William K. Thompson, Christopher A. Gallo, Lawton Crentsil, and Beth E. Lewandowski

Glenn Research Center, Cleveland, Ohio

Brad T. Humphreys

Zin Technologies, Inc., Middleburg Heights, Ohio

John K. DeWitt and Renita S. Fincke

Science, Technology and Engineering Group, Wyle Inc., Houston, Texas

Lealem Mulugeta

Universities Space Research Association, Houston, Texas

Digital Astronaut Project Biomechanical Models

Biomechanical Modeling of Squat, Single-Leg Squat and Heel 

Raise Exercises on the Hybrid Ultimate Lifting Kit (HULK)

NASA/TM—2015-218852

September 2015
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William K. Thompson, Christopher A. Gallo, Lawton Crentsil, and Beth E. Lewandowski

Glenn Research Center, Cleveland, Ohio

Brad T. Humphreys

Zin Technologies, Inc., Middleburg Heights, Ohio

John K. DeWitt and Renita S. Fincke

Science, Technology and Engineering Group, Wyle Inc., Houston, Texas

Lealem Mulugeta

Universities Space Research Association, Houston, Texas

Digital Astronaut Project Biomechanical Models

Biomechanical Modeling of Squat, Single-Leg Squat and Heel 

Raise Exercises on the Hybrid Ultimate Lifting Kit (HULK)

NASA/TM—2015-218852

September 2015

National Aeronautics and

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Glenn Research Center

Cleveland, Ohio 44135
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Acknowledgments

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Gail Perusek for their assistance in this research.
NASA/TM—2015-218852 iii

Contents

Introduction and Mission .............................................................................................................................. 1

Specific Aims......................................................................................................................................... 2

Support of the HHC Path to Risk Reduction.......................................................................................... 2

Background................................................................................................................................................... 2

Exercises................................................................................................................................................. 2

Computational Modeling of Resistance Exercise................................................................................... 3

Harness Loading..................................................................................................................................... 3

Methods ........................................................................................................................................................ 4

Hulk Exercise Device............................................................................................................................. 4

Exercise Protocols.................................................................................................................................. 4

Data Collection and Processing.............................................................................................................. 7

Simulation of Bar Versus Harness Loading ........................................................................................... 7

OpenSim Exercise Models..................................................................................................................... 8

Modifications to the Arnold Model...................................................................................................... 11

Analyses Performed and Statistical Methods....................................................................................... 12

Results......................................................................................................................................................... 12

Squat Exercise ...................................................................................................................................... 12

Joint Kinematics for Parallel and Deep Squats.............................................................................. 12

Kinematic Joint Angles for Deep and Parallel Squats................................................................... 13

Average and Peak Resultant Joint Forces for Deep and Parallel Squats ....................................... 16

Average and Peak Joint Moments for Deep and Parallel Squats................................................... 21

Average and Peak Muscle Forces by Muscle Group for Deep and Parallel Squats....................... 26

Average and Peak Residual Forces and Moments for Deep and Parallel Squats .......................... 34

Average and Peak Reserve Moments for Deep and Parallel Squats.............................................. 38

Single-Leg Squat Exercise ................................................................................................................... 43

Joint Kinematics for Single-Leg Squat.......................................................................................... 43

Joint Moments for Single-Leg Squat ............................................................................................. 45

Resultant Joint Forces for Single-Leg Squat.................................................................................. 48

Muscle Forces by Muscle Group for Single-Leg Squat................................................................. 50

Residual Forces and Moments for the Single-Leg Squat............................................................... 55

Reserve Moments for the Single-Leg Squat .................................................................................. 57

Heel Raise Exercise.............................................................................................................................. 59

Joint Kinematics for Heel Raise .................................................................................................... 59

Joint Moments for Heel Raise........................................................................................................ 61

Resultant Joint Forces for Heel Raise............................................................................................ 63

Muscle Group Forces for Heel Raise............................................................................................. 65

Residual Forces and Moments for Heel Raise............................................................................... 66

Reserve Moments for Heel Raise .................................................................................................. 68

Summary of All Exercises............................................................................................................. 69

Discussion................................................................................................................................................... 71

Significance of Results......................................................................................................................... 71

Validation of Results With Previous Exercise Studies......................................................................... 71

Squat .............................................................................................................................................. 71

Single-Leg Squat............................................................................................................................ 72

Heel Raise...................................................................................................................................... 72

Harness Loading Versus Bar Loading.................................................................................................. 73

Comparison with ARED Squat Integrated Muscle Model (ASM-im) ................................................. 73

Comparison of Squat Versus Single-Leg Squat ................................................................................... 74

Verification and Validation of the Models........................................................................................... 75
NASA/TM—2015-218852 iv

Interpretation and Limitations.............................................................................................................. 76

Future Work................................................................................................................................................ 76

Conclusions................................................................................................................................................. 77

Appendix A.—Acronyms........................................................................................................................... 79

Appendix B.—Model Parameters and Configurations............................................................................... 81

Appendix C.—Measured External Force Data ........................................................................................... 83

C.1 Squat Exercise ............................................................................................................................ 83

C.2 Single-Leg Squat Exercise.......................................................................................................... 89

C.3 Heel Raise Exercise .................................................................................................................... 90

Appendix D.—Marker Set Used For Data Collection ................................................................................ 91

Appendix E.—Procedure For Producing External Force Files From Device Load and Ground 

Reaction Force Data ............................................................................................................................. 93

References................................................................................................................................................... 97

List of Tables

Table 1.—Subject data used to develop the subject-specific exercise models ............................................. 5

Table 2.—Summary of the exercise data collected....................................................................................... 6

Table 3.—Major muscle groups and their constituent muscle actuators in OpenSim ................................ 10

Table 4.—Kinematic joint angle ranges for parallel and deep squats......................................................... 12

Table 5.—Kinematic joint angle ranges for single-leg squat...................................................................... 43

Table 6.—Kinematic joint angle ranges in degrees for heel raise .............................................................. 60

Table 7.—(a) Peak resultant joint forces expressed as a multiple of BW, (b) Joint moment 

expressed as a multiple of BW-m, (c) muscle forces expressed as a multiple of BW for key 

joints for all exercises under all loading conditions............................................................................. 70

Table 8.—Comparison of peak values of key outcomes (joint angles, joint torques, resultant joint 

forces and muscle group forces) between the ARED squat model, ASM-im, and the HULK 

squat model........................................................................................................................................... 74

Table 9.—Credibility assessment for HULK biomechanical models using methods outlined in 

NASA-STD-2009................................................................................................................................. 75

List of Figures

Figure 1.—HULK device configured in dual-tether (a) and single-tether (b) operation. Both dualtether and single tether operation are intended to connect to various accessories, including the 

bar, shown at left, or a body harness (not shown). ................................................................................. 4

Figure 2.—Subject performing (a) parallel and (b) deep squats on the HULK device. During 

parallel squats the thighs are approximately parallel to the floor at the bottom of the 

movement. During deep squats the subject descends to maximum depth.............................................. 5

Figure 3.—Subject performing single-leg squats on the HULK device with the right leg as the 

target limb............................................................................................................................................... 5

Figure 4.—Subject performing heel raise exercise on the HULK device..................................................... 6

Figure 5.—Harness loading on the Exxentric kBox 3 flywheel device (left) closely matches the 

harness loading scheme under consideration for this study. On HULK, the subject would 

straddle a single loading tether as shown in the rowing exercise depicted (right), but wearing 

a harness similar to the one shown on the left........................................................................................ 7

Figure 6.—Distribution of harness loading on the upper back (30 percent) and lower back (70 

percent) as indicated by the green arrows. Markers at the arrow tails indicate the points of 

application of the load. ........................................................................................................................... 8

Figure 7.—Detailed view of the wrapping surfaces of the Arnold lower limb model in the (a) 

upper leg and a close-up of the (b) knee joint ........................................................................................ 9
NASA/TM—2015-218852 v

Figure 8.—The OpenSim workflow used in the current study. .................................................................. 10

Figure 9.—Quadriceps path at the knee in the unmodified (a) and modified (b) Arnold models at 

maximal knee flexion angle near 140°. The patellar wrapping surface (highlighted) was 

augmented in diameter and relocated anteriorly to correct the physiologically impossible 

muscle paths depicted on the left.......................................................................................................... 11

Figure 10.—Kinematic joint angle histories during deep squats (left of each pairing) and parallel 

squats (right of each pairing) for the joints listed in Table 4................................................................ 13

Figure 11.—Resultant joint forces in Newtons for deep and parallel squats under all loading 

conditions for the (a) hip and knee (patellofemoral and tibiofemoral) joints, (b) ankle and 

subtalar joints, and (c) lumbar joint with bar and harness loading separated....................................... 16

Figure 12.—Joint moments in Newton-meters for deep and parallel squats under all loading 

conditions for the (a) hip extension, hip abduction and knee extensor joints, (b) ankle plantar 

flexor and subtalar invertor, and (c) lumbar extension joint. ............................................................... 21

Figure 13.—Muscle forces for deep and parallel squats under all loading conditions for the (a) hip 

extensor, hip flexor and hip adductor groups, (b) hip abductor, hip internal rotator and hip 

external rotator groups, (c) knee extensor, knee flexor and ankle dorsiflexor groups, and (d) 

ankle plantar flexor, subtalar evertor and subtalar invertor groups...................................................... 26

Figure 14.—Average and peak residual forces in (a) Newtons for deep and parallel squats under 

all loading conditions for the FX, FY, FZ residual forces, and (b) Newton-meters for deep 

and parallel squats under all loading conditions for the MX, MY, MZ residual moments. ................. 34

Figure 15.—Reserve actuator moments in Newton-meters for deep and parallel squats under all 

loading conditions for the (a) hip flexion, hip adduction and hip rotation joint articulations 

and (b) knee flexion, ankle dorsiflexor and lumbar extension joint articulations. ............................... 38

Figure 16.—Average reserve moments as a percentage of total joint moment for (a) deep squat 

and (b) parallel squat. ........................................................................................................................... 42

Figure 17.—Joint kinematics trajectories for single-leg squat: (a) hip flexion, (b) hip adduction, 

(c) hip internal rotation, (d) knee flexion, (e) ankle dorsiflexion, (f) subtalar inversion, (g) 

MTP flexion, and (h) lumbar extension................................................................................................ 43

Figure 18.—Peak and average joint moments in Newton-meters for single-leg squat under all 

loading conditions for the following joint articulations: (a) hip extension, (b) hip abduction, 

(c) hip internal rotation, (d) knee extension, (e) ankle plantar flexion, (f) ankle subtalar 

inversion, and (g) lumbar extension. .................................................................................................... 45

Figure 19.—Resultant joint forces in Newtons for single-leg squat under all loading conditions 

for the following joints: (a) hip, (b) patellofemoral, (c) knee, (d) ankle, (e) subtalar, and (f) 

lumbar................................................................................................................................................... 48

