ARL-TR-2764 NOVEMBER 2002

Exoskeleton Power and Torque Requirements

Based on Human Biomechanics

Harrison P. Crowell III

Angela C. Boynton

Michael Mungiole

Approved for public release; distribution is unlimited.

ARMY RESEARCH LABORATORY
NOTICES

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The findings in this report are not to be construed as an official

Department of the Army position unless so designated by other

authorized documents.

Citation of manufacturers’ or trade names does not constitute an official

endorsement or approval of the use thereof.

DESTRUCTION NOTICE Destroy this report when it is no longer

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i

Army Research Laboratory

Aberdeen Proving Ground, MD 21005-5425

______________________________________________________________________________

ARL-TR-2764 November 2002

______________________________________________________________________________

Exoskeleton Power and Torque Requirements Based on

Human Biomechanics

Harrison P. Crowell III and Angela C. Boynton

Human Research & Engineering Directorate

Michael Mungiole

Computational and Information Sciences Directorate

______________________________________________________________________________

Approved for public release; distribution is unlimited.

______________________________________________________________________________
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ACKNOWLEDGMENTS

The authors wish to thank John F. Jansen of the Oak Ridge National Laboratory, Patrick W.

Wiley of the Human Research and Engineering Directorate of the U.S. Army Research

Laboratory (ARL), and Steven Stanhope of the National Institutes of Health for their technical

reviews of this report and Nancy J. Nicholas of the Computational and Information Sciences

Directorate of ARL for her editorial review of this report.
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Contents

Executive Summary ............................................ 1

1. Introduction............................................. 5

2. Typical Infantry Missions ................................... 6

3. The Application of Human Biomechanics During Locomotion to

Exoskeleton Design ........................................ 7

4. Effects of Methods and Analyses on the Accuracy of Kinematic and

Kinetic Data ............................................. 10

4.1 Assumptions........................................... 10

4.2 Limitations............................................ 12

4.3 Variability ............................................ 13

4.4 Accuracy ............................................. 15

5. Level of Effort Required During Locomotion ...................... 16

6. Lower Limb Kinematics and Kinetics for Various Activities............ 18

6.1 Walking ............................................. 18

6.1.1 Walking at a Normal Speed ............................. 18

6.1.2 Walking at Various Speeds.............................. 20

6.1.3 Walking With Loads.................................. 21

6.2 Running ............................................. 23

6.3 Stair Climbing.......................................... 25

6.4 Jumping ............................................. 27

6.5 Kneeling ............................................. 28

7. Lower Limb Peak Power Profiles for Soldier Missions................ 29

7.1 Procedure............................................. 29

7.2 Mission Scenarios ....................................... 31

7.2.1 Movement to Contact ................................. 31

7.2.2 Clear Building ..................................... 32

8. Conclusion .............................................. 32

References ................................................... 33

Appendices

A. Lower Limb Kinematics and Kinetics for Various Activities............... 37

B. Lower Limb Peak Power Profiles for Soldier Missions .................. 47

Report Documentation Page....................................... 51
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Figures

 1. Gait cycle for the left and right legs during walking....................... 8

 2. Free body diagram of the foot in the sagittal plane at (a) heel strike and (b) toe off .... 9

 3. Subject ascending stairs with reflective markers placed on right leg ............. 11

Tables

 1. Speed and gait cycle frequency ................................... 8

 2. Maximum joint moments during walking, running, and concentric isokinetic testing ... 18

 3. Maximum joint powers generated during walking, running, and concentric

isokinetic testing ........................................... 18

 4. Peak kinetic values during one cycle of normal walking .................... 20

 5. Peak power values during one cycle of walking at three different cadences......... 21

 6. Peak moment values during one cycle of walking with four different backpack loads... 22

 7. Range of peak kinetic values for 5th to 95th percentile male soldiers during one

cycle of normal walking ....................................... 23

 8. Peak kinetic values during stance phase of normal running at 3.8 m/s ............ 23

 9. Peak kinetic values during the stance phase of running at five different speeds ...... 24

10. Peak moment values for 5th to 95th percentile male soldiers during one cycle of

running at a moderate pace (3.8 m/s) ............................... 24

11. Three-dimensional peak moment values during the stance phase of normal stair

ascent and descent .......................................... 25

12. Peak power values during one cycle of normal stair ascent and descent ........... 26

13. Peak kinetic values for 5th to 95th percentile male soldiers during one cycle of

stair ascent and descent ....................................... 27

14. Peak kinetic values during the stance phase before toe-off of a running vertical jump .. 27

15. Peak kinetic values for 5th to 95th percentile male soldiers during the stance

phase before toe-off of a running vertical jump ......................... 28

16. Loads carried ............................................. 30

17. Peak and average power values for typical soldier tasks .................... 31
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Executive Summary

The Defense Advanced Research Projects Agency (DARPA) is funding the development of

exoskeletal devices that are intended to increase the speed, strength, and endurance of soldiers in

combat environments. The purpose for this work was to provide guidance for the design of the

lower limbs of an exoskeletal device. In providing design guidance, the authors had two goals.

The first goal was to provide estimates of the angles, torques, and powers for the ankles, knees,

and hips of an exoskeleton based on data collected from humans. The second goal was to

calculate the mean power required for various tasks and the total peak power needed by the

lower limbs of the exoskeletal device for two “typical” infantry missions.

In order to apply human biomechanical data to design guidance for an exoskeleton, six

assumptions were made:

1. The size, mass, and inertial properties of the exoskeleton will be equivalent to those

of a human.

2. The exoskeleton will carry itself (including power supply) and the soldier’s load.

3. The joint torques and joint powers scale linearly with mass.

4. The exoskeleton’s gait will be the same as a human’s gait.

5. The exoskeleton will carry a load on its back in the same way that humans carry loads

on their backs.

6. The exoskeleton will move at the same speed, cover the same distance, and carry the

same load as a soldier who does not have an exoskeleton.

The human biomechanical data used in this report came from studies reported in relevant

journals and technical reports. These data are from studies of normal walking, walking at various

speeds, walking while loads are carried, running at a moderate pace, and running at various

speeds. Other activities for which joint angle, torque, and power data were obtained included

stair climbing, jumping, and kneeling. The figures in Appendix A show the joint angles, joint

moments, and joint powers for walking, walking while a load is carried, running, ascending

stairs, descending stairs, and jumping. It is important to note that the joint power data are from

calculations of the mechanical work done by the lower limbs to move the entire body, not

physiological work based on oxygen consumption.

In this report, the calculation of total peak power focused on two hypothetical missions, a

movement-to-contact mission and a clear-building mission. These missions represent the kind of

diverse missions for which an exoskeleton might be used. Also, the fundamental tasks (walking,

jogging, etc.) involved in these missions are the same tasks that occur in other infantry missions
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(e.g., infiltrate and raid). The movement-to-contact mission took place over a 16-hour period,

and the exoskeleton carried the soldier’s sustainment load (35 kg) during most of that time. In

the clear-building mission, which lasted approximately 2 hours, the exoskeleton carried the

soldier’s fighting load (24 kg). The soldier in these hypothetical missions was a 50th percentile

male whose mass was 77 kg.

The data used to calculate total peak power for the movement-to-contact and clear-building

missions came from the joint power data in Appendix A. Five simplifying assumptions about

gait and the exoskeleton were made in order to calculate peak power. The assumptions were

1. Increasing the load carried has the same effect on peak power as does increasing body

mass.

2. Joint powers in the frontal and transverse planes are small compared to the sagittal

plane. Therefore, only sagittal plane peak power profiles were calculated.

3. Normal gait is symmetrical.

4. Peak power values for assuming and leaving kneeling and prone positions, crawling,

and climbing a ladder can be approximated with the values for stair ascent.

5. Power values of other lower extremity joints, such as the metatarsophalangeal joint,

are small and therefore not included in the peak power calculation.

Then, a four-step process was used to calculate the peak power required by the lower limbs of

the exoskeleton during the movement-to-contact and clear-building missions.

1. Spreadsheets that listed each task in chronological order (walking, jogging, jumping,

etc.), which occurred during the missions were created. The time required for each task and the

load carried were also listed (see Table B-1 in Appendix B).

2. The powers required at each joint (left and right ankle, knee, and hip) were summed,

and peak and average power values were identified for each task and load combination (see

Figure B-1 and Table 17).

3. The peak power for each task and load combination was entered into the spreadsheet.

4. The peak power and the time required for each task were plotted for each mission

(see Figures B-2 and B-3).

The accuracy of the results calculated in this report is in part a reflection of the accuracy of the

original data. When biomechanical data are collected, certain assumptions, limitations, and

variabilities affect the accuracy of the data1. The accuracy of data collected in biomechanical

 

1For example, assumption: joint centers remain fixed throughout the range of motion; limitation: when position data

are differentiated to determine velocity and acceleration, the noise in the position data becomes amplified;

variability: differences in experimental methods and trial-to-trial differences in how a subject walks or runs.
3

studies is generally within 20% of their real values. It is likely that when these data are used to

calculate kinetic variables such as joint moments and powers, compensating errors keep the

overall accuracy of the results within 20% of their true values. Therefore, the power

requirements calculated in this report have a tolerance of ±20%.

During most of the movement-to-contact mission, the soldier and exoskeleton walked at a natural

pace, and the exoskeleton carried the sustainment load. Although the average power required for

this task was 200 watts (W) ±40 W, there were peak power requirements of 500 W ±100 W. The

peak powers are important because the power supply must be sized to meet the peak

requirements. If the power supply cannot meet the peak requirements at the proper frequency,

then the exoskeleton may, in contrast to its goal, decrease the soldier’s speed, strength, and

endurance. The 500 W ±100 W peaks occurred at approximately 2 Hz. This frequency coincides

with ankle plantarflexion that occurs during “toe-off” in each gait cycle. When contact was made

with the enemy, part of the sustainment load was dropped, and the soldier and the exoskeleton

performed a variety of tasks including sprinting. The average power required during this part of

the mission was 3500 W ±700 W with peaks of 5500 W ±1100 W which occurred at 4 Hz. The

4-Hz frequency coincides with ankle plantarflexion during toe-off for sprinting.

The power requirements for the clear-building mission were more variable than the power

requirements for the movement-to-contact mission. This occurred because the soldier changed

his speed many times as he moved to the building and then from room to room. For the clearbuilding mission, the average power required was 200 W ±40 W to 300 W ±60 W during much

of the mission. Peak powers rose to 400 W ±80 W for walking at a natural pace and frequently to

700 W ±140 W for walking at a fast pace. There were several times when the soldier was

jogging. At those times, the average power was 1000 W ±200 W, and the peak power was 2000

W ±400 W. The highest peak power requirement for this mission (approximately 3000 W ±600

W) occurred at the beginning when the soldier was running up to the building. As with the

movement-to-contact mission, the peak powers must be delivered at approximately 2 to 4 Hz.

