulibarri, for her technical expertise in
data gathering, processing and analysis, and for serving on my
committee.

To Dr. James J. Rechtien, for serving on my committee.

To Dr. Nicholas Altiero, for serving on my committee.

To Palmer College of Chiropractic and to the Foudation for
Chiropractic Education and Research, for their financial support.

To Michael H. Schwartz, for his help in understanding the
many idiosyncrasies of the post-processing programs.

To Damien Chapman and Mary C. Verstraete, for their help,
advice, and friendship.

To Karthy Nair, my closest friend, for her support and
encouragement when I needed it most, and for her help in
preparing this manuscript.

To my parents, for their love, encouragement and support in
all my endeavors.

iii

TABLE OF CONTENTS

Page
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . v
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . vi
Chapter
I. INTRODUCTION . . . . . . . . . . . . . . . . . . . 1
II. LITERATURE REVIEW . . . . . . . . . . . . . . . . 4
2.1 Mechanics Background: Work, Energy and Power 4
2 2 Calculation of Human Work from Potential
and Kinetic Energy . . . . . . . 7
2.3 Calculation of Mechanical Work from
Kinetic Data . . . . . . . . . . . . . . . . 15
III. ANALYTICAL METHODS . . . . . . . . . . . . . . . . 20
3.1 Analytical Model . . . . . . . . . . . . . 20
3. 2 Joint Muscle Moment Work . . . . . . . . . . 27
3.3 Summing Muscle Moment Work . . . . . . . . . 29
IV. EXPERIMENTAL METHODS . . . . . . . . . . . . . . . 31
4.1 Equipment . . . . . . . . . . . . . . . . . . 31
4. 2 Subject . . . . . . . . . . . . . . ... . . 33
4. 3 Data Collection . . . . . . . . . . . . . . . 34
4.4 Data Processing . . . . . . . . . . . . . . . 35
V. RESULTS AND DISCUSSION . . . . . . . . . . . . . . 39
5.1 Analytical Results and Discussion . . . . . . 39
5.2 Experimental Results and Discussion . . . . . 43
5.2a Segmental Work . . . . . . . . . . . . 43
5.2b Muscle Moment Work . . . . . . . . . . 55
5.2c Total Work . . . . . . . . . . . . . . 63
VI. CONCLUSIONS . . . . . . . . . . . . . . . . . . . 67
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . 69

iv

LIST OF TABLES

Table Page

1. Target position and segment definition . . . . . 34

LIST OF FIGURES

Figure

1.
2.

10.
ll.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.

22.

Forces and moments acting on the 1th body segment.

Relationship between the joint muscle moment
and the joint angular velocity to segmental
muscle moment and segmental angular velocity .
Forceplate coordinate system .

Target locations on the subject

Forceplate coordinate system and final film
data coordinate system .

Work done on the foot segment

Work done by the ankle muscle moment compared to
the work done by the ankle joint reaction forces.

Work done on the shank segment .
Work done on the thigh segment .
Work done on the hand segment
Work done on the forearm segment .
Work done on the arm segment .
Work done on the head-neck segment .
Trunk AE (work).

Ankle joint work .

Knee joint work

Hip joint work .

Shoulder joint work

Elbow joint work .

Neck joint work.

Total absolute joint work.

Total work calculated by four energy methods .

vi

Page
21

28
32

33

36

44

45
48
49
50
51
52
53
54
57
S8
S9
60
61
62
64

6S

CHAPTER I

INTRODUCTION

The study of human motion efficiency is a difficult and complex
task. In engineering terms, efficiency is defined as the ratio of
the total mechanical work done by a machine to the total energy of
the fuel consumed by the machine. Thus, an extension to measure the
efficiency of human movement would be to determine the ratio of the
total mechanical work done by the muscles of the body to the total
metabolic energy consumed.

Unfortunately, there are a myriad of complicating factors.
Methods of measuring metabolic energy usually consist of determining
oxygen uptake. However, there is difficulty with differentiating
the component of metabolic energy expended to perform the task being
measured from the component of metabolic energy used for resting
respiration. Metabolic energy calculations are further complicated
by the body's ability to use anaerobic respiration.

The methods for determining mechanical work done by the muscles
of the body are also wrought with problems. Several investigators
use the change in segmental energy as a means of calculating
mechanical work. However, the change in the energy of a limb
segment is not necessarily indicative of the work done by the
muscles attached to the limb.

In addition, the calculation of muscle efficiency is complicated

by the fact that metabolic energy is expended both when positive

work is done by the muscle and when negative work is done on the
muscle. However, negative work is more efficient than positive work
as it requires less metabolic energy. Metabolic energy is also
expended during isometric contractions; a time when the muscle is
doing no measurable mechanical work. To complicate matters further,
muscle tissue has an elastic component that can be used to reduce
the metabolic energy required when put through a negative to
positive work cycle.

In the study of human performance, investigators calculate
mechanical work from either kinematic or kinetic data. The
advantage of using kinematic data is that only cinematic film and
anthropometric measurements are needed. The segmental energy can be
calculated, and thus the mechanical work done on each segment can be
determined from the change in segmental energy. Most investigators
prefer to use the kinematic method, since data collection is
simpler.

Mechanical work can be determined directly from kinetic data,
however, this type of data is more difficult to obtain. External
forces must be measured or calculated, thus requiring additional
equipment, such as force plates. This additional equipment can be a
limiting factor and may restrict the feasibility of many studies.
But, by obtaining kinetic data, both the work done by the joint
reaction forces and the work done by joint muscle moments can be
determined. Thus, with this knowledge, an investigator can
determine the total work done on any body segment as well as the
work done by individual joint muscle moments.

The problems and disagreements in the literature arise when

using changes in segmental energy to determine the total work done

3
by the muscles of the body. The major problem arises when
researchers try to accommodate for the muscle expending metabolic
energy during both positive and negative work. Because of this
limitation, the mere summing of segmental energy changes is not
adequate for determining total muscle work. As a result, several
researchers have developed methods for summing segmental energy
changes which try to account for this limitation. Unfortunately
there has been no agreement between the methods and it is unclear as
to what these methods are physically related to.

The purpose of this thesis was to investigate the methods for
calculating mechanical work as they apply to the study of human
efficiency and to develop a model for calculating total muscle
moment work. The analytical methods investigated the problem of
trying to determine muscle work from segmental energy changes. The
physiological problem concerning the fact that metabolic energy is
required during both positive and negative muscle work is also
addressed.

Since several of the papers reviewed in this thesis are
concerned with determining muscle work from segmental energy
changes, the literature review included a background section which
reviews the relationship between mechanical work and energy. In
addition, several investigators discuss muscle power and/or the rate
of work done by muscle; therefore, the relationship between power,

work, and energy has also been discussed in this background section.

CHAPTER II

LITERATURE REVIEW

2.1 Machinics Background: Work, Energy, and Power
In rigid body mechanics the relationship between work and

energy (16) is:

2

2
1. vidt - f f1a(1/2 mivi)

2

2
- 2
1 f1 mia

2 2
' f 1/2 ”1(V12' V11)

where: F1 is the force acting on the ith particle of the
rigid body
ds is the infinitesimal distance through which each

1

force, F1, travels.

m1 is the mass of the ith particle of the rigid body.

v is the velocity of the ith particle relative to a

1

fixed reference frame.
W12 is the work done by all forces acting from point 1

to point 2.
Thus “12 - KE2 ’ KE1

2
where RE is the kinetic energy (KE - l/2 2 mivi).
i

If the velocity v for each particle is written relative to the

1

center of mass velocity, then:

2 2
(2) RE - 1/2 h v + 1/2 2 m v'
1 1 1

where: M - 2 m
1 i

‘v is the velocity of the center of mass.

vi is the velocity of the 1th particle with respect to
the velocity of the center of mass (v1 - V’+ vi).
2 2
In planar motion the term 1/2 E mivi - 1/2 Iw where "I" is the
i
moment oninertia about the axis of rotation, and w is the
angular velocity of the rigid body.

The work done by gravity on a rigid body can be written as:

(g) (g)

3 2 2 h 2

() WI? - fif! F1 ' (181 - ":1 f1 mi 3' dsi-‘fmig 1'1
(8) th

where F1 is the force of gravity and hi is the height of the i

(3)

particle. F1 is a conservative force equal to mig where g is

the acceleration of gravity. If hi is written in terms of the

height of the center of gravity, then:

(3) 2
1 1

2
|

where h is the height of the center of mass and hi is the height
of particle "1" relative to the center of mass (h1 - h + hi).
Since the body is rigid, work done by the internal potential

forces sums to zero, thus the term on the right is zero and:

(g)
(5) w,2 - M g (h2 - h,) - PE, - PEI

where PE is the potential energy.

Since the focus of discussion in several of the papers
reviewed in this study was on the rate of work and/or the power
generated by muscle, it is important to briefly discuss the
controversy over the definition of power. If power is defined as

the rate of change of kinetic energy (17), then:

2
(6) f P dt - KE2 - KE,
1

where P is the power. This is essentially a scalar first
integral of the motion. Several introductory texts in dynamics

(Meriam (26)) define power to be:

(7) P - F . v
and

(8) P - dE/dt - d/dt(KE + PE) - dW/dt

where: dE/dt is the rate of change of energy (E - KE + PE)
dW/dt is the rate of work being done.
However, other authors (Singer (33) and Harris (19)) discussed

power as either an average power or an instantaneous power:

(9) Pave - work/time

(10) Pinst - F 0‘v

Trusdell and Toupin (34) stated that there is no agreement on

what "the" flux term is for mechanical energy.