Figure 20.—Average and peak muscle forces in Newtons by muscle group for single-leg squat 

under all loading conditions for the following groups: (a) hip extensors, (b) hip flexors, (c) 

hip adductors, (d) hip abductors, (e) hip internal rotators, (f) hip external rotators, (g) knee 

extensors, (h) knee flexors, (i) dorsiflexors, (j) plantar flexors, (k) subtalar inverters, (l) 

subtalar everters, and (m) lumbar extensors......................................................................................... 50

Figure 21.—Average and peak residual forces in Newtons and moments in Newton-meters for 

single-leg squat under all loading conditions for the following residual forces: (a) FX, (b) FY, 

(c) FZ; and residual moments: (d) MX, (e), MY, (f) MZ..................................................................... 55

Figure 22.—Average and peak reserve actuator moments for single-leg squat under all loading 

conditions for the following joint articulations: (a) hip flexion, (b) hip adduction, (c) hip 

rotation, (d) knee flexion, (e) ankle dorsiflexion, (f) subtalar inversion (g) lumbar extension. ........... 57

Figure 23.—Average reserve moments as a percentage of total joint moment for single-leg squat........... 59

Figure 24.—Joint kinematics trajectories for heel raise: (a) ankle dorsiflexion, (b) subtalar 

inversion, (c) MTP flexion and (d) lumbar extension. ......................................................................... 60
NASA/TM—2015-218852 vi

Figure 25.—Peak and average joint moments in Newton-meters for heel raise under all loading 

conditions for the following joint articulations: (a) ankle angle, (b) subtalar angle, (c) MTP 

angle and (d) lumbar extension. ........................................................................................................... 61

Figure 26.—Resultant joint forces in Newtons for heel raise under all loading conditions for the 

following joints: (a) ankle, (b) subtalar, (c) MTP and (d) lumbar........................................................ 63

Figure 27.—Average and peak muscle forces by muscle group for heel raise under all loading 

conditions for the following groups: (a) plantar flexors, (b) subtalar inverters, and (c) lumbar 

extensors............................................................................................................................................... 65

Figure 28.—Average and peak residual forces in Newton and moments in Newton-meters for heel 

raise under all loading conditions for the following residual forces: (a) FX, (b) FY, (c) FZ, 

and residual moments: (d) MX, (e), MY, (f) MZ................................................................................. 66

Figure 29.—Average and peak reserve actuator moments for heel raise under all loading 

conditions for the following joint articulations: (a) ankle plantar flexion, (b) subtalar 

inversion, (c) MTP extension, and (d) lumbar extension. .................................................................... 68

Figure 30.—Average reserve moments as a percentage of total joint moment for heel raise..................... 69

Figure 31.—External force data as measured during deep and parallel squats. Average and peak 

(a) ground reaction forces in the normal (Y) direction, (b) resultant ground reaction forces in 

the shear direction, and (c) cable tension forces on the bar reported by the HULK device. ................ 83

Figure 32.—External force data as measured during single-leg squats. Average and peak ground 

reaction forces in the normal (Y) and shear directions for the SLS and average and peak cable 

tension forces on the bar reported by the HULK device. ..................................................................... 89

Figure 33.—External force data as measured during heel raises. Average and peak ground 

reaction forces in the normal (Y) and shear directions for the SLS and average and peak cable 

tension forces on the bar reported by the HULK device. ..................................................................... 90

Figure 34.—Modified plug-in gait marker set used for motion capture data collection............................. 91
NASA/TM—2015-218852 1

Digital Astronaut Project Biomechanical Models

Biomechanical Modeling of Squat, Single-Leg Squat and

Heel Raise Exercises on the Hybrid Ultimate Lifting Kit (HULK)

William K. Thompson, Christopher A. Gallo, Lawton Crentsil,* and Beth E. Lewandowski

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Brad T. Humphreys

Zin Technologies, Inc.

Middleburg Heights, Ohio 44130

John K. DeWitt and Renita S. Fincke

Science, Technology and Engineering Group

Wyle Inc.

Houston, Texas 77058

Lealem Mulugeta

Universities Space Research Association

Houston, Texas 77058

Introduction and Mission

The NASA Digital Astronaut Project (DAP) implements well-vetted computational models to predict and assess 

spaceflight health and performance risks, and to enhance countermeasure development. The DAP Musculoskeletal 

Modeling effort is developing computational models to inform exercise countermeasure development and to predict 

physical performance capabilities after a length of time in space. For example, integrated exercise devicebiomechanical models can determine localized loading, which will be used as input to muscle and bone adaptation 

models to estimate the effectiveness of the exercise countermeasure. In addition, simulations of mission tasks can be 

used to estimate the astronaut’s ability to perform the task after exposure to microgravity and after using various 

exercise countermeasures. The software package OpenSim (Stanford University, Palo Alto, CA) (Ref. 1) is being used 

to create the DAP biomechanical models and its built-in muscle model is the starting point for the DAP muscle model. 

During Exploration missions, such as those to asteroids and Mars, astronauts will be exposed to reduced gravity 

for extended periods. Therefore, the crew must have access to exercise countermeasures that can maintain their 

musculoskeletal and aerobic health. Exploration vehicles may have very limited volume and power available to 

accommodate such capabilities, even more so than the International Space Station (ISS). The exercise devices flown 

on Exploration missions must be designed to provide sufficient load during the performance of various resistance and 

aerobic/anaerobic exercises while meeting potential additional requirements of limited mass, volume and power. Given 

that it is not practical to manufacture and test (ground, analog and/or flight) all candidate devices, nor is it always 

possible to obtain data such as localized muscle and bone loading empirically, computational modeling can estimate 

the localized loading during various exercise modalities performed on a given device to help formulate exercise 

prescriptions and other operational considerations. With this in mind, NASA’s Digital Astronaut Project (DAP) is 

supporting the Advanced Exercise Concepts (AEC) Project, Exercise Physiology and Countermeasures (ExPC) 

laboratory and NSBRI-funded researchers by developing and implementing well-validated computational models of 

 * NASA Lewis’ Educational and Research Collaborative Internship (LERCIP)
NASA/TM—2015-218852 2

exercises with advanced exercise device concepts. This report focuses specifically on lower-body resistance exercises 

performed with the Hybrid Ultimate Lifting Kit (HULK) device as a deliverable to the AEC Project.

Specific Aims

This report documents the results of biomechanical modeling and analysis with two specific aims:

1. Estimate localized loading by joint (torque and force) and muscle groups (force) for the squat, heel raise and 

single-leg squat exercises on the HULK.

2. Compare localized loading when the subject exercises using a metal bar vs. a body harness, assuming similar 

kinematics between these two cases. (Data for harness loading have not yet been collected).

Support of the HHC Path to Risk Reduction

The DAP biomechanical modeling efforts help to reduce overall mission risk by addressing gaps (Ref. 2) in the 

Bone and Muscle disciplines within the Human Health and Countermeasures (HHC) Element.

Muscle

Gap M7: Can the current in-flight performance be maintained with reduced exercise volume?

Gap M8: What is the minimum exercise regimen needed to maintain fitness levels for tasks?

Gap M9: What is the minimum set of exercise hardware needed to maintain those (M8) fitness levels?

Bone

Gap Fracture 2: We need to characterize the loads applied to bone for standard in-mission activities.

Gap Fracture 3: We need a validated method to estimate the risk of fracture by evaluating the ratio of applied 

loads to bone fracture loads for expected mechanically-loaded activities during a mission.

DAP biomechanical models quantify the expected localized load stimulus at specific joints or within specific 

muscle groups for a given exercise on a particular exercise device performed in a specific manner. This informs the 

gaps listed above with quantitative information that is difficult or impractical to gather empirically.

Background

Exercises

The squat is renowned as the classic lower body resistance training exercise, working not only most of the lower 

limb musculature, but the hips and core as well (Ref. 3). For NASA, the lumbar spine, hip, knee and ankle joints are of 

particular interest in terms of loading stimulus seen by the adjacent bones and the muscles that articulate these joints, 

where high localized loss of both bone and muscle occur (Ref. 4). The single-leg squat is a related exercise with far 

less published data in the literature. Its primary interest to the NASA community lies in its potential to exercise the 

lower musculature using lower external loads and with a smaller overall device footprint, possibly making it more 

desirable for use in a spacecraft. Previous studies (e.g., Ref. 5) have shown that the single-leg version of the squat 

emphasizes hip extension and de-emphasizes knee extension versus the traditional squat. This implies that the singleleg squat and traditional squat are different exercises and will produce different outcomes in training programs or as 
NASA/TM—2015-218852 3

exercise countermeasures for spaceflight. The heel raise is a localized movement of the distal lower limbs that works 

primarily the plantar flexors, subtalar inverters/everters and the toe extensors (Refs. 6, 7, 8, and 9). The heel-raise 

exercise is of particular interest to NASA because of the lack of space-based research that has effectively minimized 

loss of musculature in the distal lower limbs during longer exposures to microgravity (Ref. 10).

Computational Modeling of Resistance Exercise

Computational simulation results for lower-body resistance training exercises, using OpenSim or equivalent tools, 

appear throughout the literature. One group reports using OpenSim to study a microgravity countermeasure combining 

artificial gravity, exercise and vibration during the performance of single- and two-legged squats; they conclude, based 

on simulation results, that the countermeasure performance may surpass that of currently deployed equipment 

(Ref. 11). Another group modeled hip muscle force during squatting movements in OpenSim for direct comparison to 

EMG measurements. They found good general correlation between loads and EMG activity, and they estimated hip 

muscle force loads well below 25 percent maximal for unweighted squats (Ref. 12). Still another group used OpenSim 

to study force depression and force enhancement induced by active muscle shortening and lengthening, respectively, to 

represent muscle history effects. Based on results from body weight and lightly-loaded squats and heel raises, they 

conclude that their modifications give a more accurate description of underlying forces and activations for the lower 

limb musculature (Ref. 13).

The study reported herein is unique in its use of computational simulation to investigate a variety of exercises at 

higher intensities (at or near the subject’s three-repetition maximum) and over the fullest range of motion to maximal 

squatting depth and heel raise trajectory. In this realm the literature is sparse, and the present study is breaking new 

ground in the study of complex human motion on a novel device, and in the context of microgravity countermeasures.