In conclusion, the data provided in this report can be used as a baseline for the initial design of

an exoskeletal device. These data can be used to evaluate currently available and near-term

technology to determine the feasibility of developing a practical exoskeleton. If such a device is

deemed to be feasible, the joint angles, torques, and powers presented in Appendix A and

Table 17 could be used to design lower limb joints and actuators, and the peak power profiles

(Figures B-2 and B-3) could be used to size the power supply.
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INTENTIONALLY LEFT BLANK
5

EXOSKELETON POWER AND TORQUE REQUIREMENTS

BASED ON HUMAN BIOMECHANICS

1. Introduction

For the purposes of this report, an exoskeleton is a user-worn device that augments and enhances

the wearer’s speed, strength, and endurance. The exoskeleton carries its own power supply and

moves synchronously with the user. Although such devices do not currently exist, efforts are

under way to create them.

The Defense Advanced Research Projects Agency (DARPA) is funding a program to develop

exoskeletal devices. DARPA has set requirements for very versatile machines ones that will

increase the speed, strength, and endurance of soldiers in combat environments. The requirements are set forth in a broad agency announcement (BAA) (DARPA, 2000). The BAA specifically solicits “devices and machines that accomplish one or more of the following: 1) assist

pack-loaded locomotion, 2) prolong locomotive endurance, 3) increase locomotive speed,

4) augment human strength, and 5) leap extraordinary heights and/or distances.” To accomplish

these goals, innovative actuators and power supplies must be developed. The information in this

report in intended for designers creating the actuators and power supplies for exoskeletons.

This report provides a baseline estimate of the total system power and the individual joint

torques required for the lower limbs of an exoskeletal device. These estimates are based on

human biomechanical data obtained from relevant journal articles and technical reports. These

data are presented in the succeeding sections of this report. Because they come from a variety of

sources, the data have been adapted from their original figures and tables so that they can be

presented in a consistent format. The data used are from calculations of the mechanical work

done by the lower limbs to move the entire body, not physiological work based on oxygen

consumption.

There are two goals for this work. The first goal is to determine the angles, torques, and powers

for the ankles, knees, and hips. These estimates can then be used to help in the design of joints

and in selection of actuators for the exoskeleton. The second goal is to determine the total mean

and peak power needed by the exoskeletal device for “typical” infantry missions. By the estimation of mean and peak power requirements, the power supply for the exoskeleton can be sized.

In the application of human biomechanical data obtained from journal articles and technical

reports to the design of an exoskeleton, several assumptions are made. The first assumption is

that the size, mass, and inertial properties of the exoskeleton will be equivalent to those of a

human. The second assumption is that the exoskeleton carries itself (including power supply)

plus the soldier’s load. The third assumption is that joint torques and joint powers scale linearly
6

with mass. Increases in vertical ground reaction forces have been shown to be proportional to

increases in load carried (Lloyd & Cooke, 2000; Tilbury-Davis & Hooper, 1999). Thus, the joint

torque and power requirements for an exoskeleton are a function of the mass of the exoskeleton

itself plus the load it is carrying. The fourth assumption is that the exoskeleton’s gait will be the

same as a human’s gait. This implies that soldiers will not be required to alter their gait to use the

exoskeleton. Changes in gait have been shown to increase the physiological energy expended

during locomotion (McMahon, Valiant, & Frederick, 1987). The fifth assumption is that the

exoskeleton will carry a load on its back in the same way that humans carry loads on their backs.

This is because carrying backpack loads high and close to the back requires less energy expenditure than carrying the same loads low and farther away from the back (Obusek, Harman,

Frykman, Palmer, & Bills, 1997). Also, carrying a load close to the body’s center of gravity

requires less energy than distributing the load to the extremities (Martin, 1985; Soule &

Goldman, 1969). The sixth assumption is that a soldier with an exoskeleton will move at the

same speed, cover the same distance, and carry the same load as a soldier who does not have an

exoskeleton. This implies that the initial exoskeleton prototype may not allow the soldiers to

perform a mission faster, but they will not become fatigued because the exoskeleton is carrying

the load.

2. Typical Infantry Missions

Infantry soldiers have many different missions, and each mission is affected by such things as the

enemy, terrain, weather, troops available, and time available. Soldiers participate in missions as

part of a larger group at least a squad or platoon. While it is not possible to define a “typical”

infantry mission, some of the more common missions for infantry soldiers include movement to

contact, react to contact, reconnaissance, infiltrate, exfiltrate, ambush, assault, raid, defend builtup area, clear building, clear wood line, clear trench line, breach obstacle, and “knock out”

bunker. The fundamental tasks of soldiers during these missions include walking, jogging,

running, crawling, kneeling, climbing, jumping, rolling, throwing a grenade, and firing a

weapon.

The analysis in this report focuses on a hypothetical movement-to-contact mission and a hypothetical clear-building mission. These missions were chosen because they represent the kind of

versatility that is expected of an exoskeleton. The hypothetical movement-to-contact mission

used in this analysis takes place over a 16-hour period, and the exoskeleton carries the soldier’s

sustainment load during most of that time. This mission has long periods with roughly constant

power requirements. However, when contact is made, there are brief periods with very high

power requirements. The clear-building mission is typical of something soldiers fighting in an

urban environment would do. Here, speed and strength are important assets. The clear-building

mission is intense, but its duration is relatively short (approximately 2 hours). In the clear-
7

building mission, periods with relatively high power requirements occur more frequently than in

the movement-to-contact mission. Also, large changes in the power required occur frequently.

Finally, the fundamental tasks (walking, jogging, etc.) involved in these two missions are representative of the tasks that take place in the other missions listed previously (react to contact,

reconnaissance, etc.).

The initial objective for the exoskeleton is for it to assist soldiers in performing their current

missions. Thus, scenarios created for this analysis describe missions in the manner that soldiers

who are not using exoskeletons might perform them. This is the baseline upon which system

development can be founded. If the development and use of exoskeletons are successful, doctrine

and tactics for various missions could change. For example, future missions by soldiers with

exoskeletons would be different because the exoskeleton would carry most of the load.

Therefore, the soldier with an exoskeleton would probably carry heavier loads for a longer time

and at faster speeds.

3. The Application of Human Biomechanics During Locomotion to

Exoskeleton Design

Figure 1 depicts a single gait cycle for the left and right legs during walking. A gait cycle is the

period of time for one stride, that is, the time from one event (usually initial foot contact) to the

next occurrence of the same event with the same foot. For each leg, the gait cycle can be divided

into a stance phase and a swing phase. Within the stance phase, there is a period of double

support: both feet on the ground. As walking speed increases, the period of double support

decreases. As speed continues to increase, the period of double support can disappear, and there

can be a period of “flight” when both feet are off the ground. The appearance of this flight phase

is one definition of running that holds for all but a few cases.

The range of gait cycle frequencies for walking and running, based on results reported by

Minetti, Ardiago, and Saibele (1994) and Fukunaga, Matsuo, Yuasa, Fujimatsu, and Asahina

(1980), are shown in Table 1. The actuators for the exoskeleton need to operate at frequencies

that are the same as the gait cycle frequencies roughly 50 to 130 cycles per minute. Gait cycle

frequencies also have implications for the exoskeleton’s power supply. The power demands are

not constant during these cycles; rather, there are peaks and valleys. For tasks such as walking,

running, and stair climbing, peak power values will occur at two times during the gait cycle

(once for the left limb and once for the right limb); therefore, the power supply must be able to

meet these peak demands at twice the frequency of the gait cycle.
8

Figure 1. Gait cycle for the left and right legs during walking (adapted from a figure that appeared

on page 26 of a chapter by Verne T. Inman et al., in Human Walking, edited by Rose

and Gamble, published by Williams & Wilkins, Baltimore, MD; 1981, and used with

permission of Lippincott Williams & Wilkins).

Table 1. Speed and gait cycle frequency

______________________________________________________________________________

Speed Gait Cycle Frequency

(meters/second) (strides/minute)

______________________________________________________________________________

Walking (Minetti et al., 1994) 1.1 52

2.4 82

Running (Minetti et al., 1994) 1.7 80

3.3 89

Running (Fukunaga et al., 1980) 3.0 81

6.0 96

9.0 128

______________________________________________________________________________

The kinematic and kinetic data collected in biomechanical studies are typically used for inverse

dynamics calculations of joint forces and moments. Joint moments and joint torques are equivalent, and both terms are used throughout this report. Figure 2 shows a free body diagram of the

foot at heel strike (Figure 2a) and at toe-off (Figure 2b). In inverse dynamics, the force

Time, percent of cycle

Double

support

R. Single support L. Single support Double

support

Double

support

L. Swing phase L. Stance phase

0% 40% 50% 90% 100%

R. Stance phase R. Swing phase

0% 10% 50% 60% 100%

Right

Initial

Contact

Left

PreSwing

Left

Initial

Contact

Right

PreSwing

Right

Initial

Contact

Left

PreSwing
9

equilibrium and moment equilibrium equations for rigid bodies are solved to give the proximal

force and proximal moment for each segment (i.e., foot, shank, and thigh). Figure 2a shows that

the net joint reaction moment about the ankle is in the negative direction. The sign (positive or

negative) is determined by the coordinate system used to define the data collection space. In this

case, it is a right-hand coordinate system, and the subject is walking in the positive x-direction.

In Figure 2b, the net joint moment is in the positive direction.

Figure 2. Free body diagram of the foot in the sagittal plane at (a) heel strike and (b) toe off.

(Notation: m = mass of the segment [in this case, the foot], g = acceleration attributable

to gravity, mg = weight of the segment, Fd = distal force (in this case, the force of the

ground on the foot), Fp = proximal force [in this case, the force on the foot at the ankle

joint], Mp = proximal moment [in this case, the moment on the foot at the ankle joint].)

Joint power (P) is the “dot product” of the moment (M) at the joint and the angular velocity ( )

of the distal segment with respect to the proximal segment (i.e., P = M • ). Depending on the

direction of the moment and the direction of the angular velocity, the power can be positive or

negative. If the signs for the moment and angular velocity are both positive or both negative, the

power is positive. If the signs for the moment and angular velocity are different, the power is

negative. In the biomechanics literature, positive power is called “power generated,” and negative power is called “power absorbed.” The term “power absorbed” is somewhat misleading. It is

important to note that power absorption is not a passive activity. In reality, the muscles are active

during this time. They are doing “eccentric contractions”. That is, they are generating forces

while they are lengthening. For exoskeleton design, this means that the actuators need to be

active and provide torques at the joints during these periods. This is particularly true of the knee

after heel strike.