The authors reviewed within this thesis defined power to be:
(11) P - F o'v .- dE/dt - dW/dt

In light of the above controversy, the definition given by
equation (11) will not be challenged. Any further argument

concerning power is beyond the scope of this thesis.

2.2 Calculation of Human.Wcrk from Potential and.Kinetic

Energy

Most researchers prefer to calculate the mechanical work of
human motion from changes in kinetic and potential energy. This
is an understandable choice from the point of view of data
collection and analysis. Velocity data and anthropometric
measurements are all that are necessary. Thus most early work
used energy as a means of calculating mechanical work.

Fenn (ll) analysed the work done in sprint running. He was
the first investigator to accurately study the mechanical work
done on each body segment by determining the change in the
segmental kinetic and potential energy. It must be pointed out
that Fenn did not calculate the work or the potential energy
relative to a fixed frame of reference, the work done on each
segment was calculated with respect to the whole body center of
gravity. This type of analysis is referred to in the literature
as "internal work".

In order to account for the physiological properties of
muscle, Fenn calculated the total work done by summing the

increase in kinetic energy of each segment and the increase in

potential energy of each segment (relative to the whole body
center of gravity). The negative work done on the segments was
not used in his analysis. The sum of the segmental work was the
total ”internal” work as calculated by Penn.

Fenn (12), used the data from his previous study (11), and
calculated the work done on the center of gravity of the body by
calculating its changes in potential and kinetic energy. This
method is termed "external” work in the literature. The total
mechanical work is then ”internal" work plus "external" work.

Cavagna and co-workers (2-6) further investigated the concept
of "internal" and "external” work. "External" work was
determined by using a combination of force plate and
accelerometer data. Their emphasis was on the comparison between
changes in potential energy (WV, for vertical work against
gravity) to the changes in horizontal kinetic energy (Wf for work
done to change the forward velocity of the body). It must be
pointed out that this type of comparison has no physical meaning.
Work is a scalar quantity, thus to compare "vertical work" to
”horizontal work" (treating work as a vector) is not necessarily
indicative of work done by vertical and horizontal forces.

”External" work has also been applied to gait analysis by
Gersten, et a1 (15), Fukunaga, et a1 (14), Keneko, et al (22),
Matsuo, et a1 (25), and by others.

The concept of "external” work has been applied to other
activities. Fletcher and Lewis (13) used cine-photography to
evaluate pole vaulting. They found the kinetic energy during the
run-up to be proportional to the potential energy at the peak of

the vault. However, Hay (20), as a result of the introduction of

the fiberglass pole, found the rates of pole-bending and pole-
straightening to be the predominate factors in pole vaulting
performance. Gray, et a1 (18) used changes in the potential
energy of the body's center of gravity to develop a method for
estimating the power generated by leg muscles in performing a
vertical jump.

The value of ”external" work in these studies was that it
provided the investigator with a relatively quick and easy method
for determining trends and patterns in an activity. From these
patterns, a researcher could then decide upon specific areas for
further, more detailed, analysis.

Cavagna and co-workers (3,6) also investigated "internal"
work using the method described by Penn (11). The changes in
energy of body segments were determined relative to the center of
mass of the body for walking and running. They obtained
efficiency values similar to Penn (11) (0.175 to 0.225
kcal/kg/min for speeds of 11 to 20 Km/hr) for running.

Ellis and Hubbard (10) divided work done by the body system
into two parts: 1) muscle forces that result in the displacement
of the body, or body parts, is work done on the body system,
increasing the internal energy of the system, and 2) muscle
forces that result in the displacement of the surroundings is
work done on the surroundings. This definition parallels the
majority of the literature, in which external work is defined as
work done by the body on an external mass, such as pushing or
pulling a load, or lifting a weight (Winter (40)). Internal work
is defined by Winter as a change in segmental energy relative to

a fixed reference frame.

10

The above definitions differ from "external" work, which
Cavagna, et a1 (3) defined as the work necessary to displace the
center of gravity of the body and ”internal" work, which is
defined using displacements relative to the body's center of
gravity rather than to a fixed frame of reference. These earlier
definitions of ”internal” and "external" work have rarely been
used in the past decade.

Norman, et al proposed to use what they termed pseudowork;
which is the summing of the absolute value of the change in

energy of each component of a segments energy:

m n

(12) w g1 (larxail + |ARKE1| + |APE1| )

n - k§1 1

number of time increments.

where: m
n - number of body segments.
1 - 1th body segment.
k - kth time increment.
TKE - translational kinetic energy.
RKE - rotational kinetic energy.
PE - potential energy.
A denotes the change in the respective energy
over the time increment, k.

Wn - work done, not allowing energy transfer

within a segment.

They hypothesized that the subject with the lowest pseudowork

(normalized by the metabolic energy expended) would be the most

11

efficient. However, this method results in an
uncharacteristically high value for the calculation of mechanical
work (29). It is also questionable as to what this method is
really measuring.

Winter (40) proposed calculating total mechanical work during

an event as:

m n
(13) "wb ' k§1 l1§1 A31 '

where: i,k,m,n are defined previously.
AE1 - ATKE1 + ARKEi + APE1 (change in segmental energy
of the 1th segment over the kth time increment).

Wwb- work done allowing the transfer of energy

within a segment and between segments.

Using this method, Winter improved on the method of Norman et al
(28) by allowing the exchange of potential and kinetic energy
within a segment and the exchange of energy between segments. It
should be noted that this method does not allow negative work
done at one point in time to cancel out positive work done at a
different point in time.

Pierrynowski, et al (29) were interested in determining the
work transferred between segments. Work is done on a segment by
muscles connecting it with adjacent segments and by the joint
reaction forces between segments. Thus, energy can be
transferred from one adjacent segment to another, either by

active contraction of muscle or by work done by the joint

12

reaction forces. In an attempt to better understand the transfer
of energy within the body Pierrynowski, et a1 defined three types
of energy transfer within the body. Tw , the total transfer of
energy within segments, was the change in energy form between
potential energy, translational kinetic energy, and rotational

kinetic energy. Tw is defined below:

Ill n
(14) Tw - k§1 1§1 [ {IATKE1| + |ARKE1| + laeai|i - |AE1| ]

Tb is the total transfer of energy between all body segments

and is defined as:

m n n
(15) Tb ' k§1 [ i§1lAE1Y ' '1§1 AEi ' 1

wa is the total energy transferred within and between body
segments for a given event, defined as the sum of Tw and Tb:

(16) T - Tw + T

wb b

The use of the above three definitions for determining the
work transferred between segments is questionable. The purpose
for determining the energy transfer within segments, Tw’ is not
clear. Tw provides a sum of the energy transferred within the
segments for an event, but provides no information on the
physical forces causing the change in energy. The amount of
energy transferred between segments (Tb) determines the net sum

of the energy transferred between all segments of the body for a

l3

given event, but again, its usefulness is questionable. Tb does
not determine what portion of energy is transferred between any
two adjacent segments and it does not separate the portion of the
energy transferred due to work done by the joint muscle moment
from that due to the work done by the joint reaction forces.
Pierrynowski, et a1 (29) compared three methods for

calculating total mechanical work; two methods by Norman, et a1

(28) and Winter (40), and an additional method defined as:

m n

(17) “w "' 131 11:1

IAE1I

where Ww is the work done, allowing energy to be transferred only
within a segment but not between segments. These three methods
were compared for treadmill walking.

Considering the definitions, it is easy to show that:

(18) Wn - Tw + ww

and

(19) Ww - Tb + Wwb

Since Tb’ Tw’ and Wwb are always positive, then Wn will always be
greater than Ww, which will always be greater than wwb'

Williams and Cavanagh (37) expanded on the work of the three
previous researchers. They argued that the definition of Wwb by
Winter (40) allowed segments that are not physically in contact
with each other to (mathematically) transfer energy to each

other. For instance, if the left foot increased its total

14

segmental energy over an increment of time and the right hand
decreased its total segmental energy while all other segments
remained unchanged then, by Winter's method, the energy of the
foot could be (mathematically) transferred to the hand. To
improve upon the previous works, Williams and Cavanagh developed
two additional algorithms. They claimed that the first algorithm
allowed energy to be transferred only between adjacent segments.
The second allowed the transfer of energy within a limb but not
across the trunk.

These algorithms were not expressed in equation form, but
were expressed only in the form of computer algorithms (Williams
(36) and Williams and Cavanagh (37)). Investigation of these
algorithms by this writer could not determine any succinct method
for expressing them in equation form. However, the adjacent
segment algorithm published by Williams and Cavanagh (37) is
directionally dependent. That is, summing from the distal
segment towards the proximal segment can, under certain
conditions, result in a different answer than if summed from the
proximal segment towards the distal segment.

The problem with the limb transfer algorithm is that the same
argument Williams and Cavanagh used against Winter (40) can be
used against it. That is, positive work done on the foot segment
could transfer energy (mathematically) to negative work done on
the thigh, despite the fact that the two are not physically
adjacent. However, with the limb transfer algorithm, energy
could not be transferred across the trunk to other body segments.