Harness Loading

Changing the loading configuration of the HULK device from two-point loading to single-point loading, may result 

in changes in body posture and to the location of the center of mass of the system. These changes could play a significant 

role in the joint torques and muscle forces that are produced. For example when comparing a narrow stance squat and a 

wide stance squat, gluteus maximus activity is greater in a wide stance compared with a narrow stance squat (Ref. 14)

and hip extension moments are greater in the medium and wide stance squats than in narrow stance squats (Ref. 15). No 

significant difference in quadriceps and hamstring activity is observed between narrow stance and wide stance squats 

(Refs. 14 and 16), however more tibiofemoral compressive force is generated during wide stance squat than narrow 

stance squat (Ref. 16) and knee extensor moments are greater in the medium and wide stance squats than in narrow stance 

squats (Ref. 15). The narrow stance squat produces more gastrocnemius activity than the wide stance squat (Ref. 16) and 

ankle plantar flexion moment is produced during narrow stance squats, whereas ankle dorsiflexor moment is produced 

during medium and wide stance squats (Ref. 15). The restriction of the knees so they do not move forward of the toes 

during a squat results in an increase in hip torque and a decrease in knee torque (Ref. 17). Front squats result in lower 

knee compressive forces and knee extensor moments than back squats, with no significant differences in quadriceps and 

hamstring activity (Ref. 18). Similarly, counterbalance squats decrease knee joint moment and quadriceps activity, while 

increasing hip joint moment and gluteus maximus activity, compared to a regular squat (Ref. 19). 

Chiu et al. compared the sagittal plane joint kinetics during front squat and single-leg squat exercises, performed 

with free weights and with a flywheel resistance device (Ref. 20). In both exercises, the net joint impulse, the average 

net joint moment and the average net joint power at the knee joint were lower when using the flywheel device, then 

when using free weights, with slight to significant increases in these measurements at the hip and ankle joints 

(Ref. 20). Performing squat and single-leg squat exercises on devices such as the flywheel device in this study, where 

there is a single point of loading, centrally located anterior to the subject, could result in less of a hypertrophic effect 

within the knee extensor muscles.
NASA/TM—2015-218852 4

(a) (b) 

Figure 1.—HULK device configured in dual-tether (a) and single-tether (b) operation. Both 

dual-tether and single tether operation are intended to connect to various accessories, 

including the bar, shown at left, or a body harness (not shown).

Methods

Hulk Exercise Device

The HULK is a compact exercise device intended to fit within the confines of NASA’s next generation launch 

vehicle, the Multi-Purpose Crew Vehicle (MPCV). Given that the volume inside MPCV is limited, the device must be 

small enough to fit, yet allow the astronauts to perform necessary exercises with sufficient intensity to generate an 

appropriate loading stimulus. The HULK is shown in Figure 1 which represents the second design iteration resulting in 

a more compact and improved exercise package over the previous concept. The base is approximately 4 ft long, 2 ft 

wide and 6 in. tall. Two removable supports can be installed on each end to rest a 45.25 in. long bar on when not 

exercising. The test subject holds onto the bar which is connected to the resistance apparatus located underneath the 

top platform through two cables on each end. Resistance is created by pneumatic cylinders and pulleys. Cable tension 

force data are obtained through wireless load cells attached in line with the cables during the exercise motion. It is 

possible to replace the dual-tethered bar with a single tethered harness using one tether of the HULK, as shown in 

Figure 1.

Exercise Protocols

The male subject was a regular resistance trainee with anthropometry within the astronaut population as shown in

Table 1.

After providing informed consent, the subject performed three exercises: squat (SQ), single-leg squat (SLS) and 

heel raise (HR), both with the device and at body weight (BW), except for SLS, where a BW trial was unintentionally 

omitted. Furthermore, the subject performed the squats to parallel (SQP), i.e., thighs parallel to the floor, and deep 

squats (SQD) as shown in Figure 2. The anterior/posterior bar position was located above the heels and the knees were 

vertically aligned with the toes at the bottom of the movement. A NASA IRB approved these exercise protocols.

The subject performed SLS using the right leg as the primary load bearing leg (Figure 3). The subject performed 

heel raises over the full ankle range of motion possible (Figure 4). Table 2 summarizes the load lifted and repetitions 

performed for each exercise.

The load settings on the device were set based on the subject’s perception of light (L), medium (M), and heavy (H) 

compared to his perceived one-repetition maximum (1 RM).
NASA/TM—2015-218852 5

TABLE 1.—SUBJECT DATA USED TO DEVELOP

THE SUBJECT-SPECIFIC EXERCISE MODELS

Subject

Gender ...................................................................... Male

Height, cm ........................................ 183 (90th percentile)

Mass, kg.............................................. 76 (75th percentile)

(a) (b)

Figure 2.—Subject performing (a) parallel and (b) deep squats on the HULK device. During parallel 

squats the thighs are approximately parallel to the floor at the bottom of the movement. During 

deep squats the subject descends to maximum depth.

Figure 3.—Subject performing single-leg squats on the 

HULK device with the right leg as the target limb.
NASA/TM—2015-218852 6

TABLE 2.—SUMMARY OF THE EXERCISE DATA COLLECTED

Exercise Load,

lb/kg

Repetitions

Deep Squat (SQD)

BW Yes 3

Light 125/57 3

Medium 155/70 3

Heavy 185/84 3

Parallel Squat (SQP)

BW Yes 3

Light 125/57 3

Medium 155/70 3

Heavy 185/84 3

Single-Leg Squat (SLS)

BW No Trial 0

Light No Trial 0

Medium 60/27 3

Heavy 100/45 3

Heel Raise (HR)

BW Yes 4

Light No Trial 0

Medium 150/68 4

Heavy 225/102 4

Figure 4.—Subject performing heel raise 

exercise on the HULK device.
NASA/TM—2015-218852 7

Data Collection and Processing

Data collection occurred in May 2014 at NASA Johnson Space Center (JSC). HULK records the applied load 

using load cells (Omega Inc., Miniature Series, LC-300) and bar displacement using encoders (US Digital, E5 Series)

at 200 Hz. Bilateral ground reaction forces (GRF) were measured at 1,000 Hz using two 40- by 60-cm quartz crystal 

piezoelectric force plates (Model 9261, Kistler Instruments AG). GRF data were down-sampled and device data upsampled to 250 Hz in Matlab to match the motion capture (mocap) data. For the heel raise exercise, the subject stood 

on metal platforms placed on each force platform to allow for full ankle range of motion as shown in Figure 4.

Mocap data were collected with the Smart-D 12 camera system at 250 Hz (BTS Bioengineering, Milan, IT). 

Three-dimensional position data were collected of spherical reflective markers approximately 10 mm in diameter and 

placed at key anatomical sites on the subject (see Appendix D for specific marker locations). Prior to data collection 

the cameras were calibrated with an activity volume encompassing the subject and device according to the 

manufacturer’s specifications and procedures. Calibration error was on the order of 0.1 mm. Mocap and GRF data 

were collected simultaneously with a single computer workstation. 

After data collection, motion capture data were processed using BTS Smart Track software, which removed 

erroneous marker trajectories and any false light reflections in the room that mimicked markers. 

Manual modification of the OpenSim files containing external loads was necessary by appending the device 

loading data synchronized with the GRF data. Appendix E describes the process by which the device load and GRF 

data were manually synced, subsampled, interpolated and resolved into their respective (x,y,z) coordinates using a 

combination of Mathworks Matlab and Microsoft Excel.

Simulation of Bar Versus Harness Loading

Specific Aim 2 of this study seeks to quantify the effects of harness loading vs. bar loading. In an effort to 

conserve volume, a single-tethered harness loading configuration, extending from the core of the body to the exercise 

device, is being considered over the two-point bar loading configuration illustrated in Figure 2. A commercially 

available equivalent of this type of harness loading is shown in Figure 5.

Figure 5.—Harness loading on the Exxentric kBox 3 flywheel device (left) closely 

matches the harness loading scheme under consideration for this study. On 

HULK, the subject would straddle a single loading tether as shown in the rowing

exercise depicted (right), but wearing a harness similar to the one shown on the 

left.
NASA/TM—2015-218852 8

Figure 6.—Distribution of harness loading on the upper back (30 percent) and 

lower back (70 percent) as indicated by the green arrows. Markers at the 

arrow tails indicate the points of application of the load.

It is desirable to know the effect of loading configuration on the joint torques, resultant joint forces and muscle 

forces produced during the exercises. To simulate the harness loading, the measured bar load was distributed between 

the upper back (70 percent) and lower back (30 percent) across total of four points of load application to the 

biomechanical model, as shown in Figure 6. The authors estimated these proportions from simple trials of cable-based 

equivalents of the exercises under study while wearing a harness.

Although kinematic and kinetic data exists for the bar loading configuration, as explained above, data has not been 

collected to date on the harness loading configuration. We accounted for the lack of kinematic and kinetic data for the 

harness loading configuration and made the following simplifying assumptions for this preliminary modeling effort:

1. The kinematics of the exercise (i.e., joint angle histories) and the measured GRF and device loads are all 

essentially the same between the bar-loaded versus harness-loaded cases. 

2. The proportional split between loading on the upper (70 percent) and lower back (30 percent) is both accurate 

and unchanging throughout the range of motion. 

3. All loads are directed at all times in the same direction as the cable tether attached to the harness.

OpenSim Exercise Models

There are individual OpenSim models for each exercise. All OpenSim models are based on a modified version of 

the Arnold lower-limb model (Ref. 21) that is publicly available from the OpenSim website (Ref. 22). The modified 

Arnold lower limb model contains 21 body segments (no arms) and 96 lower limb muscles. This model uses wrapping 

surfaces extensively in the lower limbs in order to accommodate more severe knee flexion angles.

Muscles in OpenSim are modeled as line elements between two-points. Wrap surfaces allow for the muscle 

elements to conformably follow anatomical surfaces. The wrap surfaces allow the muscles to follow a path that is a

realistic approximation to the movement of the human body. Without a wrap surface, a muscle could move through a 

bone or move at a sharp angle, resulting in a discontinuity or an incorrect muscle joint moment arm. The modeling of 

the knee joint benefited from the wrap surfaces the most, with knee force being reduced by more than half when the 

wrap surfaces were active in the model. Figure 7 shows the model both with and without wrap surfaces.
NASA/TM—2015-218852 9

(a) (b)

Figure 7.—Detailed view of the wrapping surfaces of the Arnold lower limb model in 

the (a) upper leg and a close-up of the (b) knee joint

The muscle model in the modified Arnold lower limb model was updated to the Millard muscle model (Ref. 23)

which performs better at the extremes of the range of motion (Ref. 23). The maximum isometric strength parameters 

were increased to reflect the conditioning of the subject and to ensure the model was strong enough for the heavy loads 

during kinetic analyses. The final muscle parameters selected for the models are listed in Appendix B.

An added bar object attached to the torso of the model using a custom joint that permitted three directions of bar 

rotation but no bar translations relative to the torso. The spatial location of the joint was the midpoint of the 

coordinates of the two markers at either end of the bar. This point varies slightly with each set of each exercise, and 

this variation is reflected in the models.

The modeling process followed the standard OpenSim workflow as shown in Figure 8.

The modified Arnold lower limb model was first scaled to the subject’s anthropometrics using marker position 

data from a static mocap trial in which the subject assumes a neutral posture and remains still. Methods used for 

scaling followed the procedure outlined in the OpenSim User’s Guide (Ref. 22). The subject’s mass also guided the 

calculation of the new mass distributions from the original Arnold model.