Negative Moment

(Extension)

X

Z

Y

Mp

Fp

mg

Fd

Positive Moment

(Flexion)

(b)

Fd

Fp

Mp

mg

(a)
10

4. Effects of Methods and Analyses on the Accuracy of Kinematic and

Kinetic Data

The following four sections are concerned with items that may have implications for an exoskeletal device. The first of these has to do with obtaining accurate measures to determine the

torque and power requirements for human locomotion because the exoskeleton is expected to

provide a substantial portion of these kinetic requirements. Specifically, biomechanics

researchers make several assumptions in the collection and analysis of movement data, which

contribute to the accuracy of the joint kinetics. In addition to these external factors that affect

data accuracy, there is also the variability in kinematics and kinetics that is associated with the

neural control system, which may produce slightly different muscle activity patterns for each

trial of a well-learned multiarticular movement such as locomotion. Finally, an attempt is made

to determine the accuracy of kinematic and kinetic results, based on the assumptions, variability,

and potential errors that exist in the collection and processing of measured and estimated data.

4.1 Assumptions

The biomechanical data presented in this report come from studies where camera systems

tracked markers placed on subjects’ legs (see Figure 3) as they walked, ran, or jumped on a force

plate. The camera system measures the positions of the markers, and the force plate measures the

ground reaction forces (GRFs) and moment. The marker position data and the force plate data

are then used to calculate the kinematics and kinetics of the movement. Special computer

programs use the kinematic and kinetic data to calculate joint angles, forces, moments, and

powers. Also, anthropometric measures taken for each subject are used to estimate the segmental

inertial properties for each subject. During this data collection process, several assumptions are

generally made by the researchers to allow them to obtain these data without a prohibitive

amount of effort. Indicated next are several of the main assumptions that simplify the process of

collecting and analyzing the kinematic and kinetic data during locomotion and other movements.

Some of the assumptions relate to the simplified manner in which the body is modeled. The body

is assumed to be comprised of a fairly small number of rigid bodies, such as the hands, forearms,

upper arms, feet, etc. The entire torso is usually assumed to be a single segment or rigid body,

with its length extending from the hip to the shoulder. Assuming this relatively large mass

(approximately 35% of the entire body mass) as a single segment is a simplifying assumption for

what is really a series of individual segments that are delineated by the articulations at the

vertebrae. Related to this assumption is the fact that not every articulating joint is considered

during movement analysis. As an example, the metatarsophalangeal joint of the foot is usually

ignored but it may be appropriate to be considered during locomotion, particularly during

running. Stefanyshyn and Nigg (2000) have shown that the maximum power absorbed at this
11

joint during running at 4 m/s was nearly 500 W and the energy absorbed was 27.6 J over a time

period of approximately 0.14 s.

Figure 3. Subject ascending stairs with reflective markers placed on right leg.

Also related to the assumed limited number of rigid bodies and articulating joints are the degrees

of freedom that exist at these particular joints. During locomotion, the sagittal plane has often

been the only plane of movement that was investigated, while movements in the secondary

planes (frontal and transverse) were usually ignored. Recently, however, there has been an

increase in the number of studies in which researchers performed three-dimensional analyses of

locomotion. These studies have shown that the kinetic variables in the frontal and transverse

planes can be of significant value and should not be ignored (Eng & Winter, 1995; Glitsch &

Baumann, 1997; McClay & Manal, 1999).

To obtain kinematic data, researchers place markers on the skin directly over selected anatomical

landmarks that are traditionally used to represent joint centers. It is assumed that these markers

remain at a fixed position with respect to the landmarks and accurately represent the joint centers

for the duration of the movement. The subject’s skin often slides over these landmarks, however,

resulting in the markers no longer truly representing the locations of the joint centers. To add to

the uncertainty of desired anatomical locations, the joint centers often do not remain at a fixed

location during joint rotation. For a fairly extreme case, Smidt (1973) showed that the knee joint

center moves a substantial amount when the knee joint undergoes flexion and extension.
12

Specifically, he found that as a subject’s knee is moved between 0° and 90° of flexion, the locus

of points representing the joint center at each instant forms an arc of an ellipse that is 3.2 cm in

length.

Kinematic and kinetic measures are often obtained only for one side of the subject’s body,

assuming that bilateral symmetry exists for each variable during locomotion. This is not often the

case, and research studies have shown that subjects may exhibit a substantial amount of

asymmetry during movement (Sadeghi, Allard, Prince, & Labelle, 2000).

The inertial properties of the subjects are required to be known or estimated in inverse dynamic

analyses. These properties include the mass, center of mass, and moment of inertia of each

individual segment assumed in modeling the body. A number of methods have been used to

estimate these inertial properties. The most popular method uses regression equations (Clauser,

McConville, & Young, 1969) with specific anatomical dimensions used as the independent

variables for these equations.

An important simplifying assumption in movement analysis is that the possible contributions of

joints and ligaments to movement are ignored; that is, it is assumed that the joint kinetic values

can be attributed to the muscle tendon complex only. In reality, during extreme flexion or

extension at a joint, some combination of anatomical constraints and stretched ligaments may

also contribute to the moment developed at that particular joint. If the actual contributions from

these hard and soft tissues were considered, the portion of the joint moment value assumed to be

developed by muscles spanning that joint would likely be reduced.

4.2 Limitations

Typically, the procedure to obtain linear and angular velocities and accelerations uses a motion

analysis system to obtain position data, which are then differentiated by finite difference techniques, once to obtain the velocity and again to obtain acceleration data. Because of the small

noise associated with the digitization process while the data are obtained and by the nature of the

finite difference technique, the errors associated with the acceleration data can be quite significant. This noise can be reduced by smoothing techniques that diminish high frequency components of the noise, based on the physical justification that kinematic variables (velocity and

acceleration) associated with realistic mechanical systems are band limited. This can be considered a limitation in terms of the resolution of the motion analysis equipment contributing to

noise that is magnified after differentiation.

Another limitation of movement analysis studies involves how the selected sampling rate affects

measures obtained from analog signals. As an example, if it were desired to obtain the time

period that the foot is in contact with the ground during walking, one often would select a

threshold value for the vertical force. When the force applied by the subject exceeds this

threshold value, it is assumed that the subject has made contact with the ground, but in reality,

contact was made at some earlier time that was between the instant when this sample was
13

collected and the next earlier sample. This relates to the resolution of the equipment used to

measure the kinematics and kinetics of the body during movement.

For inverse dynamic analyses in which joint power is often the variable that is determined,

several limitations exist. First, one cannot determine the degree of co-contraction between the

agonist and antagonist muscle groups. An inverse dynamic analysis only provides net joint

moment and power measures. As an example, if it is determined that the joint power generated is

60 W, that may be attributable to 60 W generated by the agonists while no power is generated by

the antagonists. It could also be some combination of power in which a value greater than 60 W

is generated by the agonists while the antagonists absorb an amount of power equivalent to the

difference between 60 W and the power generated by the agonists. Thus, an infinite number of

agonist-antagonist power combinations would be possible. This same argument that was made

for joint power would also be true for the respective moments produced by the agonist and

antagonist muscle groups.

Even if the moment and power values were able to be determined for a particular muscle group,

it is not currently feasible for researchers to accurately determine individual muscle forces,

which would be necessary to determine the individual muscle moment and power values.

Forward dynamics analyses have been performed in which muscle models were used to estimate

muscle kinematic (e.g., muscle and tendon velocities) and kinetic values. These studies have

proved somewhat useful, but other assumptions in addition to the ones indicated before must be

made. The results from these studies often deviate substantially from those found when inverse

dynamics analyses are performed (Jacobs, Bobbert, & van Ingen Schenau, 1996).

4.3 Variability

Several of the assumptions and limitations indicated previously would contribute to the variability that occurs during movement, including a well-learned task such as locomotion. In

addition, other factors contribute to the variability encountered in any type of unrestricted

movement. One of these factors would include the location and orientation of the principal axes

of each segment. Different researchers may select different anatomical landmarks to define the

principal axes of the segments. This has resulted in a substantial variation in joint angles reported

at any instant across studies while the kinematic trends over a locomotion cycle may be quite

similar among these studies.

For two-dimensional analyses, a factor that contributes to the variability of kinetic data is the

location of the center of pressure. The center of pressure location is a representation of where the

centroid of the GRF is positioned on the shoe in contact with the force platform. Because of the

potential difference in foot structure among individuals, the actual location on the foot on which

the center of pressure acts could be slightly different among individuals wearing the same

footwear. In addition, the orientation of the foot (with respect to the horizontal axis of the force

platform in the direction of walking) would contribute to a researcher’s correctly locating the

actual center of pressure on the foot. In a two-dimensional analysis, the greater the angle
14

between the longitudinal axis of the foot and this force platform axis, the greater would be the

error in the center of pressure location on the foot because the axis of the foot would be outside

the two-dimensional (sagittal) plane in which movement is assumed. These errors, in turn, would

contribute to the variability in the moment arm of the GRF acting about the ankle joint. In

addition, when the GRF values are fairly large, their moment arms are quite small compared to

overall dimensions of the foot, and thus, the kinetic variables would be fairly sensitive to the

center-of-pressure location.

In a study that specifically investigated this issue, McCaw and DeVita (1995) determined the

variation in joint torques during the stance phase of gait if the anterior-posterior location of the

center of pressure was in error by 1.0 cm. They found that this center of pressure error resulted in

an average change of 14% in the joint moments at the hip, knee, and ankle, and they concluded

that published joint moment data for gait may be in error by 7% to 14% solely because of an

inaccurate center-of-pressure location.

In general, a certain amount of variability can also be attributed to the difference in body

structure among individuals. While inertial property estimates may be quite accurate for an

individual, it is not uncommon for these estimates to be generally in error by as much as 10% of

the actual value. These errors would be carried through the calculations in the determination of

kinetic measures in an inverse dynamics analysis. As an example, Nagano, Gerritsen, and

Fukashiro (2000) simulated errors of 10% of segment length for the joint center and segment

center of mass locations and determined that the work output obtained was in error by 20% and

6%, respectively. Challis and Kerwin (1996) determined errors in the joint moment for a loaded

elbow flexion movement when kinematic, segmental inertial property, and joint center values

were varied by amounts consistent with measurement uncertainties for these respective variables.