Shorten, et al (32) investigated several energy transfer

constraints for treadmill running at various speeds. In addition

15

to the previously discussed methods of Wu, Ww, and WV , Shorten,
et a1 introduced Wfii, which permited energy transfer within
segments and between segments of the same limb. Unfortunately,
they did not explicitly define wwl' It was not clear whether
they used the algorithm of Williams (36) or if a different method

was utilized. Their results were similar to Pierrynowski, et a1

and W

(29). Wh had the greatest value, followed by Ww, wb'

wwf’
respectively. For all the data presented, WW! was always
greater than Wfib, but less than W“.

Shorten, et al emphasized that their method, as well as all
other energy methods, related only to changes in energy and that
they were not necessarily indicative of work done by the muscles
of the body. They also questioned the accuracy of energy methods
since the selection of transfer constraints was not based on any
knowledge of muscle contraction patterns. They further stated

that, with the current energy models, it was not possible to make

any definitive statements regarding mechanical efficiency.

2.3 Calculation of'Mechanical Work from Kinetic Data

Elftman (7-9) wrote a thorough series of papers regarding the
analysis of muscle work and muscle efficiency in humaanait.
Elftman (7) determined the forces and moments acting on the leg
during walking. He was one of the first human motion researchers
to apply kinetic data toward the investigation of mechanical
work. Elftman calculated the mechanical power generated at the
joints (ankle, knee, hip) by the joint reaction forces and by the
joint muscle moments. He compared the rate of work done by the

joint muscle moments of the leg to the rate of energy change of

16

each segment and also discussed the role of muscle work in
causing the segmental energy changes.

Elftman (8) investigated the work done by muscles that cross
more than one joint. For example, muscles such as the hamstrings
or quadriceps have components that cross more than one joint,
extending from the pelvis to the shank, crossing both the hip
and knee joint. This arrangement allows these muscles to do work
on both the thigh and the shank. Elftman concluded that, under
certain conditions, the multi-joint muscles can be more efficient
than single joint muscles.

Elftman (9) applied his methodology to running using the data
from Penn (12). A bilateral analysis of the power generated by
the muscles moments of the body's major joints (ankle, knee, hip,
elbow, shoulder) was performed. He summed the rate of work done
by all muscles at these joints to determine the rate of work done
by "one joint muscles" for the entire body. Negative and
positive work were treated separately, essentially summing the
absolute values of the rate of work done. He further
investigated the role of muscles crossing two joints, and again
stressed the efficiency of two joint muscles.

Elftman (9) made the following statement: "In evaluating the
work done by muscles on the basis of changes in kinetic and
potential energy, some difficulty is encountered in allowing for
the possibility that the increase in energy of one part of the
body may be derived from decrease of energy in another part,
instead of coming from muscular contraction. This difficulty can
be eliminated if the muscle forces can be determined and the

rates at which they work computed directly." (p. 672).

17

Quanbury, Winter, and Reimer (30) studied power flow to the
shank from the power generated by the knee joint reaction forces
and the knee muscle moment during the swing phase in walking.
They compared the power generated on the shank from the knee
forces and moments to the change in the total shank energy over
time (termed instantaneous power). They showed, analytically,
that power flow and instantaneous power are mathematically
equivalent.

Winter, Quanbury, and Reimer (38) expanded their previous
work by looking at both the knee and hip joint from toe-off to
heel contact. The causes of energy changes and power flow were
discussed regarding the rate of work done by the muscle moment,
joint reaction forces, and gravity. In a later study, Winter and
Robertson (39) expanded the previous study to include the ankle
joint.

Robertson and Winter (31) analysed the above concepts of
power flow and instantaneous power in walking. They improved on
the previous work by including stance phase in their analysis.
Close agreement was found between the power flow into each
segment (foot, shank, thigh) and the instantaneous power of the
segments. The only discrepancy was at the foot during heel
contact and late push-off. Winter (41) examined power generated
by the muscle moments at the ankle, knee, and hip joints in
Jogging-

Cappozzo, et al (1) analysed walking and calculated the total
mechanical work done at the lower limb joints (ankle, knee, and
hip), bilaterally. They compared the work done by the lower limb

joints to the total energy changes of a seven segment model

18

(three segments for each leg plus the head-arms-trunk (H-A-T)
modeled as the seventh segment). The differences between the sum
of the work done by the joints and the sum of the work done by
the change in energy of each segment was small, except for a
sharp discrepancy at heel impact.

It should be pointed out that Cappozzo, et al considered the
sum of the work done by the change in segmental energy to be more
reliable than summing joint work. They reasoned that segmental
energy calculations had less potential for error since only one
differentiation of the data was needed; whereas, with the joint
work method, two differentiations were necessary to obtain the
acceleration data needed for calculating the joint moments.

Martin and Siler (24) compared the transfer of energy, using
the methods described by Pierrynowski, et al (29), to the work
transferred to each segment from the joint reaction forces and
joint muscle moments. This analysis was done for a kicking
motion. They found that the sum total of the energy transfer
(wa, as denoted by Pierrynowski, et al) to be nearly the same as
the transfer of energy due to the work done by the joint reaction
forces and moments. However the rate of the energy transfer
differred markedly between the two methods. Martin and Siler
concluded that the kinetic analysis was a more appropriate method
for calculating the energy transferred between segments since it
described the mechanisms of motion, whereas the energy analysis
used the motion history without any knowledge of the mechanisms
causing that motion. Y

Hubley and Wells (21) used a work-energy approach to analyze

vertical jump performance. They normalized the absolute value of

19

the work done at each joint (ankle, knee, and hip, bilaterally)
by the sum of the total work done at all three joints. This
ratio allowed a comparison between subjects for the relative
amount of work done at a given joint. They determined the knee
contributed the majority of the work done in vertical jumping.
However, they pointed out that there were large variations in
individual patterns. They suggested that further study of this
method of normalization could have major implications on training

and rehabilitation programs.

CHAPTER III

ANALYTICAL.METHODS

3.1 Analytical Model
The following assumptions were made for the model used in this
thesis:

1.) All motion is in the sagittal plane.

2.) During stance phase the foot rolls without
slipping, therefore no work is done by the
ground reaction forces.

3.) All forces (except the ground reaction forces)
are assumed to act through the joint centers.

4.) The joint centers are assumed to be located at
fixed locations on each segment. These
locations are defined by either the target
positions on each segment or by a given location
relative to the targets on each segment.

5.) All muscle effects on a joint are represented
by a single muscle moment acting at that joint.

6.) Positive work done by a muscle consumes the same
amount of metabolic energy as an equal amount of
negative work done by that same muscle.

In a multi-segmental body, the forces and moments acting on

the ith segment are shown in Figure l.

20

21

ip

F.
1P

 

Figure 1

Forces and moments acting on the 1th body segment.

Where the following notation applies to Figure 1:
F are the joint reaction forces.

M.are the muscle moments.

i denotes the ithsegment.

d denotes the distal end of the segment.

p denotes the proximal end of the segment.

m is the mass of segment "i".

1

a1 is the acceleration of segment "1".

a1 is the angular acceleration of segment "i".

"I" is the moment of inertia of the segment about an axis
perpendicular to the sagittal plane.

g is the acceleration of the segment due to gravity.

All of the above vectors were defined with respect to a fixed

reference frame.

22

The distal and proximal forces and moments were calculated for
each segment using the procedure described by Markus (23).

Elftman (7) also provides a thorough description for calculating
the forces and moments acting at each segment. For the foot, the
distal forces (ground reaction forces) were measured, for the
stance phase of gait, using a force plate. During swing phase,
the distal foot forces were zero. From cinematic film data, the
linear and angular accelerations of the foot center of mass were
known. Thus, from dynamics, the proximal (ankle) joint reaction
forces and the ankle joint muscle moment could be determined.

For the shank, the distal shank forces and moments were equal
and opposite to the proximal foot forces and moments. Since the
linear and angular accelerations of the shank centerof mass were
known from film data, the proximal shank forces and moments could
be determined from dynamics. The same procedure was used for the
thigh segment.

For the upper limb, the distal forces on the hand segment were
zero. Thus by knowing the linear and angular accelerations of the
center of mass of the hand, the proximal hand forces and moments
were determined. The distal forces of the forearm were equal and
opposite to the proximal forces of the hand segment, thus, the
proximal forearm forces could be determined since the linear and
angular accelerations of the forearm center of mass were known
from cinematic data. Continuing this process, the distal and
proximal forces acting on each segment were determined. The
forces and moments acting on the trunk were equal and opposite to
the proximal forces acting on the thigh, upper arm, and head-neck

segments.

23

The work (AWi) done on the segment shown in Figure l, for a

given increment of time, is as follows:

(20) AW1 - rid. Asid + Fip. Asip + (M.id + Mip)-A0i + mig-AS1

where: A81 is the incremental displacement of the ith

segment's center of mass.

asid and asip are the incremental position changes of

the distal and proximal ends of the ith segment.

A01 is the incremental angular position change of

the segment.
From rigid body mechanics, the work done on a segment is equal to
the change in kinetic energy of that segment. From Figure 1,
consider the work done on the proximal portion of the 1th segment,
AWip:

(21) Awip - Fip. Asip + Hip. A01

However, asip can be expressed as:

(22) Asip - AS1 + Adix r1p
where: r1p is a vector from the center of mass of the
segment to the proximal end of the segment.
A81 and asip are as previously defined.