Data files containing marker positions produce the inverse kinematics (IK) solutions for joint angle histories. IK 

was an iterative process, whereby the marker placements and weightings were adjusted until the root mean square 

(RMS) and maximum marker position errors are within the OpenSim best practices guidelines of 2 and 4 cm, 

respectively.

Low-pass filtering of the kinematic and GRF data occurred in OpenSim using a 3rd-order low-pass IIR Butterworth 

digital filter with a cutoff frequency of 6 Hz.

The models also require compensatory residual forces and moments applied at the hip and torque reserves applied 

at all joints in order to fully execute the movements during static optimization. Residuals are non-physical forces that 

account for inconsistencies between experimental GRFs and joint accelerations estimated from experimental motion 

capture data. A model design goal is to reduce these residuals and reserves to a negligible level compared with the 

muscle forces and muscle-generated moments. However, in practice residuals can never be reduced to zero, because 

experimental data are always imperfect. Residual values are included in the results, and they are a key input to the 

model self-verification process.
NASA/TM—2015-218852 10

Muscles are grouped by the joint articulation they actuate. Table 3 shows the names of the muscle groups that 

appear in later sections of the report and their constituent muscles for the right leg only. An exception is the lumbar 

joint, which is actuated by symmetric muscles on both sides of the body.

Figure 8.—The OpenSim workflow used in the current study.

TABLE 3.—MAJOR MUSCLE GROUPS AND THEIR CONSTITUENT MUSCLE ACTUATORS IN OpenSim
NASA/TM—2015-218852 11

For all joint articulations, a positive value indicates motion in the direction specified by the name (e.g., knee 

flexion), whereas a negative value indicates motion in the opposite direction (e.g., knee extension). Joints are generally 

not abbreviated for clarity, with the exception of the metatarsophalangeal (MTP) joint.

Modifications to the Arnold Model

The Arnold lower limb model (Ref. 21) used for the squat analysis was originally developed for gait and running

motions. The squat motions in this study exhibited knee flexion angles exceeding 140° under near-maximal loading, a 

phenomenon not seen in gait and running. The base model was not designed for this extreme motion, and some of the 

muscles assumed an unnatural path as a result. The model includes wrap surfaces placed at the knee that are geometric 

shapes (e.g., sphere, cylinder, oval) to help guide the muscles to follow the correct path. Each wrap surface is linked to 

the specific muscles that are intended to wrap around them.

As shown in Figure 9, under maximal knee flexion, the quadriceps muscles in the unmodified Arnold lower limb 

model would flip from the anterior portion of the wrap surface at the knee to the opposite posterior side.

The anterior thigh muscles (rectus femoris and vastus intermedius, vastus lateralis and vastus medialis) are all knee 

extensors. The cylindrical wrap surface that guided these muscles required a change in diameter from 5 to 6 cm and 

slight translation anteriorly towards the patella. This resulted in the muscles following the wrap surface properly at the 

knee throughout the range of motion for the entire test during squat and single-leg squat exercises. Additional path 

points were also added; one near the posterior end of each of the four muscles and another proximal to that. These new 

wrap points prevented the muscle from extending into the femur or into the patella.

The biceps femoris long head and short head muscles in the posterior side of the thigh and the gastrocnemius 

lateral and medial muscles in the calf also required the location and size of their wrap surfaces to be slightly adjusted.

(a) (b) 

Figure 9.—Quadriceps path at the knee in the unmodified (a) and modified (b) Arnold models at maximal 

knee flexion angle near 140°. The patellar wrapping surface (highlighted) was augmented in diameter 

and relocated anteriorly to correct the physiologically impossible muscle paths depicted on the left.
NASA/TM—2015-218852 12

Analyses Performed and Statistical Methods

The key outcomes of interest from the modeling process are joint angle ranges, joint moments, resultant joint 

forces, muscle tension forces by muscle group and residual/reserve forces. For all key outcomes, time histories, peak 

and averaged values were computed. Since there are multiple reps for each exercise (see Table 2), peak and average 

results appear as mean values with bars indicating the standard error (SE). Pairwise comparisons (e.g., parallel vs. deep 

squats) employed Student’s t-test for hypothesis testing to determine any statistically significant differences (p < 0.05) 

in mean values.

For static optimization (SO) analyses, the polynomial exponent was 4, precision was 12 and muscle force-lengthvelocity relationship was disabled. Further analyses performed using the SO results included muscle moments, muscle 

moment arms, muscle forces and activations, and resultant joint forces. Joint reaction analysis calculates the joint 

forces and moments transferred between consecutive bodies as a result of all loads acting on the model. These forces 

and moments correspond to the internal loads carried by the joint structure (Ref. 22). Resultant joint force refers to the 

magnitude of the joint reaction force.

Results

Squat Exercise

Joint Kinematics for Parallel and Deep Squats

Table 4 summarizes the joint angle ranges for the major lower body joints during both parallel and deep squats for 

the right leg. Left leg results are similar and are omitted. The subject is right-side dominant.

Figure 10 shows the motion histories of these joints over the course of each set. Figure 11 to Figure 13 show the 

joint moments, resultant joint forces and muscle tension forces, respectively. Figure 14 shows the model’s residual 

forces and moments during the squat movement, and Figure 15 shows the reserve actuator moments. Figure 16 shows 

the reserve joint moments expressed as a percentage of the total joint moments as determined from ID.

Technical problems during the third rep of the D185 (heavy deep squat) exercise resulted in a loss of data. Results 

for the first two reps are shown.

TABLE 4.—KINEMATIC JOINT ANGLE RANGES FOR PARALLEL AND DEEP SQUATS

Parallel squat Deep squat

Joint articulation during 

squats

Angle at top of 

movement,

°

Angle at bottom of 

movement,

°

Angle at top of 

movement,

°

Angle at bottom of 

movement,

°

Hip flexion 16 116 14 129

Hip adduction –4 –31 –5 –33

Hip internal rotation –23 12 –22 30

Knee flexion –2 128 –4 145

Ankle dorsiflexion –7 34 –7 39

Subtalar inversion –13 6 –13 17

MTP flexion 15 –11 18 –8

Lumbar extension 11 –11 12 –20
NASA/TM—2015-218852 13

Kinematic Joint Angles for Deep and Parallel Squats

Figure 10.—Kinematic joint angle histories during deep squats (left of each pairing) and parallel squats (right of each pairing) for the

joints listed in Table 4.
NASA/TM—2015-218852 14

 

Figure 10.—Continued. Kinematic joint angle histories during deep squats (left of each pairing) and parallel squats (right of each 

pairing) for the joints listed in Table 4.
NASA/TM—2015-218852 15

Figure 10.—Concluded. Kinematic joint angle histories during deep squats (left of each pairing) and parallel squats (right of each 

pairing) for the joints listed in Table 4.
NASA/TM—2015-218852 16

Average and Peak Resultant Joint Forces for Deep and Parallel Squats

(a) 

Figure 11.—Resultant joint forces in Newtons for deep and parallel squats under all loading conditions for the (a) hip and knee 

(patellofemoral and tibiofemoral) joints, (b) ankle and subtalar joints, and (c) lumbar joint with bar and harness loading separated.
NASA/TM—2015-218852 17

(a)

Figure 11.—Continued. Resultant joint forces in Newtons for deep and parallel squats under all loading conditions for the (a) hip and 

knee (patellofemoral and tibiofemoral) joints, (b) ankle and subtalar joints, and (c) lumbar joint with bar and harness loading 

separated.
NASA/TM—2015-218852 18

(b)

Figure 11.—Continued. Resultant joint forces in Newtons for deep and parallel squats under all loading conditions for the (a) hip and 

knee (patellofemoral and tibiofemoral) joints, (b) ankle and subtalar joints, and (c) lumbar joint with bar and harness loading 

separated.
NASA/TM—2015-218852 19

(b)

(c)

Figure 11.—Continued. Resultant joint forces in Newtons for deep and parallel squats under all loading conditions for the (a) hip and 

knee (patellofemoral and tibiofemoral) joints, (b) ankle and subtalar joints, and (c) lumbar joint with bar and harness loading 

separated.
NASA/TM—2015-218852 20

(c)

Figure 11.—Concluded. Resultant joint forces in Newtons for deep and parallel squats under all loading conditions for the (a) hip 

and knee (patellofemoral and tibiofemoral) joints, (b) ankle and subtalar joints, and (c) lumbar joint with bar and harness loading 

separated.
NASA/TM—2015-218852 21

Average and Peak Joint Moments for Deep and Parallel Squats

(a)

Figure 12.—Joint moments in Newton-meters for deep and parallel squats under all loading conditions for the (a) hip extension, hip 

abduction and knee extensor joints, (b) ankle plantar flexor and subtalar invertor, and (c) lumbar extension joint.
NASA/TM—2015-218852 22

(a)

Figure 12.—Continued. Joint moments in Newton-meters for deep and parallel squats under all loading conditions for the (a) hip 

extension, hip abduction and knee extensor joints, (b) ankle plantar flexor and subtalar invertor, and (c) lumbar extension joint.
NASA/TM—2015-218852 23

(b)

Figure 12.—Continued. Joint moments in Newton-meters for deep and parallel squats under all loading conditions for the (a) hip 

extension, hip abduction and knee extensor joints, (b) ankle plantar flexor and subtalar invertor, and (c) lumbar extension joint.
NASA/TM—2015-218852 24

(b)

(c)

Figure 12.—Continued. Joint moments in Newton-meters for deep and parallel squats under all loading conditions for the (a) hip 

extension, hip abduction and knee extensor joints, (b) ankle plantar flexor and subtalar invertor, and (c) lumbar extension joint.
NASA/TM—2015-218852 25

(c)

Figure 12.—Concluded. Joint moments in Newton-meters for deep and parallel squats under all loading conditions for the (a) hip 

extension, hip abduction and knee extensor joints, (b) ankle plantar flexor and subtalar invertor, and (c) lumbar extension joint.
NASA/TM—2015-218852 26

Average and Peak Muscle Forces by Muscle Group for Deep and Parallel Squats

(a)

Figure 13.—Muscle forces for deep and parallel squats under all loading conditions for the (a) hip extensor, hip flexor and hip 

adductor groups, (b) hip abductor, hip internal rotator and hip external rotator groups, (c) knee extensor, knee flexor and ankle 

dorsiflexor groups, and (d) ankle plantar flexor, subtalar evertor and subtalar invertor groups.
NASA/TM—2015-218852 27

(a)

Figure 13.—Continued. Muscle forces for deep and parallel squats under all loading conditions for the (a) hip extensor, hip flexor 

and hip adductor groups, (b) hip abductor, hip internal rotator and hip external rotator groups, (c) knee extensor, knee flexor and 

ankle dorsiflexor groups, and (d) ankle plantar flexor, subtalar evertor and subtalar invertor groups.
NASA/TM—2015-218852 28