They found that varying the kinematics resulted in the largest changes in elbow joint moment,

producing a value that was 21% different from the peak joint moment.

In a fairly comprehensive study of joint moment variability during walking, Winter (1984)

obtained within- and between-subjects measures of variability. He provided plots of joint

positions, GRFs, and joint moments and determined a coefficient of variation (CV) based on the

root mean square of the standard deviation. In addition, he determined a support moment that is

the algebraic sum of the moments at the ankle, knee, and hip joints and represents the net

extensor moment during walking. For nine trials for a single subject, the CV for the joint angles,

GRFs, and ankle joint and support moments were relatively small, while the knee and hip joint

moments were approximately three times as large. When similar data were obtained for 14 to 16

subjects walking at fast, normal, and slow speeds, the same trends in variability across the kinematic and kinetic variables were obtained although the CV values were approximately two (fast

speed) to three (slow speed) times larger than those obtained for the single-subject analysis. For

this between-subject phase of the study, the kinetic variables were normalized to body mass to

account for weight differences among the subjects. These results were not surprising, given the

likely greater variability in speed across trials for a particular cadence and the variation in leg
15

length (and thus, stride length) among subjects. Winter concluded that the larger knee and hip

moment variability during walking is attributable to the flexibility of the biarticular muscles (the

“hamstrings” and the rectus femoris) that cross both joints. He also provided data showing the

strong inverse relationship between joint moments at the hip and knee. As further evidence, he

found that the CV for the sum of the knee and hip joint moments was very similar in value to

CVs obtained for the ankle joint and support moments. A major result found in this study was

that somewhat invariant kinematics were obtained for different walking trials when the knee and

hip joint moments vary quite a bit. A limitation of this study, however, is that joint power values

were not obtained.

One factor for which little information is available is how the kinetics are affected as the step

length is varied while walking speed is held constant. Martin and Marsh (1992) performed such a

study, manipulating the step length by 5% and 10% of leg length above and below the preferred

step length. This had little effect on the vertical peaks of the GRF but changed the anteriorposterior (AP) peak force values by approximately 13% when step length was varied by 10%.

While joint moments and power values were not obtained, one can get an idea of how much hip

moments may have been affected by combining these results with the sensitivity analysis that

Winter (1984) conducted. He reported that when the AP forces were varied by 10%, the average

hip joint moments varied by 40% during walking. Winter’s sensitivity analysis was for the case

when AP force was varied but the kinematics were held constant, while in the Martin and Marsh

study, the kinematics obviously varied as step length was altered and the speed was kept

constant.

4.4 Accuracy

As previously indicated, several variables are involved in determining the kinetic measures

during walking and other movements. These include the segment’s inertial properties, the joint

kinematics, the external forces (primarily the GRF) acting on the body, and the location on the

body where these forces act. These variables often depend on other variables that may be directly

measured or estimated and have a certain degree of accuracy. As an example, several anthropometric measures are often used to obtain estimates of the segment’s inertial properties. Partly

because of the variation in body structure characteristics among individuals, the inertial properties have traditionally been considered by biomechanics researchers to be accurate to within

approximately 10% of their actual values. Other errors inherent in the data collection and

processing steps would also exist. Examples of these include a determination of the joint center

(or most appropriate joint center when the true joint center position varies), the limited resolution

of data collection equipment (e.g., motion analysis equipment may only be accurate to approximately 1 cm), and the smoothing of the kinematic data. There have been very few studies

(McCaw & DeVita, 1995; Challis & Kerwin, 1996; Nagano et al., 2000), however, in which

specific variables were manipulated to determine the error they imparted to kinetic output

variables.
16

Considering the generally nonlinear dependence of the joint moment and power values on

several other variables, it would be difficult to determine the true accuracy of the kinetic

measures. The accuracy of the input variables is generally between 0% and 20% of their actual

values. Of course, inaccuracies in the data collection and processing steps can produce

compensating errors that would reduce the overall inaccuracy of the kinetic output variables.

However, it is reasonable to conclude that the accuracy of the desired joint moment and power

measures would also be within this range. Therefore, one should keep in mind that the overall

accuracy of many biomechanical variables and the kinetic results presented in this report may be

as much as 20% different from their true values. The variability in the kinetic data along with the

accuracy with which they can be determined provide the exoskeleton hardware designers with

some measure of the tolerance in determining power requirements for various movements. Thus,

the human power requirements indicated later in this report, combined with the variability and

accuracy values stated previously, provide overall ranges of power for these respective

movements.

5. Level of Effort Required During Locomotion

An important issue to consider during locomotion has to do with the level of effort that an

individual must exert, that is, what are the required forces relative to the maximum forces that

the individual is capable of developing in the various muscles used for locomotion? These

relative force levels have strong implications regarding the likelihood of fatigue and the ability to

meet particular locomotion requirements such as moving at high speed or traversing a steep

grade. In essence, it would be desirable to know the maximum strength of individual muscle

groups and the relative proportion of that strength that a subject is required to elicit during

locomotion.

The standard method to measure strength of a particular muscle group is to use an isokinetic

dynamometer, which has a rigid arm that is programmed to rotate about a fixed axis at a constant

angular speed (between approximately 30 and 300 degrees per second) in a plane perpendicular

to the axis of rotation. To test the strength of the muscle group, the subject’s limb is rigidly

attached to the dynamometer arm, and the center of the joint spanned by the muscle group is

made to coincide with the arm’s axis of rotation. The subject exerts maximal muscle effort while

trying to rotate his or her joint in the same or opposite direction as the rotation of the dynamometer arm. While the subject is not able to alter the movement of the dynamometer arm, he or she

is essentially exerting maximal concentric (shortening) or eccentric (lengthening) muscle action,

respectively.

There are several caveats, however, in trying to compare moment and power measures obtained

from isokinetic testing and joint moment and power values during locomotion. These can be
17

categorized in the areas of methodology, muscle mechanics, energy transfer, and neural factors.

In terms of methodology, researchers usually do not smooth kinetic data, but it is probably

appropriate to do so for movements in which subjects impact the ground, resulting in spikes in

the GRF data. The impacts result in artificially high values for the calculated joint moments (near

the instant of impact), which would not really exist in the muscle tendon complex because part of

that force spike would be dissipated primarily by soft tissue within the body. In the area of

muscle mechanics, the force-velocity (Hill, 1938) and length-tension (Gordon, Huxley, & Julian,

1966) relationships and force enhancement (Edman, Elzinga, & Noble, 1978) would prevent

objective comparisons of moment and power measures between locomotion and isokinetic

studies. Specifically, the muscle velocities and lengths may be different when peak kinetic values

occur for these two movement paradigms along with the muscles involved in locomotion

undergoing previous active stretching.

Another factor that would not exist during the isokinetic testing but is present during

multiarticular movements is the capability of power being transferred in a proximal to distal

direction (Jacobs et al., 1996; van Soest, Schwab, Bobbert, & van Ingen Schenau, 1993). For

movements such as locomotion and jumping, the distal muscles have an increased moment and

power-generating capability during the latter phase of ground contact. This is because

monoarticular muscles acting about the more proximal joint provide power to an antagonist

biarticular muscle that is simultaneously extending a more distal joint. A final factor that could

potentially reduce the maximum muscle forces during isokinetic dynamometer testing is the

possibility that neural inhibition may be present during isokinetic testing, resulting in a less than

maximal muscle effort being provided by the neuromuscular control system. Combining all these

factors provides ample reason to explain why locomotion is capable of producing larger joint

moment and power values than those obtained in isokinetic dynamometer studies. Thus, the

maximum moment or power results from isokinetic dynamometer studies should not be used to

determine the degree of muscle activity during locomotion.

Table 2 provides data for a qualitative comparison of locomotion versus isokinetic moment

values. Ranges of moment values for walking and running, along with values at specific angular

velocities for isokinetic testing, are given for various muscle groups. Values in brackets represent

average moment values based on the range of data obtained, and joint angular velocities are

given in parentheses. For walking and running, the peak knee extensor moments are generally

greater than the isokinetic moments, but they occur during an energy absorption phase when the

muscles are lengthening and are capable of developing larger forces than when they are

shortening (Hill, 1938). The large plantarflexor moment during walking and running is probably

attributable to the muscles being close to their optimal force-producing length, the

gastrocnemius’ shortening velocity is near zero, the existence of force enhancement, and the

distal transfer of power. For the joint power values (see Table 3), similar conclusions can be

stated when one compares locomotion and isokinetic data. The differences in kinetic measures

from locomotion studies and isokinetic studies occur because of differences in the methodology,
18

muscle mechanics, energy transfer, and neural factors. Therefore, actuator and power supply

design criteria should be based on data from locomotion studies, not isokinetic studies.

Table 2. Maximum joint moments during walking, running, and concentric isokinetic testing

______________________________________________________________________________

Joint Muscle Group Walking Running Isokinetic

______________________________________________________________________________

Hip Extensors 15-140 [100] 40-80 300

Flexors 40-120 [70] 170

Knee Extensors 5-140 [80] 125-273 235 (50°/s), 166 (60°/s),

154 (180°/s), 120 (400°/s)

Flexors 15-50 [30] 93 (60°/s), 70 (180°/s)

Ankle Plantarflexors 85-165 [130] 180-240 89 (30°/s), 50 (90°/s), 21 (180°/s)

______________________________________________________________________________

Note: Moments given in newton meters; average peak values in brackets; angular velocities in parentheses. For walking, knee

angular velocity is 100°/s, and ankle angular velocity is 50°/s at the time when peak moment occurs.

Table 3. Maximum joint powers generated during walking, running, and concentric isokinetic testing

______________________________________________________________________________

Joint Muscle Group Walking Running Isokinetic

______________________________________________________________________________

Hip Extensors 0-175 160-660 200 (100°/s)

Knee Extensors 10-235 210-1050 205 (50°/s), 840 (400°/s)

Flexors 10-50 97 (60°/s), 220 (180°/s)

Ankle Plantarflexors 180-790 550-1580 47 (30°/s), 79 (90°/s), 66 (180°/s)

______________________________________________________________________________

Note: Powers given in watts; angular velocities in parentheses. For walking, ankle angular velocity is 200°/s at the time when

peak power occurs.