Thus, equation (21) can be rewritten as:

(23) Awip - Fip'lAsi + (Aoix rip)] + Hip. A01

24

Using the vector identity A9(B X C) - B-(C X A) equation (23) can

be written as:

-Al

(24) aw - F . A8 + [(ripx Pip) + nip] 1

ip ip 1

Similarly, the work done on the distal segment is:

(25) AW1d — Fid°Asid + MidoAli
As with Asip’ AS1d can be rewritten in terms of the segment's
change in its center of mass position (A81) and the change in the

angular position of the segment (A01):

(26) AS1d - ASi + A0i X rid
where r1d is the vector from the segment's center of mass to the
distal joint of the segment.
Thus the work done on the distal end of the segment can be

written as:

(27) AW - F - as + [(ridx F) + Mid]oA0

id id 1 i

The total work done on the segment is:

(28) AW - AW + AW + mig-AS

1 ip id 1

25

or:

(29) M11 - (Fid+ F1p+ mig)°Asi+(nid+ H + r x F + r

1p id id xrip).A0

ip i

The portion in brackets in the first part of equation (29) is
the sum of the forces acting on the center of mass of a segment
dotted with the distance through which these forces travel. This
is equivalent to the change in the translational kinetic energy:

(30) (Fid + Pip + mig)-ASi - mini-ASi

miaioAsi - m1[(vi2tv11)/At]-[(v12+v11)/2]At

Where‘v11 and'v12 are the velocities of the 1th segment's center
of mass at the beginning and end of the time interval,
respectively. Note that the accelerations and forces are assumed
to be constant over the time interval.

Similarly, the second part of equation (29) is the sum of the
moments about the center of mass, dotted with the change in
angular position of the segment. This is equivalent to the change

in the rotational kinetic energy:

- I 0 0A0

(31) (Hid+ Hip+ r X F + r X F1P)-A0i 1 i 1

id id ip

- I1[(w12- w11)/At]o[(w12+ wil)/2]At

26

2 2
- 1/2 11(w12 - mil)

Where 011 and 012 are the angular velocities of the ithsegment at
the beginning and end of the time interval, respectively.

Thus the total work done on the segment can be written as:
. 2 2 2 2
(32) AW1 - 1/2 m1(vi2- v11) + 1/2 Ii(w12- wil)

In motion analysis, time is a more convenient variable over
which to sum than variables such as distance or angular position.
With this in mind, the variable of summation will be changed to

time and the following definitions will be made:

mam1 - Fido asid - Fid'(Asia/At)“t - Fid- vidAt

AWFpi - Pip. AS1p - Pip. vipAt

Adei - Mid. A'i - “id. 01 At

Apri - Hip. A01 - Hip. mi At

where AWFdi and AWFpi are the work done by the distal and proximal

joint reaction forces and AWMdi and AWMp1 represent the work done
by the distal and proximal muscle moments acting on segment "1".
Note that vid’ vip’ and 01 are the average velocities and angular

velocities, respectively, over the time interval.

27

3.2 Joint Muscle Moment Work

In order to study human efficiency, the work done by the
muscles of the body must be determined. The following analysis
determines the work done by a joint muscle moment, which does not
necessarily account for the work done by all the muscles acting at
a joint. The work performed by antagonistic muscle contractions
or by isometric contractions is not included.

The joint reaction forces between adjacent segments (shown in
Figure 2) are equal and opposite and act through very nearly the
the same distance. If the joints were in pure rotation, the net
work done by the joint reaction forces would be exactly zero.
However, there is some compliance within each joint and thus these
forces do work. But this work is small relative to the work done
by the joint muscle moment, thus the net work done by the joint
reaction forces can be assumed negligible.

The work done by the joint muscle moment at joint "j" is equal
to the muscle moment at the joint dotted with the change in
angular position of the joint. Using time as the variable of

summation, the work done by a joint muscle moment (AwMj) is:
(33) AW - M m: At

where M1 is the moment acting at the joint and "j is the average
angular velocity of the joint over the time increment, At. The
jth joint is defined as shown in Figure 2. Joint "j" is between

distal segment "i" and proximal segment "1+1". Thus, relative to

the segmental data, the joint moment is equal to the proximal

28

moment acting on segment "i" and the joint angular velocity is
equal to the difference in the angular velocities between segment

”i" and segment ”1+1”.

cf“
M) =wind
Fi+1d
M. = M.
J 11)

ip

   
 

(0.

 

Figure 2
Relationship between the joint muscle moment and the joint

angular velocity to segmental muscle moments and segmental

angular velocity.

The following notation applies to Figure 2:
Hip - proximal muscle moment of segment "i".
Hi+ld- distal muscle moment of segment "1+1".
”1 and ”1+1 are the angular velocities of the

respective segments.

“3 ' “1p ' ' l“1+1a
“H - wi ' ”1+1

29

3.3 Summing Muscle Moment Work
The simplest model for summing muscle moment work would be to

sum the work done by each joint:

(34) jgl AW'Mj

where q is the total number of joints in the model. However, this
would be assuming perfect efficiency. Positive work done by one
joint could be recovered by negative work done at any other joint,
without any losses in work efficiency.

It was assumed that the muscle moment about each joint was
caused by "one-joint" muscles as defined by Elftman (8). That is,
the effect of "two-joint" muscles, such as the hamstrings (which
cross two joints, the hip and the knee, and are thus capable of
doing work at both joints), will not be considered. Thus, by
definition, energy can only be transferred to segments that are
immediately adjacent to each other by work done by the joint
reaction forces and/or the joint muscle moments. Hence, the work
done by a series of joints over any given instant in time is the

sum of the absolute value of the work done at each joint:

(35) W M

q q
:31 |AWMj| - j§1 | j-wj| At

k'j

where: Wk - the work done during the kth time interval.

q - number of joints in the model.

30

Hence positive work done at one joint is not cancelled out by
negative work done at a different joint. Equation (35) ignores
oscillatory motions during the time interval, and therefore
requires that the time interval be small enough so that the work
calculated for the time period is representative of the actual
work done by the muscle moments involved.

If the total work done by the muscles of the body is desired

for a given event, then:

m q m q
(36) w u.- 3' At

total ' k§1 j§1'wnj' ' k§1 j§1 ' j

where W is the work done by all the muscle moments of the

total
body for the entire event.

CHAPTER IV

EXPERIMENTAL.METHODS

The experimental methods were divided into four sections:

equipment, subject, data collection, and data processing.

4.1 Equipment

Two LOCAM 16mm cine-cameras operating at 100 frames per
second were used to record position data. The cameras were
positioned so that anterolateral and posterolateral views of the
subject within the force plate area were filmed. The camera
positions were such that all targets on the left side of the
subject's body were visible in both camera views during the
stance phase of the subject on the force plate. The cameras were
connected to a single switch, allowing both cameras to be
triggered at approximately the same time. In order to
synchronize the film data each camera's field of view contained a
timing light box. The timing lights were synchronized and
accurate to l/lOOO seconds. The timing lights allowed the
processed film to be time-matched after digitization.

A calibration structure, consisting of 12 targets of known
position, was placed in the view field of the cameras. The
calibration structure provided a known coordinate system to
define the space of the viewing area. Using the method of direct

linear transformation (Walton (35)) the appropriate

31

32

transformation matrices were determined; thus the three
dimensional coordinates of any target within the field of view of
both cameras could be calculated. The calibration structure was
removed to allow data to be filmed of the subject standing and
running.

Ground reaction forces were measured using an AMTl three
dimensional strain gage force platform (model OR6—3 Advanced
Mechanical Technology, 141 California Street, Newton, MA 02158).
The strain gage voltage output was converted to digital data with
an A to D converter sampling the output at the rate of 1000
samples per second. The digital data was calibrated and
processed such that force and moment data (measured in Newtons
and Newton-meters, respectively) were recorded for the three
principle directions (X,Y,Z) on an 8 inch floppy disk. The data
was transferred to a Prime mainframe computer in the Case Center
for Computer-Aided Design. The orientation of the force plate

coordinate system is shown in Figure 3.
M

’2’"

"/—
9;st / 4/76—‘7
‘T"' Y

’ 0.73"

 

 

 

.7
3.29'

 

 

M
2

K/

V

Y.— 20.0" _..Y

Direction of runner progression.
Arrows indicate positive input.

 

 

Figure 3

Force plate coordinate system

33

4.2 Subject

The subject of this study was a 30 year old male weighing 64
Kg with a running experience of 13 years at 70 miles per week.
Fourteen 1/2 inch diameter cotton pom poms were used as targets
to define eight body segments. The target positions are shown in
Figure 4. Symmetry was not assumed in this study. Table I gives
the target number, the anatomical landmark over which the target
was placed, and the body segment the targets defined.

The appropriate anthropometric measurements were recorded so
that segment mass, center of mass, and moment of inertia could be
determined. NASA Reference Publication 1024 (27) was used as the

anthropometric reference for this study.

‘E ‘33

 

elie()
Y 9
(3
(l
,‘9
I) E)
Figure 4

Target locations on the subject.