(b)

Figure 13.—Continued. Muscle forces for deep and parallel squats under all loading conditions for the (a) hip extensor, hip flexor 

and hip adductor groups, (b) hip abductor, hip internal rotator and hip external rotator groups, (c) knee extensor, knee flexor and 

ankle dorsiflexor groups, and (d) ankle plantar flexor, subtalar evertor and subtalar invertor groups.
NASA/TM—2015-218852 29

(b)

Figure 13.—Continued. Muscle forces for deep and parallel squats under all loading conditions for the (a) hip extensor, hip flexor 

and hip adductor groups, (b) hip abductor, hip internal rotator and hip external rotator groups, (c) knee extensor, knee flexor and 

ankle dorsiflexor groups, and (d) ankle plantar flexor, subtalar evertor and subtalar invertor groups.
NASA/TM—2015-218852 30

(c)

Figure 13.—Continued. Muscle forces for deep and parallel squats under all loading conditions for the (a) hip extensor, hip flexor 

and hip adductor groups, (b) hip abductor, hip internal rotator and hip external rotator groups, (c) knee extensor, knee flexor and 

ankle dorsiflexor groups, and (d) ankle plantar flexor, subtalar evertor and subtalar invertor groups.
NASA/TM—2015-218852 31

(c)

Figure 13.—Continued. Muscle forces for deep and parallel squats under all loading conditions for the (a) hip extensor, hip flexor 

and hip adductor groups, (b) hip abductor, hip internal rotator and hip external rotator groups, (c) knee extensor, knee flexor and 

ankle dorsiflexor groups, and (d) ankle plantar flexor, subtalar evertor and subtalar invertor groups.
NASA/TM—2015-218852 32

(d)

Figure 13.—Continued. Muscle forces for deep and parallel squats under all loading conditions for the (a) hip extensor, hip flexor 

and hip adductor groups, (b) hip abductor, hip internal rotator and hip external rotator groups, (c) knee extensor, knee flexor and 

ankle dorsiflexor groups, and (d) ankle plantar flexor, subtalar evertor and subtalar invertor groups.
NASA/TM—2015-218852 33

(d)

Figure 13.—Concluded. Muscle forces for deep and parallel squats under all loading conditions for the (a) hip extensor, hip flexor 

and hip adductor groups, (b) hip abductor, hip internal rotator and hip external rotator groups, (c) knee extensor, knee flexor and 

ankle dorsiflexor groups, and (d) ankle plantar flexor, subtalar evertor and subtalar invertor groups.
NASA/TM—2015-218852 34

Average and Peak Residual Forces and Moments for Deep and Parallel Squats

(a)

Figure 14.—Average and peak residual forces in (a) Newtons for deep and parallel squats under all loading conditions for the FX, 

FY, FZ residual forces, and (b) Newton-meters for deep and parallel squats under all loading conditions for the MX, MY, MZ 

residual moments.
NASA/TM—2015-218852 35

(a)

Figure 14.—Continued. Average and peak residual forces in (a) Newtons for deep and parallel squats under all loading conditions 

for the FX, FY, FZ residual forces, and (b) Newton-meters for deep and parallel squats under all loading conditions for the MX, 

MY, MZ residual moments.
NASA/TM—2015-218852 36

(b)

Figure 14.—Continued. Average and peak residual forces in (a) Newtons for deep and parallel squats under all loading conditions 

for the FX, FY, FZ residual forces, and (b) Newton-meters for deep and parallel squats under all loading conditions for the MX, 

MY, MZ residual moments.
NASA/TM—2015-218852 37

(b)

Figure 14.—Concluded. Average and peak residual forces in (a) Newtons for deep and parallel squats under all loading conditions 

for the FX, FY, FZ residual forces, and (b) Newton-meters for deep and parallel squats under all loading conditions for the MX, 

MY, MZ residual moments.
NASA/TM—2015-218852 38

Average and Peak Reserve Moments for Deep and Parallel Squats

(a)

Figure 15.—Reserve actuator moments in Newton-meters for deep and parallel squats under all loading conditions for the (a) hip 

flexion, hip adduction and hip rotation joint articulations and (b) knee flexion, ankle dorsiflexor and lumbar extension joint 

articulations. 
NASA/TM—2015-218852 39

(a)

Figure 15.—Continued. Reserve actuator moments in Newton-meters for deep and parallel squats under all loading conditions for 

the (a) hip flexion, hip adduction and hip rotation joint articulations, and (b) knee flexion, ankle dorsiflexor and lumbar extension 

joint articulations. 
NASA/TM—2015-218852 40

(b)

Figure 15.—Continued. Reserve actuator moments in Newton-meters for deep and parallel squats under all loading conditions for 

the (a) hip flexion, hip adduction and hip rotation joint articulations, and (b) knee flexion, ankle dorsiflexor and lumbar extension 

joint articulations. 
NASA/TM—2015-218852 41

(b)

Figure 15.—Concluded. Reserve actuator moments in Newton-meters for deep and parallel squats under all loading conditions for 

the (a) hip flexion, hip adduction and hip rotation joint articulations, and (b) knee flexion, ankle dorsiflexor and lumbar extension 

joint articulations. 
NASA/TM—2015-218852 42

(a)

(b)

Figure 16.—Average reserve moments as a percentage of total joint 

moment for (a) deep squat and (b) parallel squat.
NASA/TM—2015-218852 43

Single-Leg Squat Exercise

Joint Kinematics for Single-Leg Squat

Table 5 summarizes the joint angle ranges for the major lower body joints during the single-leg squat for the right 

leg. Figure 17 shows kinematic trajectories for the major joints on the right side of the body. Left leg (unloaded) results 

are omitted for brevity. Figure 18 to Figure 20 describe the kinetics of the model, i.e., joint moments, resultant joint 

forces and muscle tension forces, respectively. Figure 21 describes the model’s residual forces and moments during the 

squat movement, and Figure 22 describes the reserve actuator moments. Figure 23 shows the reserve joint moments 

expressed as a percentage of the total joint moments as determined from ID.

TABLE 5.—KINEMATIC JOINT ANGLE

RANGES FOR SINGLE-LEG SQUAT

Joint articulation during 

single-leg squat

Angle at top of 

movement,

°

Angle at bottom of 

movement,

°

Hip flexion 3 37

Hip abduction –1 7

Hip internal rotation –4 –14

Knee flexion 10 122

Ankle dorsiflexion –6 32

Subtalar inversion –3 –22

MTP flexion 6 –9

Lumbar extension 13 1

(a) (b)

Figure 17.—Joint kinematics trajectories for single-leg squat: (a) hip flexion, (b) hip adduction, (c) hip internal rotation, (d) knee 

flexion, (e) ankle dorsiflexion, (f) subtalar inversion, (g) MTP flexion, and (h) lumbar extension.
NASA/TM—2015-218852 44

(c) (d)

(e) (f)

(g) (h)

Figure 17.—Concluded. Joint kinematics trajectories for single-leg squat: (a) hip flexion, (b) hip adduction, (c) hip internal rotation, 

(d) knee flexion, (e) ankle dorsiflexion, (f) subtalar inversion, (g) MTP flexion and (h) lumbar extension.
NASA/TM—2015-218852 45

Joint Moments for Single-Leg Squat

(a)

(b)

(c)

Figure 18.—Peak and average joint moments in Newton-meters for single-leg squat under all loading conditions for the following 

joint articulations: (a) hip extension, (b) hip abduction, (c) hip internal rotation, (d) knee extension, (e) ankle plantar flexion, 

(f) ankle subtalar inversion, and (g) lumbar extension.
NASA/TM—2015-218852 46

(d)

(e)

(f)

Figure 18.—Continued. Peak and average joint moments in Newton-meters for single-leg squat under all loading conditions for the 

following joint articulations: (a) hip extension, (b) hip abduction, (c) hip internal rotation, (d) knee extension, (e) ankle plantar 

flexion, (f) ankle subtalar inversion, and (g) lumbar extension.
NASA/TM—2015-218852 47

(g)

Figure 18.—Concluded. Peak and average joint moments in Newton-meters for single-leg squat under all loading conditions for the 

following joint articulations: (a) hip extension, (b) hip abduction, (c) hip internal rotation, (d) knee extension, (e) ankle plantar 

flexion, (f) ankle subtalar inversion, and (g) lumbar extension.
NASA/TM—2015-218852 48

Resultant Joint Forces for Single-Leg Squat

(a)

(b)

(c)

Figure 19.—Resultant joint forces in Newtons for single-leg squat under all loading conditions for the following joints: (a) hip, 

(b) patellofemoral, (c) knee, (d) ankle, (e) subtalar, and (f) lumbar.
NASA/TM—2015-218852 49

(d)

(e)

(f)

Figure 19.—Concluded. Resultant joint forces in Newtons for single-leg squat under all loading conditions for the following joints: 

(a) hip, (b) patellofemoral, (c) knee, (d) ankle, (e) subtalar, and (f) lumbar.
NASA/TM—2015-218852 50

Muscle Forces by Muscle Group for Single-Leg Squat

(a)

(b)

(c)

Figure 20.—Average and peak muscle forces in Newtons by muscle group for single-leg squat under all loading conditions for the 

following groups: (a) hip extensors, (b) hip flexors, (c) hip adductors, (d) hip abductors, (e) hip internal rotators, (f) hip external 

rotators, (g) knee extensors, (h) knee flexors, (i) dorsiflexors, (j) plantar flexors, (k) subtalar inverters, (l) subtalar everters, and 

(m) lumbar extensors.
NASA/TM—2015-218852 51

(d)

(e)

(f)

Figure 20.—Continued. Average and peak muscle forces in Newtons by muscle group for single-leg squat under all loading 

conditions for the following groups: (a) hip extensors, (b) hip flexors, (c) hip adductors, (d) hip abductors, (e) hip internal rotators, 

(f) hip external rotators, (g) knee extensors, (h) knee flexors, (i) dorsiflexors, (j) plantar flexors, (k) subtalar inverters, (l) subtalar 

everters, and (m) lumbar extensors.
NASA/TM—2015-218852 52

(g)

(h)

(i)

Figure 20.—Continued. Average and peak muscle forces in Newtons by muscle group for single-leg squat under all loading 

conditions for the following groups: (a) hip extensors, (b) hip flexors, (c) hip adductors, (d) hip abductors, (e) hip internal rotators, 

(f) hip external rotators, (g) knee extensors, (h) knee flexors, (i) dorsiflexors, (j) plantar flexors, (k) subtalar inverters, (l) subtalar 

everters, and (m) lumbar extensors.
NASA/TM—2015-218852 53

(j)

(k)

(l)