6. Lower Limb Kinematics and Kinetics for Various Activities

6.1 Walking

6.1.1 Walking at a Normal Speed

The biomechanics of “normal” walking at a natural pace are well established. Kinematic

(Kadaba, Ramakrishnan, & Wootten, 1990) and normalized (to body mass) kinetic (Eng &

Winter, 1995) data for all three planes of motion are given in Appendix A (Figures A-1, A-2, and

A-3 for the hip, knee, and ankle, respectively). Examining the joint angle data, one finds that the
19

greatest range of motion in the sagittal plane occurs at the knee ( 60°), followed by the hip

( 40°), and finally the ankle ( 25°). In the frontal plane, however, the hip exhibits the greatest

range of motion ( 10°), while motion of the knee is around 6° and that of the ankle is nearly

zero. The range of motion for all three joints in the transverse plane is approximately 10°.

With respect to sagittal plane joint moments, the largest peak extensor moment occurs at the

ankle before toe-off ( 47% gait cycle), meanwhile, the largest peak flexor moment occurs

almost simultaneously at the hip ( 50% gait cycle). During this phase of the locomotion cycle,

the foot is pushing off from the ground and the ankle plantarflexor muscles are providing a

forward thrust. Frontal plane joint moments at the ankle, as well as transverse plane joint

moments for all three joints, appear to be very small in comparison with those of the sagittal

plane. This is not the case, however, for the nearly equal peak knee and hip abductor moments

that occur just after contralateral toe-off ( 10% gait cycle). While the peak hip abductor moment

is comparable to the peak hip extensor moment, the peak knee abductor moment is more than

twice as large as the peak knee extensor moment, indicating the necessity of conducting threedimensional analyses of joint kinetics instead of the typical sagittal plane analysis. In addition,

such locomotion biomechanics results are particularly useful in that they are quite helpful in

determining the necessary design requirements for the exoskeleton.

When the power data are examined, some different trends exist as compared to the moment data

when one considers kinetic measures about the three orthogonal axes during walking.

Specifically, the angular velocities are larger in the sagittal plane versus the other two planes,

resulting in proportionately larger power values for this primary plane of movement. For

example, knee and hip peak power generated in the frontal plane is only one-third the respective

sagittal plane values, while the knee and hip peak moments in the frontal plane are larger than

their respective values in the sagittal plane. Thus, for normal speed walking, it is more important

to conduct a three-dimensional analysis when one is considering joint moments, as compared to

joint powers. In terms of describing the joint power results in Appendix A, in the sagittal plane,

the largest peak power generated is at the ankle (just before toe-off), while the largest peak

power absorbed is at the knee. Both of these occur in the sagittal plane. The peak power

absorbed at the hip in the frontal and sagittal planes is approximately equal. Similar to the joint

moment results, the joint powers for the ankle in the frontal plane and for all three joints in the

transverse plane were quite small. During normal walking, toe-off occurs at approximately 60%

of the gait cycle, and it is evident from these figures that the moments and powers are generally

small during the swing phase (60% to 100% gait cycle). An exception to this is the power

absorbed at the knee (see Figure A-2) in the sagittal plane since the hamstring muscles provide a

braking action to knee extension before heel contact. A summary of the peak kinetic values

associated with all three planes of motion for each joint is given in Table 4.
20

Table 4. Peak kinetic values during one cycle of normal walking

______________________________________________________________________________

Variable Plane Action Hip Knee Ankle

______________________________________________________________________________

Moment Extensor 1.15 0.46 1.73

(Nm/kg) Sagittal (0.30) (0.35) (0.22)

Flexor 1.10 0.43 0.20

(0.30) (0.18) (0.10)

Abductor 1.20 1.10 0.13

Frontal (0.25) (0.20) (0.10)

Adductor 0.10 * 0.04

(0.10) (0.04)

Inversion 0.20 0.11 *

Transverse (0.04) (0.03)

Eversion 0.20 0.09 0.10

(0.06) (0.05) (0.04)

Power Generation 1.80 0.60 4.40

(W/kg) Sagittal (0.50) (0.50) (1.10)

Absorption 1.0 1.50 0.50

(0.55) (0.50) (0.30)

Generation 0.55 0.18 0.07

Frontal (0.15) (0.13) (0.06)

Absorption 0.90 0.18 0.12

(0.60) (0.12) (0.08)

Generation 0.02 0.04 0.01

Transverse (0.06) (0.02) (0.03)

Absorption 0.17 0.15 0.02

(0.16) (0.10) (0.02)

______________________________________________________________________________

Note: Values in parentheses are ± one standard deviation.

*Indicates value 0.

6.1.2 Walking at Various Speeds

The effects of walking speed on lower extremity biomechanics have been reported for a study

conducted by Winter (1983). Sagittal plane joint angles and powers were measured and

calculated for all three joints at slow (85 steps/min), natural (105 steps/min), and fast (122

steps/min) cadences. Plots of these data are presented in Figure A-4. The point at which toe-off

occurs in the gait cycle was found to be unaffected by change in walking speed, occurring at

approximately 63% of the gait cycle for all three cadences. Although the joint angles for all three

joints are seen to vary slightly with change in walking speed, these differences are considered to

be very small when compared to the range of motion of each joint. With respect to joint power,

the timing of transitions from power generation to absorption or absorption to generation was

generally unaffected by change in walking speed; however, a high correlation between peak joint
21

powers and walking velocity was observed for all three joints. Several power bursts have been

identified at the hip, knee, and ankle joints during one cycle of normal walking (see Figure A-4).

Peak values occurring during these power bursts are presented in Table 5. An increase in peak

joint power was shown to occur with increased walking speed for all power bursts except H1.

Table 5. Peak power values during one cycle of walking at three different cadences

______________________________________________________________________________

 Cadence Hip Knee Ankle

(steps/min) H1* H2 H3 K1 K2 K3 K4 A1 A2

______________________________________________________________________________

85 0.16 -0.15 0.33 -0.35 0.10 -0.60 -0.51 -0.48 2.08

105 0.31 -0.25 0.68 -0.60 0.35 -0.70 -0.85 -0.50 3.33

122 0.26 -0.90 1.39 -2.10 1.08 -1.65 -1.30 -0.60 5.00

______________________________________________________________________________

Note: Powers given in watts per kilogram body mass. Positive values indicate power generated; negative values indicate power

absorbed.

*The locations of each power burst within the gait cycle are indicated in Figure A-4.

6.1.3 Walking With Loads

In 2000, Harman, Hoon, Frykman, and Pandorf reported about the effects of load carriage on

lower extremity biomechanics during walking. Joint angle data were collected and joint moments

were calculated for carried backpack loads of 6, 20, 33, and 47 kg while subjects walked at a

speed of approximately 1.33 m/s; plots of these data are given in Figure A-5. In contrast to

change in walking speed, the instant when toe-off occurs in the gait cycle was affected by change

in carried load. As carried load increased from 6 to 47 kg, the duration of the stance phase was

observed to increase from approximately 63.4% to 65.2% of the gait cycle. Timing of transitions

from flexion to extension and extension to flexion also appears to be affected by change in

carried load. The effect of change in carried load on hip joint angles was not reported, but slight

changes in knee and ankle joint angles were. Peak knee flexion during mid-stance ( 10% to

30% gait cycle) was found to increase from approximately 22.5 to 27.5 degrees, while peak knee

flexion at the transition from initial to mid-swing ( 72% gait cycle) was found to decrease from

approximately 68 to 64 degrees with an increase in carried load. At the ankle, peak dorsiflexion

during terminal stance ( 30% to 50% gait cycle) was found to decrease from approximately

11.5 to 10 degrees, and peak plantarflexion at the transition from mid- to terminal swing ( 90%

gait cycle) was found to decrease from approximately 5 to 3.5 degrees with an increase in carried

load. As with the joint angles, timing of transitions from extensor to flexor and flexor to extensor

moments, as well as peak values obtained at each joint, appears to be affected by change in

carried load. At the hip, peak extensor moment values during loading response, as well as peak

flexor moment values during terminal stance, were found to increase with an increase in carried
22

load. Peak knee extensor moment values during mid-stance and peak ankle plantarflexor moment

values during terminal stance were also found to increase with an increase in carried load, while

peak knee flexor and ankle dorsiflexor moments did not follow a monotonically increasing trend.

The peak extensor and flexor moment values obtained at each joint under each of the four

different backpack loads are summarized in Table 6.

Table 6. Peak moment values during one cycle of walking with four different backpack loads

______________________________________________________________________________

Load Hip Knee Ankle

(kg) Extensor Flexor Extensor Flexor Plantarflexor Dorsiflexor

______________________________________________________________________________

6 0.81 0.78 0.72 0.34 1.76 0.13

20 0.85 0.88 0.81 0.40 2.08 0.10

33 0.88 1.12 1.20 0.33 2.15 0.20

47 1.00 1.24 1.37 0.35 2.41 0.16

______________________________________________________________________________

Note: Moments given in newton meters per kilogram body mass.

As previously mentioned, the mass, size, and inertial properties of the exoskeleton are assumed

to be equivalent to those of a human. Because humans vary in these dimensions, exoskeletons

must be designed to fit a range of soldiers. Typically, equipment is developed to fit soldiers from

the 5th to 95th percentile for a particular body dimension. For the analyses in this report, body

mass is the dimension that will be used because of the assumption that joint moments and joint

powers scale linearly with mass. Also, the body masses of male soldiers will be used because

according to the DARPA BAA, the exoskeleton is initially being developed for combat soldiers.

According to the anthropometric survey of U.S. Army personnel conducted in 1988 (Gordon et

al., 1989), the body masses of 5th and 95th percentile male soldiers are 61.59 and 98.07 kg,

respectively. For normal walking, we obtain estimates of the range of peak sagittal plane kinetic

values for male soldiers from the 5th to 95th percentile (by mass) by multiplying the given body

mass by the moment and power values given in Table 4. The resulting ranges of peak moment

and power values obtained by these calculations are presented in Table 7.
23

Table 7. Range of peak kinetic values for 5th to 95th percentile male soldiers during one cycle of normal

walking

______________________________________________________________________________

Variable Action Hip Knee Ankle

______________________________________________________________________________

Moment

(Nm) Extensor 71 to 113 28 to 45 106 to 169

Flexor 68 to 108 26 to 42 12 to 20

Power

(W) Generation 111 to 177 37 to 59 271 to 432

Absorption 62 to 98 92 to 147 31 to 49

______________________________________________________________________________

6.2 Running

Sagittal plane kinetic data for the stance phase of “normal” running at a moderate pace of

approximately 3.8 m/s have been published by DeVita, Torry, Glover, and Speroni (1996); plots

of these data are shown in Figure A-6. Peak moment and power values associated with these data

are summarized in Table 8. When the joint moment data are examined, it can be seen that,

similar to walking, the largest peak extensor moment occurs at the ankle (in this case, near midstance, 50% stance phase), while the largest peak flexor moment again occurs at the hip. With

respect to joint power, the largest peak power generation again occurs at the ankle, and the

largest peak power absorption value is found at the knee during the loading response ( 10% to

30% stance phase). With the exceptions of peak hip and ankle flexor moments, all the peak

kinetic values for running at a moderate pace are much higher than those for walking at a natural

pace (see Table 4).