34

Table 1
Target position and segment definition

Target Landmark Segment
(on left side of body)

th

1 5 metatarsal tuberosity
2 Upper portion of calcaneus -------
::>>Foot
3 Lower portion of calcaneus -------
4 Lateral malleolus ----------------
::>>Shank
5 Fibular head .....................
6

Lateral femoral condyle ----------
Thigh

7 Greater trochanter ...............
Trunk

8 Greater tuberosity of humerus----

Upper arm

9 Lateral condyle of humerus -------
10 Head of radius ...................
Forearm

11 Lunate (dorsal aspect) -----------
rd Hand

12 Head of 3 metacarpal -----------

l3 Ant. portion of zygomatic arch-~-
:::>Head

14 Post. portion of zygomatic arch--

4.3 Data Collection

Three trials were filmed of the subject striking the
force plate during the stance phase of running. The subject was
encouraged to keep his stride natural and unforced. If the
subject missed the force plate or if he felt his stride was
forced in any manner, then the trial was repeated. A subject
identification board, visible in both camera views, was used to

identify the subject and trial number of the run.

35

The film was digitized using an Altek Datatab rear projection
digitizer (Altek Corporation, 2150 Industrial Parkway, Silver
Spring, MD 20904). The calibration structure was digitized
first, followed by the subject standing position. The force
plate was also digitized in order to define the force plate
position with respect to the calibration coordinate system. The
film frothhe three successful running trials was then digitized.
Fifteen frames before heel strike and 4 frames after toe-off were
digitized. Unfortunately only 4 film frames after toe-off could
be digitized due to the loss of target visualization on one
camera view. The digitized data was recorded on a floppy disk
and transferred to the Prime mainframe in the Case Center for

Computer-Aided Design.

4.4 Data Processing

During the digitizing process it was noted that the timing
light for camera one (the anterolateral view) was not
consistently synchronized with the primary timing light.
The variability of the frame time for camera one was calculated
for several portions of the film and was found to vary by
+/-0.00026 seconds per frame. This indicated that the timing
light was consistent, in spite of the loss of synchronization.
The data for each running trial was time-matched by assuming heel
contact occurred simultaneously in both camera views. The
initial and final times for camera one were adjusted relative to
the heel contact time. The three dimensional position for each
target was then determined from the time-matched data using a

series of computer programs. The data was filtered through a two

36

pass Butterworth filter with a cutoff frequency of 8 Hz. The
position data was run through a transformation program so that
the center of the force plate was the origin of the coordinate
system. Figure 5 shows the relationship between the force plate
coordinate system and the final coordinate system used for data
analysis. The number of data points were reduced so that only
five time intervals (1/100 seconds each) before heel strike and
four time intervals after toe-off were analyzed. The purpose for
this was to reduce the effect of the filter which is reported to

attenuate target accelerations during swing phase (31).

TR

 

 

 

 

 

 

 

 

iY
Zr
(XF’YF’ZF) = Force plate coordinate system.

= Final coordinate system for

(XR,Y
data analysis.

R, ZR)

Figure 5
Force plate coordinate system and final film data

coordinate system.

37

The three dimensional position data was collapsed to a two
dimensional plane parallel to the XR-ZR plane shown in Figure 5.
This plane was approximately parallel with the sagittal plane of
the subject during the run. The position data was then
differentiated. The velocity data was obtained using a three
point forward difference for the first two time intervals, a five
point central difference for the remaining time intervals, except
the last two intervals, where a three point backward difference
was used. A similar method was used for the acceleration data,
except the forward and backward differences were four point.

With this method, no data was lost due to numerical
differentiation.

The kinematic data was calculated for each segment using
methods similar to those described by Markus (23). The kinetic
data for the lower limb was obtained by time-matching the
kinematic data and the force plate data. Since the force plate
data was initiated by the impact of heel strike, it was assumed
that the first frame of heel strike and the first force plate
data sample occurred at the same instant in time. The center of
pressure between the foot and force plate was determined for each
time interval of kinematic data. Since data collection for the
force plate was at 1000 Hz and data collection for the filmed
data was at 100 Hz, every 10th force plate data point was used.
The center of pressure was then transformed to the two
dimensional runner coordinate system. Thus, the position and
magnitude of the forces acting on the foot segment were known.
Simple dynamics allowed the calculation of the forces and moments

acting on the ankle, knee, and hip. For the upper limb and for

38

the head and neck, the forces at the wrist, elbow, shoulder, and
neck were determined from the kinematic and inertial data. The
forces and moments acting at the distal and proximal ends of each
segment on the left side of the subjects body were determined for
the stance phase of running.

The kinematic data allowed the calculation of the kinetic
energy components for each segment. The position data was used
to determine the potential energy, and the kinetic data, combined
with the kinematic data, allowed the work done by the forces and

moments acting on each segment to be calculated.

CHAPTER V

RESUETS AND DISCUSSION

5.1 Analytical Results and Discussion

The literature concentrates almost exclusively on the use of
segmental energy changes for calculating total body work.
However, it is not immediately apparent as to what these methods
are physically related to. Shorten, et a1 (32) pointed out that
the energy methods currently available do not necessarily relate
to the work done by the muscles of the body. The purpose of this
discussion is to ascertain the physical significance of the
energy methods that have been reviewed and to relate the results
of the analytical methods to the literature.

Equations (21) through (32) show the relationship between
the work done on a segment to the change in the kinetic energy of
that segment. If the work done by gravity on a segment is

written in its potential form, it can be expressed on the energy

side of the work-energy equation. Thus:
(37) AW + AW + AW + AW = AE = ATKE + ARKE + APE

Fdi Fpi Mdi Mpi i i i i

The sum of the segmental change in energy can be written as:

(38) 1§1AE1 - 1§1 AWFdi+ AWFpi+ Adei+ Apr1

39

40

The net work done by the joint reaction forces between two
adjacent segments is assumed small compared to the work done by

the joint muscle moment. Thus, equation (38) can be written as:

n n
(39) 1E1 Adei+ Apri ' 1E1 (Hid+ ”1p)""i At

The relationship between joint "j" with distal segment "i"
and proximal segment "i+1" is shown in Figure 2 and equation

(33). Therefore the work can be summed over the joints ”j":

n q
(40) 1.3104“? Mip)-wi At - 12 n on)

At
'1JJ
Equation (38) can be summed over the time intervals for the event

of interest to give:

m n m q m q

(“1) "a " 131 1§1 AEi " 131 3531 "3'”3 At ' k§1 j§1 AwMj

where WE is the sum of the segmental energy changes for the
entire event.

The above analysis relates the sum of the energy changes in
body segments to the sum of the work done by the muscles of the
body. Equation (41) represents the most idealistic transfer of
work between joints that is possible. Equation (41) can be
applied to determine the physical significance of some of the
energy methods discussed previously.

In the method of Norman, et a1 (28), Wn was defined in

equation (12). The problems associated with this method are

41

immediately apparent. Disregarding the transfer of energy within
a segment (translational kinetic energy to rotational kinetic
energy to potential energy, or any combination of the three
energy forms) does not relate to any physical behavior of the
work done by the joint reaction forces or muscle moments.

In the method of Winter (40), Wvb is shown in equation (13).
To understand its physical significance, it is rewritten here in

its component form:

m n
(42) W AW + AW + AW

wb ' k§1 ' 1§1 Fdi Fpi Mp1+ Adeil
Using the same argument regarding the negligible work done by the

joint reaction forces, equation (42) can be written as:

m 9
(43) W

wb ' k§1 ' 3§1 AWM

J l

Thus, Winter's method allowed for the perfect transfer of
work done between all body joints for a given instant in time.
This method was an improvement over the simple summation of
segmental work, because it did not allow positive work done
during one interval of time to be cancelled out by negative work
done during some other interval of time.

Pierrynowski, et al (29) defined Ww as shown by equation

(17). This can be written in component form as:

m n m n

(4“) "w ‘ k§1 1§1 IAEiI ' k§1 1§1 lAdei+ AwFpi+ Adei+ AwMpi'

42

The work done by the joint reaction forces is within the absolute
value signs thus the work done by the proximal forces of one
segment cannot be (mathematically) cancelled out by work done by
the distal force of the adjacent segment. As a result, the
previous assumption that allowed the work done by the joint
reaction forces to be considered negligible is not valid for
equation (44).

Summing the absolute value of the joint work is not
entirely new to the literature. Elftman (9) used similar
assumptions to arrive at the same basic conclusion of equation
(36). Elftman summed the absolute values of the power generated
at each joint, but did not express his analysis nor his
conclusions in equation form. He investigated the rate of work
done by one- and two-joint muscles in running. He used the same
basic idea of equation (36) as a model for the least efficient
use of joint muscle power. For the upper bounds of efficiency,
Elftman used a model in which work could be transferred from or
to any other joint in the body without loss. This model would be
equivalent to equation (41), written in terms of power. The
emphasis of Elftman's study was that two-joint muscles must be
taken into consideration because of the great improvement in
efficiency that they provide.

Hubley and Wells (21) also used the concept of summing the
absolute value of the work done at each joint. However, they
used this value as a method for normalizing the work done by the
hip, knee, and ankle joints in a vertical jump. This ratio
allowed a comparison between subjects for the work done at each

of these joints.

43

5.2 Experimental Results and Discussion
5.2a Segmental work

Theoretically, the work done on a segment is equal to the
change in energy of that segment. In order to verify the accuracy
of the data collected and the accuracy of the model, the work done
on each segment by the joint reaction forces and by the joint
muscle moments was compared to the change in energy of each
segment. The two methods were found to be almost identical for
all segments except for the foot.