Figure 20.—Continued. Average and peak muscle forces in Newtons by muscle group for single-leg squat under all loading 

conditions for the following groups: (a) hip extensors, (b) hip flexors, (c) hip adductors, (d) hip abductors, (e) hip internal rotators, 

(f) hip external rotators, (g) knee extensors, (h) knee flexors, (i) dorsiflexors, (j) plantar flexors, (k) subtalar inverters, (l) subtalar 

everters, and (m) lumbar extensors.
NASA/TM—2015-218852 54

(m)

Figure 20.—Concluded. Average and peak muscle forces in Newtons by muscle group for single-leg squat under all loading 

conditions for the following groups: (a) hip extensors, (b) hip flexors, (c) hip adductors, (d) hip abductors, (e) hip internal rotators, 

(f) hip external rotators, (g) knee extensors, (h) knee flexors, (i) dorsiflexors, (j) plantar flexors, (k) subtalar inverters, (l) subtalar 

everters, and (m) lumbar extensors.
NASA/TM—2015-218852 55

Residual Forces and Moments for the Single-Leg Squat

(a)

(b)

(c)

Figure 21.—Average and peak residual forces in Newtons and moments in Newton-meters for single-leg squat under all loading 

conditions for the following residual forces: (a) FX, (b) FY, (c) FZ; and residual moments: (d) MX, (e), MY, (f) MZ
NASA/TM—2015-218852 56

(d)

(e)

(f)

Figure 21.—Concluded. Average and peak residual forces in Newtons and moments in Newton-meters for single-leg squat under all 

loading conditions for the following residual forces: (a) FX, (b) FY, (c) FZ; and residual moments: (d) MX, (e), MY, (f) MZ
NASA/TM—2015-218852 57

Reserve Moments for the Single-Leg Squat

(a)

(b)

(c)

Figure 22.—Average and peak reserve actuator moments for single-leg squat under all loading conditions for the following joint 

articulations: (a) hip flexion, (b) hip adduction, (c) hip rotation, (d) knee flexion, (e) ankle dorsiflexion, (f) subtalar inversion 

(g) lumbar extension. 
NASA/TM—2015-218852 58

(d)

(e)

(f)

Figure 22.—Continued. Average and peak reserve actuator moments for single-leg squat under all loading conditions for the 

following joint articulations: (a) hip flexion, (b) hip adduction, (c) hip rotation, (d) knee flexion, (e) ankle dorsiflexion, (f) subtalar 

inversion (g) lumbar extension. 
NASA/TM—2015-218852 59

(g)

Figure 22.—Concluded. Average and peak reserve actuator moments for single-leg squat under all loading conditions for the 

following joint articulations: (a) hip flexion, (b) hip adduction, (c) hip rotation, (d) knee flexion, (e) ankle dorsiflexion, (f) subtalar 

inversion and (g) lumbar extension. 

Figure 23.—Average reserve moments as a percentage of total 

joint moment for single-leg squat.

Heel Raise Exercise

Joint Kinematics for Heel Raise

Table 6 summarizes the joint angle ranges for the major lower body joints during the heel raise for the right leg.

Left leg results are omitted, but are generally similar to the right leg. The subject is right-leg dominant. Because the 

heel raise is an isolation movement that targets the lower limb musculature, results for the hip and knee are not shown.

Figure 24 describes the joint kinematics trajectories for the heel raise. Figure 25 to Figure 27 describe the kinetics 

of the model, i.e., joint moments, resultant joint forces and muscle tension forces, respectively. Figure 28 describes the 

model’s residual forces and moments during the heel raise movement. Figure 29 describes the model’s reserve actuator 

moments during the heel raise movement. Figure 30 shows the reserve joint moments expressed as a percentage of the 

total joint moments as determined from ID.
NASA/TM—2015-218852 60

TABLE 6.—KINEMATIC JOINT ANGLE

RANGES IN DEGREES FOR HEEL RAISE

Joint articulation during 

heel raise

Angle at top of 

movement,

°

Angle at bottom 

of movement,

°

Hip flexion 12 27

Knee flexion 8 21

Ankle dorsiflexion –33 18

Subtalar inversion 20 –13

MTP flexion –41 11

(a) (b)

(c) (d)

Figure 24.—Joint kinematics trajectories for heel raise: (a) ankle dorsiflexion, (b) subtalar inversion, (c) MTP flexion and (d) lumbar 

extension.
NASA/TM—2015-218852 61

Joint Moments for Heel Raise

(a)

(b)

(c)

Figure 25.—Peak and average joint moments in Newton-meters for heel raise under all loading conditions for the following joint

articulations: (a) ankle angle, (b) subtalar angle, (c) MTP angle and (d) lumbar extension.
NASA/TM—2015-218852 62

(d)

Figure 25.—Peak and average joint moments in Newton-meters for heel raise under all loading conditions for the following joints: 

(a) ankle angle, (b) subtalar angle, (c) MTP angle and (d) lumbar extension.
NASA/TM—2015-218852 63

Resultant Joint Forces for Heel Raise

(a)

(b)

(c)

Figure 26.—Resultant joint forces in Newtons for heel raise under all loading conditions for the following joints: (a) ankle, (b) 

subtalar, (c) MTP and (d) lumbar.
NASA/TM—2015-218852 64

(d)

Figure 26.—Resultant joint forces in Newtons for heel raise under all loading conditions for the following joints: (a) ankle, (b) 

subtalar, (c) MTP and (d) lumbar.
NASA/TM—2015-218852 65

Muscle Group Forces for Heel Raise

(a)

(b)

(c)

Figure 27.—Average and peak muscle forces by muscle group for heel raise under all loading conditions for the following groups: 

(a) plantar flexors, (b) subtalar inverters, and (c) lumbar extensors.
NASA/TM—2015-218852 66

Residual Forces and Moments for Heel Raise

(a)

(b)

(c)

Figure 28.—Average and peak residual forces in Newton and moments in Newton-meters for heel raise under all loading conditions 

for the following residual forces: (a) FX, (b) FY, (c) FZ, and residual moments: (d) MX, (e), MY, (f) MZ.
NASA/TM—2015-218852 67

(d)

(e)

(f)

Figure 28.—Concluded. Average and peak residual forces in Newton and moments in Newton-meters for heel raise under all 

loading conditions for the following residual forces: (a) FX, (b) FY, (c) FZ, and residual moments: (d) MX, (e), MY, (f) MZ.
NASA/TM—2015-218852 68

Reserve Moments for Heel Raise

(a)

(b)

(c)

Figure 29.—Average and peak reserve actuator moments for heel raise under all loading conditions for the following joint 

articulations: (a) ankle plantar flexion, (b) subtalar inversion, (c) MTP extension, and (d) lumbar extension. 
NASA/TM—2015-218852 69

(d)

Figure 29.—Concluded. Average and peak reserve actuator moments for heel raise under all loading conditions for the following 

joint articulations: (a) ankle plantar flexion, (b) subtalar inversion, (c) MTP extension, and (d) lumbar extension. 

Figure 30.—Average reserve moments as a percentage of total 

joint moment for heel raise.

Summary of All Exercises

Peak resultant joint forces, joint moments, and muscle group forces increase with applied load. Table 7

summarizes these quantities as multiples of BW for forces, and BW-m for moments.
NASA/TM—2015-218852 70

TABLE 7.—(a) PEAK RESULTANT JOINT FORCES EXPRESSED AS A MULTIPLE OF BW, (b) JOINT MOMENT

EXPRESSED AS A MULTIPLE OF BW-m, (c) MUSCLE FORCES EXPRESSED AS A MULTIPLE OF

BW FOR KEY JOINTS FOR ALL EXERCISES UNDER ALL LOADING CONDITIONS

(a)

Resultant Joint Forces (xBW) Parallel Squat Deep Squat Single‐Leg Squat Heel Raise

BW L125 M155 H185 L125 M155 H185 M60 H100 BW M150 H225

Hip, average, bar/harness 4.0 7.0 7.9 8.5 6.7 7.9 8.3 5.5 7.5 2.8 2.6 3.6

Knee patellofemoral, average, bar/harness 3.8 6.6 7.8 7.4 6.9 7.4 8.3 4.1 4.7 1.7 2.8 3.5

Knee tibiofemoral, average, bar/harness 0.6 1.0 1.1 1.2 1.0 1.1 1.2 4.9 6.5 0.2 0.3 0.2

Ankle, average, bar/harness 5.7 9.3 10.5 12.0 9.9 11.1 12.0 4.6 5.4 2.1 6.1 6.6

Lumbar, average 2.0 5.7 7.5 8.4 6.3 7.5 8.6 3.1 4.4 0.4 4.0 4.2

Lumbar, average, harness 2.0 3.2 4.1 4.5 3.7 4.2 4.6 2.4 2.7 0.4 2.3 2.0

Hip, peak, bar/harness 5.7 10.7 11.9 12.7 10.8 12.9 12.4 8.1 11.3 4.5 3.3 5.1

Knee patellofemoral, peak, bar/harness 7.6 12.8 14.0 14.2 11.7 12.8 13.9 6.7 8.4 2.6 3.7 4.4

Knee tibiofemoral, peak, bar/harness 0.8 1.3 1.4 1.5 1.3 1.3 1.5 7.5 9.5 0.5 0.4 0.5

Ankle, peak, bar/harness 7.5 11.5 12.8 14.8 13.8 15.0 15.9 6.5 7.1 3.1 8.5 9.1

Lumbar, peak, bar 3.5 9.3 11.7 14.1 10.3 12.4 13.6 4.4 5.4 0.5 5.1 5.6

Lumbar, peak, harness 3.5 5.9 7.2 8.7 6.4 7.7 8.3 3.3 3.7 0.5 2.9 2.4

(b)

Joint Moments (xBW‐m)

Parallel Squat Deep Squat Single‐Leg Squat Heel Raise

BW L125 M155 H185 L125 M155 H185 M60 H100 BW M150 H225

Hip extension, average, bar/harness 0.03 0.09 0.11 0.13 0.09 0.11 0.11 0.16 0.21 0.04 0.02 0.06

Hip adduction, average, bar/harness 0.08 0.11 0.10 0.12 0.06 0.07 0.08 0.02 0.02 0.03 0.00 0.00

Knee extension, average, bar/harness 0.15 0.25 0.29 0.28 0.30 0.34 0.38 0.08 0.09 0.04 0.03 0.07

Ankle, Plantar flexion, average, bar/harness 0.08 0.12 0.15 0.14 0.18 0.21 0.21 0.09 0.13 0.04 0.13 0.15

Lumbar extension, average 0.07 0.19 0.25 0.27 0.20 0.25 0.28 0.10 0.13 0.00 0.10 0.11

Lumbar extension, average, harness 0.07 0.09 0.12 0.12 0.10 0.12 0.12 0.06 0.07 0.00 0.03 0.02

Hip extension, peak, bar/harness 0.06 0.17 0.22 0.24 0.19 0.23 0.26 0.26 0.33 0.13 0.04 0.09