Table 8. Peak kinetic values during stance phase of normal running at 3.8 m/s

______________________________________________________________________________

Variable Action Hip Knee Ankle

______________________________________________________________________________

Moment

(Nm/kg) Extensor 2.81 (0.30) 2.74 (0.38) 3.34 (0.12)

Flexor 0.61 (0.23) 0.53 (0.00) *

Power

 (W/kg) Generation 3.80 (1.52) 12.9 (2.08) 17.5 (0.76)

Absorption 11.0 (4.18) 18.2 (1.52) 12.2 (0.69)

______________________________________________________________________________

Note: Values in parentheses are ± one standard deviation.

* indicates a value 0.
24

Arampatzis, Brüggemann, and Metzler (1999) have reported about the effects of change in speed

on lower limb biomechanics during the stance phase of running. Sagittal plane data were

collected at the knee and ankle for subjects running at five speeds ranging from jogging

(2.61 m/s) to sprinting (6.59 m/s), and the resulting joint moments and powers occurring during

the stance phase were calculated. Plots of these results are shown in Figure A-7, and a summary

of the peak moment and power values obtained is provided in Table 9. Similar to the effects of

change in speed on walking biomechanics, all the peak kinetic values during the stance phase of

running are shown to increase with increased speed.

As with walking, an estimate of the peak kinetic values for the range of 5th to 95th percentile

male soldiers running at a moderate pace can be obtained. This is done by multiplying the

corresponding body masses with the mean normalized joint moment and power data for running,

as reported in Table 8. The resulting values are presented in Table 10.

Table 9. Peak kinetic values during the stance phase of running at five different speeds

______________________________________________________________________________

Knee Ankle

Speed Moment Power Moment Power

 (m/s) Extensor Generated Absorbed Extensor Generated Absorbed

______________________________________________________________________________

2.61 2.00 4.23 7.75 2.45 6.60 3.30

3.55 2.57 5.62 12.0 2.78 10.1 4.60

4.47 2.64 6.92 13.2 2.99 12.3 5.90

5.60 2.74 9.89 14.2 3.20 16.4 8.70

6.59 2.99 10.7 16.8 3.44 21.0 12.2

______________________________________________________________________________

Note: Moments given in newton meters per kilogram; powers given in watts per kilogram.

Table 10. Peak moment values for 5th to 95th percentile male soldiers during one cycle of running at a

moderate pace (3.8 m/s)

______________________________________________________________________________

Variable Action Hip Knee Ankle

______________________________________________________________________________

Moment

(Nm) Extensor 173 to 276 168 to 268 206 to 328

Flexor 37 to 60 33 to 52 *

Power

(W) Generation 234 to 373 796 to 1267 1076 to 1714

Absorption 679 to 1081 1123 to 1789 749 to 1192

______________________________________________________________________________

Note: * indicates a value 0.
25

6.3 Stair Climbing

In 1980, Andriacchi, Anderson, Fermier, Stern, and Galante performed an analysis of stair ascent

and descent, reporting the stance phase joint moments for all three planes of motion. In this study,

subjects ascended and descended a three-step staircase, and kinematic data were collected for one

stride between the first and third steps. Joint moments were calculated during the stance phase for

all three planes of motion at each joint, and these resulting data are shown in Figure A-8. A

summary of the peak joint moment values obtained for each plane of motion is presented in

Table 11. During the stance phase of stair ascent, the largest joint moments appear to have

occurred in the sagittal plane, but peak abductor moments in the frontal plane are also significant,

with values equal to approximately one-half to three-quarters of their corresponding peak extensor

moments. Similarly, during the stance phase of stair descent, the largest peak joint moments again

appear to have occurred in the sagittal plane, while peak abductor moments range in value from

approximately one-half to two-thirds of their corresponding peak extensor moment. Transverse

moments during the stance phase of both stair ascent and descent appear to be rather small for all

three joints.

Table 11. Three-dimensional peak moment values during the stance phase of normal stair ascent and

descent

______________________________________________________________________________

Plane Action Hip Knee Ankle

______________________________________________________________________________

Ascent Sagittal Extensor 1.27 0.89 1.34

Flexor * 0.28 *

Frontal Abductor 0.63 0.77 0.60

Adductor 0.05 * *

Transverse Inversion 0.03 0.08 0.02

Eversion 0.21 0.05 0.10

Descent Sagittal Extensor 0.99 1.55 1.20

Flexor 0.35 0.70 *

Frontal Abductor 0.65 0.44 0.63

Adductor 0.14 0.14 *

Transverse Inversion 0.04 0.13 0.03

Eversion 0.21 0.03 0.06

______________________________________________________________________________

Note: Moments given in newton meters per kilogram

* indicates a value 0.

Sagittal plane lower extremity joint powers have been published by Duncan, Kowalk, and

Vaughan (1997) for normal stair ascent and descent. In their study, subjects also ascended and

descended a three-step staircase, kinematic data were collected for each lower extremity joint,

and joint powers were calculated with a six-degree-of-freedom approach. Plots of the resulting

joint powers are shown in Figure A-9, and a summary of the peak power values obtained for
26

each joint is given in Table 12. During both stair ascent and descent, the largest peak power

generation appears to have occurred at the ankle, while the largest peak power absorption during

stair ascent occurred at the knee and during stair descent at the ankle. In contrast to walking,

during stair ascent, peak power generation at the knee is approximately four times greater, while

peak power generation at the ankle decreases by about one-third. Peak power absorption values

at all three joints are also reduced by one-half to three-fourths in comparison to those values seen

during walking. The most notable difference between normal walking and stair ascent is the role

reversal of the knee joint from power absorber to power generator. During stair descent, peak

power generation values at all three joints and peak power absorption at the hip are also reduced

to approximately one-third to one-half of their corresponding values for normal walking, while

peak power absorption values at the knee and ankle are approximately one and one-third and five

times larger, respectively. The role of the ankle joint is split nearly evenly between power

generation and absorption, rather than acting solely as a power generator as seen in normal

walking.

Table 12. Peak power values during one cycle of normal stair ascent and descent

______________________________________________________________________________

Action Hip Knee Ankle

______________________________________________________________________________

Ascent Generation 1.50 2.10 2.90

Absorption 0.50 0.70 0.10

Descent Generation 0.65 0.25 2.05

Absorption 0.50 2.00 2.40

______________________________________________________________________________

Note: Powers given in watts per kilogram.

Sagittal plane peak kinetic values during stair ascent and descent for the range of 5th to 95th

percentile male soldiers can again be estimated through multiplication of the appropriate body

masses with the normalized sagittal plane joint moment data reported in Table 11 and the

normalized joint power data reported in Table 12. The resulting values are presented in Table 13.
27

Table 13. Peak kinetic values for 5th to 95th percentile male soldiers during one cycle of stair ascent and

descent

______________________________________________________________________________

Variable Action Hip Knee Ankle

______________________________________________________________________________

Ascent Moment Extensor 78 to 125 55 to 87 83 to 131

 (Nm) Flexor * 17 to 27 *

Power Generation 92 to 147 129 to 206 179 to 284

(W) Absorption 31 to 49 43 to 69 6 to 10

Descent Moment Extensor 61 to 97 95 to 152 74 to 118

(Nm) Flexor 22 to 34 43 to 69 *

Power Generation 40 to 64 15 to 25 123 to 195

(W) Absorption 31 to 49 123 to 196 148 to 235

______________________________________________________________________________

Note: * indicates a value 0.

6.4 Jumping

The lower extremity kinetics of a running vertical jump with a single-legged take-off have been

reported by Stefanyshyn and Nigg (1998). In this study, five subjects performed running vertical

jumps, and kinematic data were collected for the stance phase of the take-off leg before toe-off.

Plots of the averaged data from this report are shown in Figure A-10, where the normalized

stance phase represents time periods ranging from 0.23 to 0.35 seconds, 0% stance phase is the

instant of foot contact with the floor, and 100% stance phase is the instant of toe-off. The peak

kinetic values obtained for each joint during the running vertical jump are summarized in

Table 14. During the running vertical jump, it appears that the largest peak extensor moment

occurs at the hip, while the largest peak flexor moment occurs at the knee. With respect to joint

power, the largest peak generation during the running vertical jump occurs at the ankle, and the

largest peak power absorption appears to occur at the ankle.

Table 14. Peak kinetic values during the stance phase before toe-off of a running vertical jump

______________________________________________________________________________

Variable Action Hip Knee Ankle

______________________________________________________________________________

Moment Extensor 4.18 (1.15) 2.77 (0.72) 4.08 (0.59)

(Nm/kg) Flexor 0.35 (1.47) 1.07 (0.45) 0.09 (0.29)

Power Generation 9.24 (6.48) 10.7 (8.15) 26.8 (3.33)

(W/kg) Absorption 3.02 (0.56) 6.09 (5.31) 7.81 (3.74)

______________________________________________________________________________

Note: Values in parentheses are ± one standard deviation.
28

We estimated the range of peak kinetic values for 5th to 95th percentile male soldiers during the

take-off stance phase of a running vertical jump by multiplying their respective body masses by

the values given in Table 14. The values resulting from this process are presented in Table 15.