The work done on the foot, calculated using both the energy
method and the kinetic (work) method, is shown in Figure 6. Note
the differences between the two methods during the entire stance
phase; especially at heel contact and before toe-off. The energy
method of calculating work shows that the work done on the foot is
negative at heel contact and becomes increasingly positive between
mid-stance and toe-off. The work calculated using force and
moment data shows a sharp positive work increase for the work done
on the foot at heel contact, followed by negative work done during
mid-stance, remaining negative until toe-off. In Figure 7 the
work done by the ankle joint reaction forces on the foot is
compared to the work done by the ankle joint muscle moment on the
foot. The work done by the ankle joint muscle moment is nearly
equal in magnitude, but opposite in sign, to the work done by the
ankle joint reaction forces on the foot. Thus, small errors in
measuring or calculating either one of these components could
explain the discrepancy.

Robertson and Winter (31) obtained results similar to Figure 6

and Figure 7. They compared the power generated from the ankle

 

  

44

 

 

  

 

.. +«:
E 3 HC TO
8 ’1
a ,3 was...»
if I 35
§ _2; Time (Sec./100)
-41
Figure 6a Run #1
8.
5:
4‘: TO
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Q :
:3; 0‘ . . fi—, v v . . “we- “.mflrhem 44.6“...“
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S -2. / f Time (Sec. /1()0)
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Figure 6b Run #2
A 1 HC TO
3 .
‘ K
2.:
3, . /
CE I
x o? , . ‘
g . "Xr" , K I - . 35
3-21 I,» . _/' Time (Sec./100)
Y I‘ \f')’
Y
-4s

 

Figure 6c Run #3

H Energy Method
I—I Work Method

Figure 6 Work done on the foot segment.

Work (Joules)

 

  
 

45

 

 

 

so 35
Time (Sec./100)

Figure 7a Run #1

 

 

 

 

  

51°: HC .r-a TO
U) s .f
o 1 I’
'3 5: I, \
O . ,1"
MO‘;==gfivvr ...r....,v... .
:4 . f4. 10 is 20 25 so 35
g -5: ‘ Time (Sec./100)
-ma: 1/
1
Figure 7b Run #2

A 10:
3 j HC ', TO

1 I'

. /
S 5 ,r
B I ’kH\H- I; \“

0: j " £3233»-
? “We ‘1! we 20 25 / so 35
2 _5€ \ , Time (Sec./100)

a \

'10: \Hla’

 

Figure 7c Run #3

H Joint Force Work
H Joint Moment Work

Figure 7 Work done by the ankle muscle moment compared to
the work done by the ankle joint reaction forces.

46

joint reaction forces and muscle moment acting on the foot to the
rate of change of the kinetic energy of the foot. They reported a
discrepancy between the two methods for the foot at heel contact
and late push-off. They proposed that changes in the ankle joint
center of rotation may explain the discrepancy. The model used by
Robertson and Winter and the model used in this study assumed a
fixed center of rotation for the ankle joint. However, it is
known that the actual center of rotation changes during stance
phase. Thus, the ankle joint moment calculated for a fixed joint
model would differ from that of a model which included the change
in the center of rotation of the joint. Hence, the work done by
the muscle moment would change accordingly. Additionally, the
work done by the joint reaction force would change. Although the
magnitude of the force would remain essentially the same, the
force would be located at different points on the ankle joint and
would travel through a different path, thus changing the amount of
work done by that force.

Figures 8 through 13 are presented to show the comparison
between the work done on each segment to the change in energy of
each segment for the left shank, thigh, hand, forearm, upper arm,
and head. The two methods were found to be almost identical, as
one would expect.

The above argument concerning the joint center of rotation
should apply to all segments, not just the foot. A possible
reason that there is little discrepancy for the remaining segments
is that any change in the distal kinetics of a segment will alter
the dynamic equations so that the proximal kinetics will also

change. Thus, although the work done by the distal and proximal

47

forces would change, the total work done on a segment would remain
the same. The foot, however, is constrained by the assumption
that the ground reaction forces do no work. Thus, if the exact
path that the ankle forces and moments travel through is not
known, there will be a good chance of discrepancy between the
energy method of calculating work and the kinetic method of
calculating work. By this argument, the energy method of
calculating segmental work is probably the more accurate of the
two.

The work done on the segments of the lower limb followed a
general trend: negative work was done on the foot, shank, and
thigh segments as they decelerated before heel contact. The
segmental work remained negative for approximately half of stance
phase. Positive work was done on these segments during the latter
half of stance phase and increased to a peak near toe off.
Immediately after toe off, the work was found to decrease at a
rapid rate, and became negative for the shank and thigh as these
segments decelerated during the back swing phase of the movement.
Williams and Cavanagh (37) showed similar trends for the total
lower limb energy changes.

The work patterns for the segments of the upper limb were
found to be almost a mirror image of that of the lower limb. Both
before and after heel contact, positive work was done on the hand,
forearm and upper arm segments, but in a decreasing amount. At
approximately the first quarter of stance phase the work done on
these segments was negative and remained negative, with the

exception of Run #1 for the upper arm. After toe off the work

Work (Joules)

Work (Joules)

Work (Joules)

48

 

 

 

JY HC
2.
Y
i.
0‘ - f, . -
i 5
4., _
_21 M Time (Sec./100)
-3; .u‘fl

 

Figure 8a Run #1

 

10 I
’1.) Time (Sec./100)

We!”
a"
I
Figure 8b Run #2

 

 

 

5"”10" 'i' _
(V’s.- Time (Sec./100)

Figure 8c Rwi #3

H Energy Method
H Work Method

Figure 8 Work done on the shank segment.

WOrk (Joules) WOrk (Joules)

Work (Joules)

49

 

 

 

 

 

'2Eo""25"' S'af "is
Time
(Sec./100)

Figure 9a Run #1

HC

 

II Y5 " ' 1b ' . is 20 '7 25 so If}!
. ‘ Time
, M (Sec./100)

\V’/

Figure 9b Run #2
HC TO

 

 

 

'23" . 30.. .rga
Time
(Sec./100)

 

Figure 9c Run #1
*4 Energy Method
*‘ Work Method

Figure 9 Work done on the thigh segment.

50

 

 

 

 

 

 

 

 

 

 
 
  

HC TO
oso«
"a?
(D
'5' 000
:‘i ' '5' '33
.s Time
8 (Sec./100)
:2
-0.50-
Figure 10a Run #1
HC TO
0.50-
”a?
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'3
0.00 n . v .
53 5 #33
,9 Time
8 (Sec./100)
:2
-050.
Figure 10b Run-#2
HC TO
0.502
a 4 "‘u
H
a .0, \
C3 ' '5 "'1o "33
'fi Time
5,: (Sec./100)
-o'm.

 

Figure 10

Figure 10c Run #3

** Energy Method
H Work Method

Work done on the hand segment.

Work (Joules) WOrk (Joules)

Werk (Joules)

1.01

 

 

51

'

 

 

 

 

 

 

 

 

 

Time
(Sec. /100)
Y Y
Figure 11a Run #1
HC T0
1.0«
0.5«
on - . 'fig
-¢5* Time
. (Sec. /100)
-10.
Figure 11b Run #2
HC TO
1n~
J
05-
on
0
-n5 Tm
< (Sec. /100)
-11].

Figure 11c Run #2

*4 Energy Method
“ W0rk.Method

Figure 11 Work done on the forearm segment.

werk (Joules)

werk (Joules)

werk (Joules)
J:

52

 

 

  

 

 

 

 

 

  
  
  

"5‘ HC T0
1.01 l
0.3-
rink
0.0 . ‘lm ...s -1
S I: 35
Time
(Sec./100)
.43..
_'.3-
-20«
Figure 12a Run #1
TO
T" "2‘s"":.'o"”z.'s
Time
(Sec./100)
Figure 12b Run #2
1.5«
10.
os~
no .19
. 35
-ms: Time
—LO- (Sec./100)
l
41.51
-204
l
. Figure 12c Run #3

 

H Energy Method
H Work Method

Figure 12 Work done on the arm segment.

Work (Joules) Werk (Joules)

Work (Joules)

53

 

 

  
 
 

 

 

  
  

 

 

HC TO
2. Y
j:
a ; .-. .. .., ... - . . - T
E to 15 20 35
.4. Time
(Sec./100)
-2.
-3.
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Figure 133 Run #1
HC TO
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H
o F t Y I V r
lo 15 35
.41 Time
(Sec./100)
-z.
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Figure 13b Run #2
2. HC RF
is
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_“ Time
(Sec./100)
-2.
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-4. Figure 13c Run #3

 

»4 Energy Method
FJ WOrk Method

Figure 13 Work done on the head-neck segment.

15-
lO<

54

HC

 

 

 

 

 

 

”a?
0)
o "'l""I""I "" .. vrfi
'é s to 15 2M? 35
r: -5 .
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.fi -40« (Sec./100)
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3 -io~
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Figure 14a Run #1
15- HQ TO
10«
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o 5 lo 5 “w 25 so 35
B -5~ - T'
A me
.54 .1
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Figure 14b Run #2
‘5‘ HC [‘0
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.3 o .- ... ... . KTTEI> . ,.. .-:§... ... ..fi
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1

Figure 14c Run #3

Figure 14 Trunk AE (work).

55

done became increasingly negative as these segments were
decelerated in their forward swing.