Hip adduction, peak, bar/harness 0.14 0.21 0.25 0.26 0.31 0.22 0.24 0.07 0.09 0.06 0.02 0.03

Knee extension, peak, bar/harness 0.26 0.43 0.49 0.50 0.53 0.57 0.60 0.17 0.19 0.08 0.04 0.09

Ankle, Plantar flexion, peak, bar/harness 0.12 0.18 0.22 0.23 0.28 0.30 0.32 0.15 0.18 0.07 0.15 0.17

Lumbar extension, peak 0.12 0.33 0.42 0.47 0.36 0.45 0.45 0.14 0.18 0.00 0.12 0.14

Lumbar extension, peak, harness 0.12 0.19 0.24 0.28 0.21 0.26 0.25 0.09 0.11 0.00 0.04 0.04

(c)

Muscle Group Forces (xBW)

Parallel Squat Deep Squat Single‐Leg Squat Heel Raise

BW L125 M155 H185 L125 M155 H185 M60 H100 M150 H225

Hip extensors, average, bar/harness 3.2 5.7 6.7 7.2 5.7 6.9 7.2 5.2 7.0

Hip flexors, average, bar/harness 0.6 0.7 0.8 0.9 0.9 0.9 1.0 0.0 0.2

Hip adductors, average, bar/harness 0.0 0.0 0.0 0.0 0.0 0.1 0.2 1.7 2.3

Hip abductors, average, bar/harness 3.2 5.4 6.2 6.6 5.3 6.3 6.5 2.4 3.2

Knee extensors, average, bar/harness 3.8 6.6 7.8 7.4 7.0 7.4 8.3 4.1 4.7 0.3 0.2

Knee flexors, average, bar/harness 0.1 0.0 0.1 0.1 0.2 0.2 0.3 2.8 3.9 1.9 2.8

Ankle, Plantar flexors, average, bar/harness 3.6 6.0 6.7 8.1 6.2 7.1 7.9 3.6 4.3 5.2 5.8

Hip extensors, peak, bar/harness 5.2 9.8 11.3 13.1 10.7 13.5 13.4 8.6 11.5 0.0 0.0

Hip flexors, peak, bar/harness 1.3 1.7 2.5 1.9 2.3 1.8 2.1 0.1 1.0

Hip adductors, peak, bar/harness 0.0 0.0 0.1 0.9 0.6 0.6 1.4 3.4 4.5

Hip abductors, peak, bar/harness 4.7 8.5 9.4 10.2 8.4 9.8 9.3 3.2 4.4

Knee extensors, peak, bar/harness 7.6 12.9 14.1 14.3 11.7 12.9 13.9 6.8 8.5 0.4 0.5

Knee flexors, peak, bar/harness 0.1 0.2 0.3 0.6 0.9 0.9 1.1 4.7 6.6 2.7 3.8

Ankle, Plantar flexors, peak, bar/harness 6.1 9.7 10.4 13.1 7.9 8.7 9.5 5.7 6.1 7.4 8.0
NASA/TM—2015-218852 71

Discussion

Significance of Results

These models represent a significant extension of the application of the OpenSim modeling software to highintensity resistance training exercise. The high degree of external loading on the subject combined with the very large 

ranges of motion for the joints, especially the knee and hip, challenge the ability of the models to estimate the desired 

outcomes of joint torque, resultant joint force and muscle group force in a physiologically relevant manner. Our 

modifications to the Arnold lower limb model have extended its useful operating ranges for hip and knee flexion as 

seen during deep squats and single-leg squats. The models provide important information and insight about the 

exercises themselves and about the HULK exercise device as a means for performing them.

The models generally show forces and torques that scale with applied external load and reach the local maximum 

value with maximal squatting depth or maxima heel raise height.

Another interesting finding is that the peak knee and hip resultant joint loads trend lower or are statistically equal 

for deep squat vs. parallel squat (p > 0.05). This is counterintuitive, but is consistent with the position of advocates of 

the deep squat who report similar knee stresses during deep squats vs. parallel squats (Ref. 24, 25, and 26). Replicating 

this finding boosts confidence in the ability of the squat model to estimate relative differences in joint force due to an 

altered range of motion as well as in the ability of subjects to exercise safely over a wide range of motion, as long as 

proper form is strictly maintained.

Validation of Results With Previous Exercise Studies

A frequent problem encountered when comparing exercise studies is the high variability in outcomes due to 

differences in exercise form, range of motion, subjects, cadence, loading and stance. Validating our models is, 

therefore, a matter of matching trends and relative values of outcomes across studies, rather than duplicating absolute 

values of outcomes.

Squat

Our subject’s body weight translates to a 745 N load, and the applied squat loads of 125, 155 and 185 lb translate 

to applied loads of 557, 690, and 824 N, respectively, and a range spanning from 75 to 110 percent of BW.

Joint forces: The squat simulation results showed lumbar spine compressive force increasing proportionately with 

applied load during the squat exercise, which is consistent with previous exercise studies (Refs. 27 and 28).

Additionally, when differences in squat depth and cadence are accounted for, our peak lumbar resultant joint forces are 

consistent with these studies, both at body weight (2,600 vs. 2,100 N (Ref. 27)) and over our applied load range (5,000

to 10,400 N vs. 5,400 to 9,500 N (Ref. 28)). Our peak patellofemoral forces at BW of 5,600 N are consistent with a 

slower cadence BW squat to 90° (3,750 N) performed with an instrumented artificial knee joint (Ref. 29).

Patellofemoral force increases with applied load, but is actually slightly lower for deep squats (8,700 to 10,300 N-m) 

than for parallel (9,600 to 10,600 N-m), a counterintuitive finding that is supported by previous studies (Refs. 24, 25, 

and 26), as well as the trends in the measured external loading data (Appendix C, which are slightly higher (0 to 

5 percent) for the parallel case than the deep case at similar loads (p > 0.05). 

Joint Torques: The models are also consistent with other studies that show hip and knee torque increasing with hip 

flexion and external load (Refs. 30, 31, and 32) and greater hip torque being generated for deep squats than for parallel 

squats (Refs. 31 and 32). However, peak hip torques for deep and parallel squats (130 to 190 N-m) are lower than 

similar studies using barbell squats heavier loads (200 to 300 N-m (Refs. 31 and 32)), even after accounting for 

loading differences, while peak knee torques in our models (300 to 450 N-m) exceed the knee torques (100 to 200 Nm) of those same studies. This finding warrants further investigation to determine if this is caused by the loading 

profile of the HULK device, the technique of the subject or an inconsistency between the model and the subject’s true 
NASA/TM—2015-218852 72

anatomy and physiology. As with results reported elsewhere, knee torque does increase with knee flexion and load

(Refs. 33 and 34), and greater knee torque is generated for deep squats than for parallel squats (Ref. 31).

Muscle forces: Despite our study’s lack of EMG data, which can resolve the contributions of individual muscles 

within groups, the models can provide useful comparisons of relative muscle group force contributions versus both 

load and squatting depth with results in the literature. As reported elsewhere (Refs. 31, 35, 14, and 36) hip extensor 

and adductor activity increases with external load and squat depth in our models. Quadriceps, hamstrings and 

gastrocnemius activity all increase as knee flexion increases during the execution of the squat, as previously reported

in (Ref. 3). There were no significant differences (p > 0.05) found in quadriceps activity between deep and parallel 

squats, as in (Refs. 31, 32, and 36), but the parallel squat trended higher than the deep squat for all loading cases, 

consistent with the findings noted above. Hamstring activity remained constant both with load, as in (Ref. 14), and 

with squat depth, as in (Refs. 31 and 36), however our model underreports estimated hamstring activity relative to 

studies, e.g., (Refs. 33 and 37). We attribute this to a lack of EMG data to properly guide activation levels, thereby 

transferring too much of the hip extension loading to the gluteal muscles, whose activity tends to be overestimated by 

our model. Ankle plantar flexor activity in our squat models increases with external load and increases slightly with 

squat depth, as in (Ref. 35). That study reports 70 percent of maximal voluntary contraction (MVC) for 90 percent of 

maximal squat loads in the plantar flexors, and our findings are generally consistent with that estimate. 

Single-Leg Squat

The single-leg squat loads of 60 and 100 lb translate to applied loads of 267 and 445 N, respectively, and a range 

spanning from 35 to 60 percent BW.

Published results for the single-leg squat exercise are far less abundant than those for the squat. Therefore, not all 

outcomes of this study can be validated by the literature. The peak joint torques for hip (54 N-m), knee (126 N-m) and 

ankle (113 N-m) during a light load SLS in our study compared favorably to a previous study of body weight squats 

with the unloaded leg forward (Ref. 38). This same study found that patellar tendon force (roughly 70 percent of the 

sum of all knee extensor forces (Ref. 39)) peaks around 8.2 times body weight for 120° of knee flexion, and our model 

is consistent with this finding (8.4 times body weight) once differences in methods between the two studies are 

accounted for. This is less true for patellofemoral joint force where our results underreport the cited study (8.4 vs. 

10.2 times body weight). We attribute these differences to the variation in cadence and exercise technique between the 

two studies, and the different methods employed to estimate patellofemoral joint force.

Heel Raise

The heel raise loads of 150 and 225 lb translate to applied loads of 668 and 1,000 N, respectively, and a range 

spanning from 90 to 135 percent BW.

Published results for the heel raise exercise are also far less abundant than those for the squat. Therefore, not all 

outcomes of this study can be validated by the literature. Furthermore, not all studies use blocks or other means that 

allow the full range of motion, as were used in this study. During unilateral body weight heel raises, with a 10° tilted 

wedge and a cadence of 0.65 sec, the average peak ankle joint torque was 2.6 N-m/kg (Ref. 7), which compares 

favorably with this present study when cadence and bilateral stance are accounted for. During double-leg heel raise 

exercises, performed without blocks, the average peak ankle plantar-flexion net joint moment was 0.85 N-m/kg for 

body weight exercises, 0.9 N-m/kg with an additional 5 percent of body weight and 0.95 N-m/kg with an additional 

10 percent of body weight (Ref. 8). After noting differences in the test setup and cadence, our model roughly correlates 

with this trending.

Achilles tendon forces, which approximate the aggregate sum of the plantar flexor muscles, approach 5,000 N 

during unilateral BW heel raises (Ref. 40), and our model agrees with these findings for bilateral heel raises with an 

applied load close to the subject’s body weight.
NASA/TM—2015-218852 73

Harness Loading Versus Bar Loading

The outcomes for the simulated harness loading versus bar loading are generally identical (well within 1 percent) 

for all joints and muscle groups, with the exception of the lumbar joint, the six torso muscles, the residuals and the 

reserve actuators, for which some statistically significant differences do occur. For this reason, only the lumbar joint is 

reported separately for the bar case vs. the harness case in Table 7. This indicates that the model has reached a solution 

whereby the lumbar joint muscles, the residuals and the reserves experience the bulk of the changes in response due to 

the changes in loading configuration.