Table 15. Peak kinetic values for 5th to 95th percentile male soldiers during the stance phase before toeoff of a running vertical jump

______________________________________________________________________________

Variable Action Hip Knee Ankle

______________________________________________________________________________

Moment Extensor 257 to 410 171 to 272 251 to 400

(Nm) Flexor 22 to 35 66 to 106 5 to 9

Power Generation 569 to 906 658 to 1048 1648 to 2624

(W) Absorption 186 to 297 375 to 598 481 to 766

______________________________________________________________________________

6.5 Kneeling

Very little published biomechanics data exist for kneeling, but some information concerning

range of motion and joint moments is presented in an American Society of Biomechanics (ASB)

conference abstract (Nagura et al., 2000) and American Society of Mechanical Engineers

(ASME) conference abstract (Nagura, Dyrby, Alexander, and Andriacchi, 2001). The ASB

abstract discusses results for all three joints from a study in which subjects performed four tasks,

single- and double-legged rises from a kneeling position, and single- and double-legged kneeling

from a standing position. Ranges of motion for each joint (approximately 65.9 degrees at the hip,

149.7 degrees at the knee, and 88.6 degrees at the ankle) were similar across the four different

tasks. These values are significantly higher than those seen during normal walking or stair

climbing. During the single-legged rise, the largest peak extensor moment occurred at the hip

( 1.4 Nm/kg), followed closely by the knee ( 1.3 Nm/kg), and ankle ( 0.8 Nm/kg). Peak

flexor moments were negligible for all three joints during this task. During the double-legged

rise, the largest peak extensor moment occurred at the knee ( 2.4 Nm/kg), followed by the ankle

( 1.4 Nm/kg), and hip ( 0.2 Nm/kg). Peak flexor moments were again negligible at the knee

and ankle, but the peak hip flexor moment was approximately 1.4 Nm/kg. Joint moments for the

single- and double-legged kneeling tasks were reported to be similar to those for the single- and

double-legged rising tasks. In the ASME abstract, range of motion and joint moments at the knee

during the same four tasks are discussed. Range of motion at the knee is reported to vary from

approximately 126 to 152 degrees, depending on the task. Peak knee extensor moments for the

single-legged rising and kneeling tasks are reported to be approximately 1.0 and 1.1 Nm/kg,

respectively, while peak knee extensor moments for the double-legged rising and kneeling tasks

are reported to be approximately 2.3 and 2.1 Nm/kg, respectively.
29

7. Lower Limb Peak Power Profiles for Soldier Missions

7.1 Procedure

With the hip, knee, and ankle joint power data reported in biomechanical literature and a series

of simple steps, lower extremity peak power profiles were generated for two soldier missions

consisting of various tasks. Several assumptions were made in this process. Each of these five

assumptions should be considered as potential sources of error in the values resulting from this

process.

1. Increasing carried load has the same effect on peak joint power as does increasing

body mass,

2. The power values observed in the frontal plane are generally small and in the

transverse plane generally very small in comparison to those in the sagittal plane; therefore, only

the power generated and absorbed in the sagittal plane was considered,

3. Normal gait is symmetric,

4. Based on range of motion and peak extensor moments, peak power values for

assuming and getting out of kneeling and prone positions, crawling, and climbing a ladder can be

approximated with values of stair ascent, and

5. Power values of other lower extremity joints, such as the metatarsophalangeal joint,

are small and therefore not included in the calculation of peak power.

The first step in this process involved the development of mission spreadsheets containing time,

task, and load information for each of the missions examined (see Appendix B, Table B-1).

Estimations of the peak and average powers required for each of the task and load combinations

were then made according to the method described in the following paragraph. Finally, the peak

power values obtained for each task and load combination were entered into the mission

spreadsheets appropriately, and peak power profiles were generated for each mission scenario.

This process could be applied to any mission scenario that anyone would want to create.

Several steps were taken in order to estimate the peak and average powers required for each task

and load combination. Based on the first assumption listed previously, we estimated the total

power required during one cycle of each task and load combination by first multiplying the

appropriate normalized hip, knee, and ankle joint power data for each task by the correct mass

value. The mass values used in this calculation are as follow: 50th percentile male soldier

( 77 kg) plus fighting load ( 24 kg) or sustainment load ( 35 kg), resulting in values of

101 and 112 kg, respectively. The mass of the 50th percentile male soldier is used to keep the

analyses simple and to provide initial guidance. Table 16 shows the individual masses of each

component included in the fighting and sustainment loads. Then, based on the second and third

assumptions listed previously, the absolute joint power data for each task and load combination
30

(except for the running vertical jump) were plotted simultaneously for the hip, knee, and ankle

joints of the left and right lower limbs, offsetting the curves of each leg by 50% of the gait cycle

(see Figure B-1a). For the running vertical jump, the absolute joint power data were simultaneously plotted for the hip, knee, and ankle joints of the take-off leg only. The actuators of the

exoskeleton will need to develop power during the power generation and power absorption

phases of these tasks; therefore, the absolute values of the resulting joint powers for each task

and load combination were taken. Next, a total power curve was obtained for each task and load

combination via the equation =

N

i

i TP(t) P (t) ,

in which t is percent time in the gait cycle (i.e., between 0% and 100%), TP is the total power, P

is the joint power, i indicates the joint (i.e., left or right hip, knee, or ankle), and N is the number

of joints (three for running vertical jump; six for all other tasks). Finally, the peak power value

was obtained through identification of the maximum value along the total power curve (see

Figure B-1b), and the average power value was calculated for each task and load combination.

These values are summarized in Table 17.

Table 16. Loads carried

______________________________________________________________________________

Load Mass (kilograms) 

Fighting Load

 Battle dress uniform 1.7

 Boots 1.5

 Personal armored system for ground troops (PASGT) helmet 1.4

 PASGT vest 5.4

 M16A2 3.7

 Bayonet 0.6

 Load-carrying equipment (LCE) 0.7

 Ammunition pouches (2) with 180 rounds in six magazines 3.2

 Hand grenades (2) 0.9

 Canteens (2) with water 2.9

 Protective mask and hood 1.3

 Poncho 0.7

TOTAL 24.0

Existence Load

 Army lightweight individual carrying equipment (ALICE) pack 1.1

 Additional clothing 0.5

 Personal hygiene kit 1.2

 Food 1.3

 Sleeping bag 3.4

 Sleeping mat 1.6

Field Jacket and Gloves 1.9

TOTAL 11.0

Sustainment Load

 Fighting load + existence load 35.0 
31

Table 17. Peak and average power values for typical soldier tasks

______________________________________________________________________________

Total Mass (soldier plus carried load)

 Task Fighting (101 kg) Sustainment (112 kg)

______________________________________________________________________________

Slow Walk (85 steps/min) 283 (119) 314 (131)

Natural Walk (105 steps/min) 411 (180) 456 (200)

Fast Walk (122 steps/min) 693 (315) 769 (349)

Jog (2.7 m/s) 1966 (1041) 2180 (1155)

Run (3.8 m/s) 3147 (1693) 3489 (1877)

Sprint (7.6 m/s) 5547 (3522) 6151 (3906)

Running Vertical Jump 3559 (1325) 3947 (1369)

Ascend Stairs 501 (229) 556 (254)

Descend Stairs 478 (270) 530 (300)

______________________________________________________________________________

Note: All peak(average) power values are given in watts. All values represent absolute power for all six lower extremity joints

(left and right hip, knee, and ankle joints) during the given task and load combination, except for jumping, which assumes a

running jump with single-legged take-off.

7.2 Mission Scenarios

7.2.1 Movement to Contact

In the movement-to-contact mission, a platoon is moving through a rural area. They are carrying

their sustainment loads (35 kg). At the beginning of the mission, the platoon marches and takes

rest breaks according to Field Manual (FM) 21-18 (Department of the Army, 1990). When the

platoon makes contact with the enemy, they drop their existence loads and carry only their

fighting loads (24 kg). The platoon members who will engage the enemy use cover and concealment to move according to FM 7-8 (Department of the Army, 1992) and FM 21-75 (Department

of the Army, 1984). This movement includes a series of rushes, that is, running for 3 to 5 seconds,

going prone, crawling, rolling left or right, getting up and repeating the sequence until they are

within approximately 100 yards of the enemy. They engage the enemy from covered positions

and then move in another series of rushes to close with and destroy the enemy. They consolidate

and reorganize. Then they remove casualties. After resting briefly, they return to pick up their

existence loads. They repeat the tasks from the first part of the mission and engage another group

of enemy soldiers. After they go back to pick up their existence loads this time, they march and

take rest breaks until they find a safe place to rest for the night. The entire mission takes 16 hours,

and the resulting peak power profile is shown in Figure B-2 for a 50th percentile male soldier.

With the assumptions stated earlier concerning the exoskeleton’s design, its power requirements

can be estimated from Figure B-2 and assumed to be within 20% of their actual values. Thus, a

power supply that is capable of producing a nearly constant mean value of approximately 200
32

±40 W, and peak values of 500 ±100 to 5500 ±1100 W at frequencies ranging from

approximately 2 to 4 Hz, depending on the task, would be required for this mission.

7.2.2 Clear Building

In this scenario, a platoon is going to clear a building during daylight. The soldiers are carrying

their fighting loads (24 kg). The building is three stories high and has a basement. Each floor is

approximately 17,850 square feet. There are six to ten enemy soldiers in the building. The platoon

follows FM 90-10-1 (Department of the Army, 1993) and FM 7-8 (Department of the Army,

1992). The platoon divides into squads. One squad provides security outside the building. Another squad is held in reserve. Two squads enter and clear the building. The two squads that enter

and clear the building approach from the back. They use a ladder and enter a second floor room

through a window. Then they work their way to the stairs. Inside the building, one squad is

responsible for securing the stairs, and the other squad is responsible for clearing the rooms. The

squad that clears the rooms divides into two fire teams and goes up to the third floor. One fire

team provides security in the hallway while the other team clears rooms. A fire team clears about

four to six rooms and then switches to security while the other team clears rooms. They alternate

roles in this fashion, clearing the third floor, the second floor, the first floor, and finally, the basement. The entire mission takes 2 hours and 12.5 minutes, and the resulting peak power profile is

shown in Figure B-3 for a 50th percentile male soldier on one of the room-clearing fire teams. As

with the movement-to-contact mission, the exoskeleton’s power requirements during a clearbuilding mission can be estimated from Figure B-3 and assumed to be within 20% of their actual

values. Although this power profile varies much more than that of the previous scenario, it

appears that a power supply capable of producing a mean power value between 100 ±20 and 300

±60 W, and peak values of 400 ±80 to 3500 ±700 W at 2 to 4 Hz, depending upon the task, would

be required for such a mission.

8. Conclusions

The goals for this work were to determine the angles, torques, and powers at the lower limb joints

of an exoskeleton and to estimate the requirements for a system to power the lower limbs of that

exoskeleton. It was assumed that the angles, torques, and powers could be estimated from biomechanical data collected from humans. Based on biomechanical data gathered from various published sources, we have provided estimates of angle, torque, and power values at the hip, knee, and

ankle joints during various activities. Estimated peak power values were also determined for two

hypothetical missions to produce lower limb peak power profiles. Keeping in mind the limitations

and variability of kinematic and kinetic data and the assumptions made in the application of such

data to an exoskeleton, these estimated values (see Appendix A, Table 17, and Figures B-2 and

B-3) could be used to design lower limb joints and actuators and to size the power supply for an

exoskeleton.
33

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Figure A-1. Hip joint angles, moments, and powers in the sagittal, frontal, and transverse planes during one cycle of normal walking. (Solid lines

are mean values and dotted lines are ± one standard deviation.)