The work done on the trunk calculated by the change in energy
of the trunk, is shown in Figure 14. This was not compared to
kinetic calculations of work on the trunk since data for the right
side of the body was not recorded. The work done on the trunk was
similar to the trends noted for the lower limb. Both before heel
contact, and for approximately half of stance phase, the work done
on the trunk was negative as the trunk decelerated. The remaining
half of stance phase is characterized by a double peak. The
negative portion of the graph was due to the work done against
gravity as the center of gravity of the trunk reached a peak at
that time. The final positive portion of the graph peaked near
tee off and was followed by a rapidly decreasing amount of work
immediately after toe off. These results were consistent with the
slopes of the energy for the trunk as published by Williams and
Cavanagh (37).

5.2b Joint Muscle Moment Work

The work done by the ankle joint muscle moment is illustrated
in Figure 15. At heel contact, the work done by the ankle joint
remained near zero. About 0.04 sec after heel contact a large
amount of negative work was done, then, approximately half way
through the stance phase, this was followed by a large positive
work peak which dropped to near zero at toe off. This pattern of
work followed the same pattern for power generated by the ankle

joint moment as reported by Winter (41) and by Elftman (9).

56

The work done by the knee joint is shown in Figure 16. In all
three trials a relatively large negative work peak followed heel
contact, then, again, approximately half-way through stance phase,
a positive work peak was found, which dropped to zero about 0.04
see before toe off. This pattern was similar to the pattern
reported by Winter (41), except for a slight positive peak
immediately after heel contact. Winter did not report this small
peak. The pattern of power generated by the knee joint reported
by Elftman (9) followed the same pattern as that of Winter (41).

Figure 17 shows the work done at the hip joint. The work
pattern differs from the patterns reported by Winter and by
Elftman. However, Winter stated that out of eleven subjects there
was no consistent pattern evident for power generated at the hip.
The three trials shown in Figure 17 support Winter's statement.
Even within the same subject, the only consistent pattern was a
large negative work peak immediately after heel contact.

The work done at the shoulder and elbow joints is shown in
Figures 18 and 19, respectively. The work done followed the same
basic trends as reported by Elftman (9). The work done at the
shoulder was positive before heel contact but became negative
about 0.04 see. after heel contact. Thus it appeared that the
work done at the shoulder caused the arm to decelerate as it swung
forward through stance phase. The subject filmed for this data
had large out of plane motions for his forearm. Although he was
requested to limit the motion as strictly as possible to the
sagittal plane, the left forearm would consistently swing medially
after left toe off. Thus the work done by the elbow joint shown

in Figure 19 is probably not an accurate representation of the

S7

 

  
  

 

 

 

 

 

 

  

 

 

 

 

 

 

TO
7:?
0)
'3
o
3 .. . . .
A4 20 25 30 35
’35 Time (Sec./100)
Figure 15a Run #1
"u?
G)
.—4 . , . . . . ,
:03 20 25 .30 35
to
‘J Time (Sec./100)
E?
:2
Figure 15b Run #2
”u?
G.)
r...
'fi Time (Sec./100)
2

 

 

Figure 15c Run #3

Figure 15 Ankle joint work.

Work (Joules)
l

l
c:
1

 

I
‘
U"
_-__J

 

58

Time (Sec./100)

Figure 16a Run #1

 

 

 

 

1,7 5. TC TO
°’ l
'é o .. 9459221., .. ”iffiftj55h
3 1‘; i \r w /is 20 ‘E' 3'0 35
.fi -3. “\rf» Time (Sec./100)
2’
-m.
Figure 16b Run #2
U) I l
0 ,
Ft . ,-
8 0- r vlvvv'vvv‘v""’-T‘\W
:3 to 20 25 so 35
'25 -=~ Time (Sec./100)
;§
-10.

 

 

Figure 16c Run #3

Figure 16 Knee joint work.

59

 

 
  

 

 

 

 

 

 

 

 

  

4‘ HC TO
A 2'
U)
m i
'3 0‘ :.j
a 7 35
.54 -2. Time (Sec./100)
3.4
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:2 _4‘
1
Figure 17a Run #1
7 HC TO
4..
3? .
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g~.
O ,
'1 . . . e
V 1 i’r .35
.2 .
8 Time (Sec./100)
:2
Figure 17b Run #2
4 HC TO
2.
f“ . r‘
3’3 /
:3 " ' :5
v Time (SeC./100)
.54
H
:3
1
-8~

 

Figure 17c Run #3

Figure 17 Hip joint work.

 

60

 

 

 

 

 

 

 

QO~ HC
fa? 1
(D
'3‘
5% mo 1... 'SB
Ag Time (Sec. /100)
:2
41.5-
% HC TO
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.2 .
8 Time
: (Sec./100)
Figure 18b Run #2
05. HC TO
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H
5
o
:3 mo .. ... .. ..41. .. .j
;‘ 25
8 Time
3 (Sec ./100)

-05 a

 

 

Figure 18c Run #3

Figure 18 Shoulder joint work.

Work (Joules)

WOrk (Joules)

Work (Joules)

0.5~

0.0 *

l
P
m

 

005‘

0.0 ‘

 

455-1

006 "

_‘4P.4F§4=p“5h;\;;4;}ip "£3" f'is so 35
. ’ Time (Sec./100)

9
o

61

HC TO

’4‘ ,2)
20 25 30 35
Time (Sec./100)

Figure 19a Run #1

HC T0

5 J-‘ m 20 25 _. so 35
Time (Sec./100)

Figure 19b Run #2

HC TO

 

Figure 19c Run #3

Figure 19 Elbow joint work.

WOrk (Joules)

WOrk (Joules)

Work (Joules)

0.5-4

 

62

DOO‘#:‘V-f'fi"'vvvv'vvvv'vvvvy-Wfi
.5 10 '5 20 25 30 35

Time (Sec./100)

 

 

 

-05.
Figure 20a Run #1
HC TO ~
0.54 .
mo ... ,.. .., ... ... ... ,.. ..
5 1o 15 20 25 3o 35
Time (Sec./100)
-D.5"
Figure 20b Run #2
no- HC TO
M »M‘M
‘Wr ...,..rv,..v.,
5 15 20 25 so 35
Time (Sec./100)
-osJ

 

Figure 20c Run #3

Figure 20 Neck joint work.

 

63

actual work done at that joint. However, as would be expected,
the work done by these joints is small compared to the work done
by the joints of the lower limb.

The work done by the neck ”joint" is illustrated in Figure 20.
No comparison was available in the literature for this "joint".
No pattern was consistent within the three trials. The work done
by this joint was small compared to the work done by the lower

limbs.

5.2c Total work:

The total work done by the joint muscle moments of the left
side of the body, including the neck, was calculated using
equation (36) and is shown in Figure 21. For comparison, the sum
of the segmental energy changes (WE) is shown in Figure 22 as well
as the method of Norman, et a1 (28) (Wu), the method used by
Winter (40) (wwb)’ and the method utilized by Pierrynowski, et a1
(29) (ww).

As indicated by the sum of the absolute value of the joint
work found in Figure 21, the work done by the muscles of the left
side of the body was on the order of 200 joules for the stance
phase of running for this subject. Since Figure 21 represents the
absolute value of joint work summed over time, a steeper slope
indicates a greater rate of work being done. The slope of the
total joint work curve is steepest between heel contact and toe
off. This slope indicates that the majority of work is done
during stance phase. Very little work is done before heel contact

and after toe off. This is what would be expected since stance

 

 

64

 

 

 

 

 

 

 

HC 1?
re 1
g I" .
:3 150 /
£3 ‘ 2'
ea 2 1
A4 4 A;
IOO~
H ,1
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g I r”Ir
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‘ 4"”,-
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O S 10 15 20 25 30 35
Figure 21a Run #1 Tlme (Sec./100)
1 HC To
4
200~
A ‘ W
o 4 ,r
F4 ' /{
150‘
"'> i
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E; '00: fl.
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Figure 21b Run #2 Tme (seC°/1°0)
um: HC T0
1 l
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200-1 f
”u? . I"
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QTime {gem/100)

Figure 21

Figure 21c Run #3
Total absolute joint work.

—.

1H.

Work (Joules)

WOrk (Joules)

WOrk (Joules)

HC

 

 

V I V V V V " U U V V ' V U ' V I ‘ ' V T 1 ' ' 'fi'fi

  

 

Figure 22a Run #1

 

 

Time
Wm (Sec ./100)

am.
300.. %%
an- ’
"IF
0 v r' v ' fi
30 35
4Q). Time
(Sec./100)
—2m.
-300.

 

 

 

 

Figure 22c Run #3

Figure 22 Total work calculated by four
energy methods

I I I I:
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"‘ s " . '1b‘ ' ' VTB' . ' '20'7' . '25' . ' '30. ' ' r33
-mo. Time
fl (Sec./100)
-200. W

W

n

b

66

phase is the only phase during which energy is added to the body
by the propulsion of the muscles of the lower limb.

A comparison between the energy methods of Figure 22 to the
joint work method of Figure 21 would be difficult. The analytical
discussion showed great differences in the relationship of each of
the methods to the physical work done by the muscles and joint
reaction forces. The results of the energy methods differed from
each other and from the joint work method.

The results of the four energy methods, shown in Figure 22,
include the change in energy of the trunk. Thus, indirectly,
these methods included work done on the trunk by the right hip and
shoulder. Since data collection and analysis was limited to the
left side of the subject, the kinetic data for the right hip and
shoulder were not available. This lack of data created an
additional problem concerning the comparison of the methods.
Although the final values for some of the energy methods appear
close to the final values of the joint work method, this was
merely a coincidence.

As would be expected by the definitions of Wu, WW, and Wfib,
the value obtained for Wu was the largest of the energy methods
calculated, followed by Ww, and W

wb'
equation (41)) was negative throughout stance phase. This

In Figure 22, WE (defined in

negative energy change indicated a deceleration on all segments
until near toe off. At toe-off, the slope of the total energy

curve was positive, indicating that the body was gaining energy.

CHAPTER‘VI

GONCDDSIONS

The purpose of this study was to investigate the methods of
calculating mechanical work as they apply to the study of human
efficiency. Segmental energy methods have been shown to be
inadequate for calculating muscle moment work. The model used in
this study was found to be an improvement over the previous
methods presented in the literature. However, this model also has
several limitations:

1) The relative efficiency of negative and positive work

was not taken into consideration.

2) The elastic component of muscle can do work but its

effects were not considered in this thesis.

3) Isometric contractions and antagonistic muscle

contractions were ignored.

4) The effect of multi-joint muscles were not considered.

5) Studies are limited to planar motion, restricting the

types of motion that can be investigated.

The concept of human efficiency is to provide a normalized
quantity to allow the comparison of new athletic (or prosthetic)
equipment, techniques, and styles. Sensitivity and reliability
are essential. Unfortunately, normalizing mechanical work with
metabolic energy does not provide a very sensitive method for

measuring efficiency. As is apparent by the limitations listed

67

68

above, further study of mechanical work calculations is needed to
improve the sensitivity of measurement. The metabolic energy
consumed for a given event is difficult to differentiate from
resting respiration and requires bulky equipment that limits the
type of motion that can be studied.
Other methods of normalizing mechanical work must be

considered. Hubley and Wells (21) normalized work done at each ,
joint with the total absolute value of work done at all joints and

compared the ratio of work done at each joint.

 

The underlying concepts of human efficiency need further
questioning and study. If mechanical work is used as the
numerator for calculating human efficiency, the sensitivity of
measuring mechanical work must be improved. It must then be
normalized by a parameter that is both physically meaningful but
yet sensitive enough to pick up the effects of minor changes in

the equipment or technique being studied.

BIBLIOGRAPHY

10.

11.

12.

13.

14.

BIBLIOGRAPHY

Cappozzo, A., Figura, F., Marchetti, M. (1976). The
Interplay of Muscular and External Forces in Human
Ambulation, J. Biomech., 9, 35-43.

Cavagna, G.A., Saibene, F.P., Margaria, R. (1963).
External Work in Walking, J. Appl. Physiol., 18, 1-9.

Cavagna, G.A., Saibene, F.P., Margaria, P. (1964).
Mechanical work in Running, J. Appl. Physiol., 19, 249-
256.

Cavagna, G.A., Margaria, R. (1966). Mechanics of Walking,
J. Appl. Physiol., 21, 271-278.

Cavagna, G.A., Thys, H., Zamboni, A. (1976). The Sources
of External Work in Level Walking and Running, J.
Physiol., 262, 630-657.

Cavagna, G.A., Kaneko, M. (1977). Mechanical Work and
Efficiency in Level Walking and Running, J. Physiol., 268,
467-481.

Elftman, H. (1939a). Forces and Energy Changes in the Leg
During Walking, Am. J. Physiol., 125, 339-356.

Elftman, H. (1939b). The Function of Muscles in
Locomotion, Am. J. of Physiol., 125, 357-366.

Elftman, H. (1940). The Work Done by Muscles in Running,
Am. J. of Physiol., 129,672-684.

Ellis, M.J., Hubbard, R.P. (1973). Human and Mechanical
Factors in Ergometry. Quest Monograph XX, June, 3-16.

Fenn, W.O. (1929). Frictional and Kinetic Factors in the
Work of Sprint Running, Am. J. of Physiol., 92, 583-611.

Fenn W.O. (1930). Work Against Gravity and Work due to

Velocity Changes in Running, Am. J. of Physiol., 93, 433-
462.

Fletcher, J.G., Lewis, H.E., Wilkie, D.R. (1960). Human
Power Output: The Mechanics of Pole Vaulting, Ergonomics,
3, 30-34.

Fukunaga, T., Matsuo, A., Yuasa K., Fujimtsu, H., Asahina,
K. (1978). Mechanical Power Output in Running, in
Biomechanics VI-B International Series on Biomechanics,
University Park Press, Baltimore, 17-22.

69

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

70

Gersten, J.W., Orr, W., Sexton, A.W., Okin, D. (1969).
External Work in Level Walking, J. Appl. Physiol., 26,
286-289.

Goldstein, H. (1956). Classical Mechanics. Addison-Wesley
Publishing company, Inc., Cambridge, Mass, 1-20.

Goodman, L.E., Warner, W.H. (1963). Dynamics. Wadsworth
Publishing Company, Inc., Belmont, California, 95-96.

Gray, R.R., Start, K.B., Glencross, D.J. (1962). A Test
of Leg Power, Research Quarterly, 33, 44-50.

Harris, C.O. (1965). Mechanics for Engineers. The Ronald
Press Company, New York, 413-414.

Hay, J.G. (1971). Mechanical Energy Relationships in
Vaulting With A Fiberglass Pole, Ergonomics, 14, 437-448.

Hubley, C.L., Wells, R.P. (1983). A Work-Energy Approach
to Determine Individual Joint Contributions to Vertical
Jump Performance, European J. of Applied Physiology, 50,
247-254.

Kaneko, M., Ito, A., Fuchimoto, T., Shishikura, Y.,
Toyooka, J. (1985). Influence of Running Speed on the
Mechanical Work due to Velocity Changes of the Limb in
Working on A Bicycle Ergometer, in Biomechanics VI-A, Int.
Series on Biomechanics, E. Asmussen, K. Jorgensen (Eds),
Baltimore: University Press, 86-92.

Markus, T.L. (1986). A Procedure for the Dynamic
Investigation of Human Gait. M.S. Thesis, Michigan State
University.

Martin, P.E., Siler, W.L. (1986). An Examination of
Mechanical Energy Transfers Amongst Lower Extermity
Segments During A Kicking Motion, North American Congress

on Biomechanics, Montreal, Quebec, Canada, Aug. 25-27, 41-
42.

Matsuo, A., Fukunag, T., Asami, T. (1985). Relation
Between External Work and Running Performance in Athletes,
in Biomechanics IX-B, Winter, D.A., Norman, R.W., Wells,
R.P, Hayes, K.C., Patta, A.E. (Eds), Baltimore, University
Park Press, 319-324.

Meriam, J.L. (1978). Engineering Mechanics Volume 2:
Dynamics. John Wiley & Sons, 1978, pp 130,370.

NASA Reference Publication 1024 (1978). Anthropometric
Source Book Volume I: Anthropometry for Designers.

Norman, R.W., Sharratt, M.T., Pezzack, J.C., Noble, E.G.
(1976). Reexamination of the Mechanical Efficiency of
Horizontal Treadmill Running, in Biomechanics V-B,
International Series on Biomechanics, P. Komi (Ed),
Baltimore: University Press, 87-93.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

71

Pierrynowski, M.R., Winter, D.A., Norman, R.W. (1980).
Transfer of Mechanical Energy Within the Total Body and
Mechanical Efficiency During Treadmill Walking,
Ergonomics, 23, 147-156.

Quanbury, A.O, Winter, D.A., Reimer, G.D. (1975).
Instantaneous Power and Power Flow in Body Segments During
Walking, J. of Human Movement Studies, 1, 59-67.

Robertson, D.G., Winter, D.A. (1980). Mechanical Energy
Generation Absorption and Transfer Amongst Segments During
Walking, J. Biomech., 13, 845-854.

Shorten, M.R., Wootton, S.A., Williams, C. (1981).
Mechanical Energy Changes and the Oxygen Cost of Running,
Engineering in Medicine, 10, 213-217.

Singer, F.L. (1954). Engineering Mechanics, (second ed.)
Harper 8 Brothers, New York, 398.

Truesdell C., Toupin, R. (1960). The Classical Field
Theories. Encyclopedia of Physics, 8. Flugge (Ed.),
Springer-Verlag, 569-71.

Walton, J.S. (1981). Close-range Cine-photogrammetry: A
Generalized Technique for Quantifying Gross Human Motion,
Ph.D. Dissertation, Pennsylvania State University.

Williams, K.R. (1980). A Biomechanical and Physiological
Evaluation of Running Efficiency, Ph.D. Thesis,
Pennsylvania State University.

Williams, K.R., Cavanagh, P.R. (1983). A Model for the
Caculation of Mechanical Power During Distance Running, J.
Biomech., 16, 115-128.

Winter, D.A., Quanbury, A.D., Reimer, G.D. (1976).
Instantaneous Energy and Power Flow in Normal Human Gait,
in Biomechanics V-A, Int. Series on Biomechanics, P.V.
Komi (Ed), Baltimore: University Park Press, 334-340.

Winter, D.A., Robertson, D.G.E. (1978). Joint Torque and
Energy Patterns in Normal Gait, Biol. Cybernetics, 29,
137-142.

Winter, D.A. (1979). A New Definition of Mechanical Work
Done in Human Movement, J. Appl. Physiol., 46, 79-83.

Winter, D.A. (1983). Moments of Force and Mechanical
Power in Jogging, J. Biomech., 16, 91-97.

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