Sagittal Plane Frontal Plane Transverse Plane

Percent Gait Cycle Percent Gait Cycle Percent Gait Cycle

Angle (degrees) Moment (Nm/kg) Power (W/kg)

Flexion

Abduction AdductionInt. Rotation Ext. Rotation

 Flexor Extensor

 Abductor

 Ext. Rotator Int. Rotator

Absorbed Generated

Absorbed Generated

Absorbed

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 10 20 30 40 50 60 70 80 90 100

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0 10 20 30 40 50 60 70 80 90 100

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 10 20 30 40 50 60 70 80 90 100

-2

-1.5

-1

-0.5

0

0.5

1

0 10 20 30 40 50 60 70 80 90 100

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40 50 60 70 80 90 100

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80 90 100

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70 80 90 100

-10

0

10

20

30

40

50

0 10 20 30 40 50 60 70 80 90 100

-8

-6

-4

-2

0

2

4

6

8

10

0 10 20 30 40 50 60 70 80 90 100

37

Appendix A: Lower Limb Kinematics and Kinetics for

Various Activities
 Figure A-2. Knee Joint angles, moments, and powers in the sagittal, frontal and transverse planes during one cycle of normal walking.

Sagittal Plane Frontal Plane Transverse Plane

Percent Gait Cycle Percent Gait Cycle Percent Gait Cycle

Angle (degrees) Moment (Nm/kg) Power (W/kg)

 Flexion

 Adduction

Int. Rotation Ext. Rotation

 Flexor Extensor

 Abductor

 Ext. Rotator Int. Rotator

 Absorbed Generated

Absorbed Generated

Absorbed

-8

-6

-4

-2

0

2

4

6

8

10

0 10 20 30 40 50 60 70 80 90 100

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0 10 20 30 40 50 60 70 80 90 100

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 10 20 30 40 50 60 70 80 90 100

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60 70 80 90 100

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40 50 60 70 80 90 100

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 10 20 30 40 50 60 70 80 90 100

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70 80 90 100

-10

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90 100

-4

-2

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100

38
 Figure A-3. Ankle joint angles, moments, and powers in the sagittal, frontal and transverse planes during one cycle of normal walking.

Sagittal Plane Frontal Plane Transverse Plane

Percent Gait Cycle Percent Gait Cycle Percent Gait Cycle

Angle (degrees) Moment (Nm/kg) Power (W/kg)

Plantarflexion Dorsiflexion

 Ext. Rotation

Plantarflexor

 Adductor Abductor

 Ext. Rotator

 Generated

 Absorbed Generated

Absorbed Generated

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90 100

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 10 20 30 40 50 60 70 80 90 100

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0 10 20 30 40 50 60 70 80 90 100

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 10 20 30 40 50 60 70 80 90 100

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40 50 60 70 80 90 100

-2

-1

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90 100

-0.5

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80 90 100

-20

-15

-10

-5

0

5

10

15

20

0 10 20 30 40 50 60 70 80 90 100

39

(These data not reported.)
Figure A-4. Sagittal plane joint angles and powers during one cycle of walking at three cadences ( = slow, = natural, = fast).

Joint Angle (degrees) Joint Power (W/kg)

Percent Gait Cycle Percent Gait Cycle

 Hip Knee Ankle

Absorbed Generated Generated Absorbed Generated

Extension Flexion Flexion Plantarflexion Dorsiflexion

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70 80 90 100

-1

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90 100

-25

-20

-15

-10

-5

0

5

10

15

0 10 20 30 40 50 60 70 80 90 100

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 10 20 30 40 50 60 70 80 90 100

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80 90 100

-15

-10

-5

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100

 A1

 A2

K1

 K2

 K3 K4

H1

H2

 H3

40
Figure A-5. Sagittal Plane Joint Angles and Moments During One Cycle of Walking at 1.33 m/s With Four Different Backpack Loads

( = 6 kg, = 20 kg, = 33 kg, = 47 kg).

Joint Angle (degrees) Joint Moment (Nm/kg)

Percent Gait Cycle Percent Gait Cycle

 Hip Knee Ankle

Flexion Plantarflexion Dorsiflexion

 Flexor Extensor Extensor Plantarflexor

-1.5

-1

-0.5

0

0.5

1

1.5

0 10 20 30 40 50 60 70 80 90 100

-0.5

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60 70 80 90 100

-20

-15

-10

-5

0

5

10

15

0 10 20 30 40 50 60 70 80 90 100

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40 50 60 70 80 90 100

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80 90 100

41

(These data not reported.)
Figure A-6. Sagittal plane joint moments and powers during the stance phase of running at a moderate pace (3.8 m/s). (Solid lines are mean values

and dotted lines are ± one standard deviation.)

Joint Moment (Nm/kg) Joint Power (W/kg)

Percent Stance Phase Percent Stance Phase

 Hip Knee Ankle

 Flexor Extensor Extensor Plantarflexor

 Absorbed Generated Absorbed Generated Absorbed Generated

-20

-15

-10

-5

0

5

10

0 10 20 30 40 50 60 70 80 90 100

-15

-10

-5

0

5

10

15

20

0 10 20 30 40 50 60 70 80 90 100

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70 80 90 100

-25

-20

-15

-10

-5

0

5

10

15

20

0 10 20 30 40 50 60 70 80 90 100

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 10 20 30 40 50 60 70 80 90 100

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 10 20 30 40 50 60 70 80 90 100

42
Figure A-7. Sagittal plane joint moments and powers during the stance phase of running at five velocities ( = 2.61 m/s, = 3.55 m/s,

 = 4.47 m/s, = 5.60 m/s, = 6.59 m/s).

Joint Moment (Nm/kg) Joint Power (W/kg)

Percent Stance Phase Percent Stance Phase

 Knee Ankle Extensor Plantarflexor

Absorbed Generated Absorbed Generated

-20

-15

-10

-5

0

5

10

15

0 10 20 30 40 50 60 70 80 90 100

-15

-10

-5

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70 80 90 100

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 10 20 30 40 50 60 70 80 90 100

43
Figure A-8. Joint moments in the sagittal, frontal, and transverse planes during stance phase of stair ascent and descent.

( = hip, = knee, = ankle). (Values are in newton meters per kilogram.) Extensor/Plantarflexor Abductor Ext. Rotator Int. Rotator

 Stair Ascent Stair Descent

Percent Stance Phase Percent Stance Phase

 Sagittal Frontal Transverse

 Extensor/Plantarflexor Abductor Ext. Rotator

-1

-0.5

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70 80 90 100

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 10 20 30 40 50 60 70 80 90 100

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0 10 20 30 40 50 60 70 80 90 100

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60 70 80 90 100

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 10 20 30 40 50 60 70 80 90 100

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40 50 60 70 80 90 100

44
 Figure A-9. Sagittal plane joint powers during one cycle of stair ascent and descent. (Values are in watts per kilogram.)

 Stair Ascent Stair Descent

Percent Cycle Percent Cycle

 Hip Knee Ankle

 Absorbed Generated Absorbed Generated Generated

 Absorbed Generated Absorbed Absorbed Generated

-1

-0.5

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70 80 90 100

-1

-0.5

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80 90 100

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 10 20 30 40 50 60 70 80 90 100

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80 90 100

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 10 20 30 40 50 60 70 80 90 100

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 10 20 30 40 50 60 70 80 90 100

45
Figure A-10. Sagittal plane joint moments and power during the stance phase before toe-off of a running vertical jump. (Solid lines are mean

values, and dotted lines are ± one standard deviation.)

 Joint Moment (Nm/kg) Joint Power (W/kg)

Percent Stance Phase Percent Stance Phase

 Hip Knee Ankle

 Extensor Flexor Extensor Plantarflexor

 Absorbed Generated Absorbed Generated Generated

-2

-1

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90 100

-3

-2

-1

0

1

2

3

4

0 10 20 30 40 50 60 70 80 90 100

-1

0

1

2

3

4

5

0 10 20 30 40 50 60 70 80 90 100

-15

-10

-5

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80 90 100

-15

-10

-5

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100

-10

-5

0

5

10

15

20

0 10 20 30 40 50 60 70 80 90 100

46
47

Appendix B: Lower Limb Peak Power Profiles for Soldier Missions

Table B-1. Example of the peak total power spreadsheet set up for a typical soldier

mission. (In this case, the soldier walks for 45 minutes with a

sustainment load, rests for 15 minutes, walks for 30 minutes with a

sustainment load, kneels and rests for 2 minutes, etc.)

Time (min) Task Load

0 Walking Sustainment

45 Resting

60 Walking Sustainment

90 Kneeling and Resting Sustainment

92 Walking Sustainment

110 Resting

120 Walking Sustainment

130 Kneeling and Resting Sustainment

134 Walking Sustainment

150 Prone - Security Sustainment

152 Walking Sustainment

170 Resting

180 Walking Sustainment

200 Prone - Security Sustainment

205 Walking Sustainment

230 Resting

240 Walking Sustainment
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U.S. Army Research Laboratory

Human Research & Engineering Directorate 

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51

60

Exoskeleton Power and Torque Requirements Based on Human Biomechanics

This report provides baseline estimates of the power and torque requirements for the lower limbs of an exoskeleton1 for two 

hypothetical dismounted missions. The missions are “movement to contact” and “clear a building”. The power and torque estimates 

can be used to size key components such as the power supply and actuators. The estimates are based on human biomechanical data 

reported in journal articles and technical reports. The variability of biomechanical measures and the assumptions and potential 

errors involved in data collection and processing are discussed. The accuracy of the joint angle, torque, and power output variables 

is estimated to be within 20% of the reported values. In the use of these data, several assumptions are made regarding the 

equivalence of the exoskeleton and a human. To obtain peak power profiles for the hypothetical missions, each mission was broken 

into the tasks (walking, jogging, kneeling, jumping, etc.) that the soldier (50th percentile, by body mass, male carrying a load) 

performed. Then, the total power requirement over one cycle of each task was calculated, and the peak and average powers 

required during that cycle were identified. Combining the peak power requirements of the tasks in a chronological sequence results 

in a peak power profile for the entire mission. For the movement-to-contact mission, a nearly constant peak power of 500 W is 

required, with short-term requirements as great as 5.5 kW. For the clear-building mission, a nearly constant peak power of 400 to 

700 W is required, with short-term requirements of 2 to 3.5 kW.

Approved for public release; distribution is unlimited.

biomechanics power

exoskeleton torque

1A user-worn device that augments and enhances the wearer’s speed, strength, and endurance