Given this, the result of the bar loading vs. harness loading analysis was a decrease in the resultant lumbar joint 

force in all exercises with the harness. A peak resultant lumbar joint force of approximately 10 kN was predicted for 

the deep and parallel squats performed at high external load when using the bar loading configuration. The predicted 

peak resultant lumbar joint force for deep and parallel squats performed at high external load when using the harness 

configuration was about 40 percent lower (~6 kN). This reduction is due to the redistribution of load to 70 percent

applied to the upper back and 30 percent applied to the lower back. The resultant lumbar joint forces in the single-leg

squat and the heel raise exercises were only approximately 4,000 N for each exercise during bar loading, and harness 

loading reduced this by between one-third and one-half. If maintenance of bone mineral density at the lumbar spine is 

dependent on stimulating forces greater than those provided by the single-leg squat and heel raise exercises, then,

based on these preliminary findings, the harness loading configuration may be less effective in maintaining lumbar 

spine bone mineral density than the bar loading. 

Similarly, a decrease in the peak lumbar extension joint moment was predicted in harness loading (~200 N-m) vs. 

bar loading (~350 N-m) for the high-intensity squat exercises. The peak lumbar extension joint moment was predicted 

to be lower in the single-leg squat exercise performed with medium external weight and higher when high external 

weight was used. However, the peak lumbar extension joint moments only ranged from 100 to 135 N-m in the singleleg exercise. For the heel raise, the lumbar joint moments were not statistically different between medium and high 

loads, and the harness reduced these moments by one-half.

In these analyses, the joint moments, resultant joint forces and muscle forces all remained nearly constant for all 

joints and muscles below the lumbar spine for all of the exercises. More investigation is needed to determine whether 

this is physiologically relevant or simply an artifact of our assumption of identical kinematics between the two cases.

Laboratory testing of both cases with full motion capture and load data capture is needed to determine the veracity of 

our assumption. Testing is currently scheduled for spring 2015, after which another assessment of bar loading vs. 

harness loading will be made.

Comparison with ARED Squat Integrated Muscle Model (ASM-im)

In 2012 the Digital Astronaut Project released reports similar to that of the current study for the squat (Ref. 41) and 

deadlift (Ref. 42) exercises on the Advanced Resistive Exercise Device (ARED). Our previous ARED studies used 

LifeMOD (Life Modeler) as the modeling platform, and it is informative to compare the results of both studies. 

The following differences should be noted when interpreting the comparative results:

1. The HULK and ARED devices are based on inherently different mechanisms and have different loading 

profiles vs. bar displacement for the same nominal load (Ref. 43). As such, one could expect different results 

for the same exercise on different devices.

2. The LifeMOD and OpenSim modeling software packages employ different methods for solving for the 

outcomes of this study. LifeMOD results were produced from forward dynamic analyses with an active 

controller minimizing the error relative to the known kinematics (Ref. 44), whereas OpenSim results were 

produced from inverse dynamics and static optimization without an active controller. Although they are 

estimating the same outcomes, the two packages are solving different mathematical problems.
NASA/TM—2015-218852 74

3. The LifeMOD and OpenSim models differ in an anatomical sense. Each model uses 45 muscle actuators in the 

lower limb, however, differences exist in which small muscles are included. The LifeMOD model does not 

include wrapping surfaces at the knees as the OpenSim model does. Additionally, the LifeMOD model 

includes a 4-joint spine, but no torso muscles, only torque actuators; whereas, the OpenSim model includes a 

single a spine joint (lumbar) with 6 torso muscles representing the spinal erectors, abdominals, and obliques.

4. The kinematics differ somewhat between the exercises performed in the two models, particularly squat depth.

Motion capture techniques employed a different marker set in the ARED study (Ref. 41) vs. the current study 

(Appendix D), with the former study having known deficiencies that were later corrected in this study. 

With these differences in mind, Table 8 compares some of the key outcomes between the ARED and HULK squat 

models.

It is interesting to note the similarity in hip forces and the dissimilarity in the lower limb forces. The HULK model 

joint and muscle group forces for the knee and ankle are between 3x-4x those of the ARED model. Further 

investigation is required to determine the underlying causes of these discrepancies, e.g., device differences, motion 

capture differences or modeling approach differences.

Also noteworthy is the higher degree of ankle dorsiflexion (>50 percent) and hip flexion (10 percent) required to 

squat to parallel on the HULK device vs. the ARED. ARED loads the subject with a bar connected via pivot joint to a 

lever arm, whereas HULK uses tethering cables. This may result in a different foot placement to maintain comfort on 

the HULK, which may explain the differences in kinematics.

Comparison of Squat Versus Single-Leg Squat

For single-leg squat, our model estimates aggregate peak knee extensor forces (5,200 N) that are just over one-half 

of the hip extensors (9,800 N) for the single-leg squat with a 100 lb (45 kg) external load. Similar proportions are 

exhibited by the joint moments in the knee (143 N-m) and hip (244 N-m) joints. Ground reaction force data from these 

trials suggests that nearly three-quarters (73 percent) of the load is borne by the target right leg.

TABLE 8.—COMPARISON OF PEAK VALUES OF KEY OUTCOMES (JOINT ANGLES, JOINT TORQUES,

RESULTANT JOINT FORCES AND MUSCLE GROUP FORCES) BETWEEN THE

ARED SQUAT MODEL, ASM-im, AND THE HULK SQUAT MODEL

Load = 185 lb Peak

HULK ARED

Kinematic angles, ° Hip_Flexion_Angle 115 105

Knee_Flexion_Angle 124 121

Ankle_Dorsiflexion_Angle 36 23

Joint torques, N‐m Hip_Extension_Torque 182 230

Knee_Extension_Torque 374 100

Ankle_Joint_Torque 174 52

Resultant joint forces, KN Hip_Joint_Force 10.0 11.1

Knee_Joint_Force 10.4 4.3

Ankle_Joint_Force 11.0 4.3

Muscle tension forces, KN Hip_Extensors_Muscle_Force 11.2 5.6

Knee_Extensors_Muscle_Force 10.4 5.3

Plantar_Flexors_Muscle_Force 7.5 3.3
NASA/TM—2015-218852 75

In contrast, the traditional parallel squat model estimates that peak knee extensor forces (9,600 N) exceed hip 

extensor forces (7,300 N) with a 125 lb (57 kg) external load. A greater difference occurs in the joint moments of the 

knee (320 N-m) and hip (125 N-m). In this case, due to the subject’s right-side dominance, 51 percent of the load is 

borne by the right leg. 

These results clearly support the consistent findings in the literature asserting that single-leg and two-leg squats are 

not interchangeable exercises, even at similar intensities. This is because the single-leg version shifts the loading more 

heavily toward extending the hip, at the expense of extending the knee (Refs. 38, 39, 5, and 45). This behavior 

becomes even more pronounced with a greater degree of lumbar flexion (Ref. 45), but this factor was not investigated 

in our study. 

Verification and Validation of the Models

In accordance with the Human Research Program’s (HRP) Unique Processes, Criteria, and Guidelines 

(HRP-47069), all DAP models are vetted in accordance with NASA Standard for Models and Simulations (NASASTD-7009) (Ref. 46). This standard consists of a comprehensive set of requirements and processes for developing and 

applying models and simulations (M&S), while ensuring appropriate verification, validation and credibility of the 

M&S results. It was established as a result of the recommendations from the Columbia accident report to ensure that 

all M&S implemented by NASA that can potentially impact the crew or mission must be:

• Sufficiently vetted for the problem under consideration

• Well documented to capture the limitations and caveats

• Developed and implemented by personnel that are well qualified to address the problem under consideration

• Developed and implemented using processes that are appropriate for the problem under consideration

The credibility assessment for the HULK biomechanical models essentially mirrors the credibility assessment for 

the ARED Squat model with muscles (ASM-i) described previously (Ref. 41). The credibility score is a 2.3, as 

summarized in Table 9.

TABLE 9.—CREDIBILITY ASSESSMENT FOR HULK BIOMECHANICAL

MODELS USING METHODS OUTLINED IN NASA-STD-2009

CAS score Overall

weight

Overall

credibility

Thresholds MAX

Verification 2 0.4

2.3

3 4

Validation 2 0.5 2 4

Input pedigree 3 0.3 3 4

Results uncertainty 1 0.1 2 4

Results robustness 1 0.1 2 4

Use history 1 0.15 2 4

M&S management 2 0.1 3 4

People qualifications 3 0.6 3 4
NASA/TM—2015-218852 76

Interpretation and Limitations

Readers should interpret results from these models with the following points in mind:

• One cannot verify the true accuracy of the outcomes estimated by the models in an absolute sense. The 

quantities cannot be measured directly, and validation with similar results in the literature is confounded by 

differences in subjects, exercise techniques, cadence, form and posture among studies. Estimating relative 

differences due to perturbations is likely to be more useful.

• The models are currently only valid for 1g estimations. Estimating results for microgravity requires knowledge 

of the kinematic changes that occur in space. Motion capture as done for this study is generally infeasible in 

space. While limited estimation of joint angles is possible from in-flight videos, a predictive model with an 

adaptive controller is required to make a more thorough and accurate estimation. The Digital Astronaut Project 

is currently developing such a controller, outside the scope of this study. Given accurate kinematics and 

measured loading profiles, these models will be useful for estimating the resulting kinetic outcomes.

• The muscle model used in these analyses was not a full representation of the Millard (Ref. 23) and Hill 

actuator model (Ref. 47) (i.e., they did not include active and passive force-length characteristics, forcevelocity characteristics and activation dynamics). Instead, the muscle model was a simple force actuator with a 

given maximum isometric force and the rest of the muscle parameters turned off. This was done to simplify 

the static optimization methods. 

• Prediction of the muscle activations and force levels during the exercises is a difficult problem because the 

static optimization used to calculate these values is an under-constrained problem. Comparison of the muscle 

activations to EMG data is a method that can be used for validation, but was not performed in these analyses 

due to the lack of EMG data. Alternatively, EMG data can be used to help constrain the optimization problem 

during analysis. Future studies will include the collection of EMG data and their appropriate use in the analysis 

procedure will be determined.

• Residual and reserve actuator contributions remain somewhat high for both the squat and single-leg squat, both 

of which exceed OpenSim best practice guidelines for residual and reserve values (Ref. 22). While these 

guidelines were developed mostly with gait applications in mind, the value of some residual actuators remain 

significant compared with the contributions of the muscles in the model. Further refinement of these models 

could reduce the residuals to more acceptable values.

• The subjectively-determined estimation for harness loading (70-30 percent split) and the lack of control for 

cadence are potentially confounding variables.

Future Work

This work is preliminary, pending the results of the aforementioned harness testing and the subsequent modeling

efforts. Many further refinements of the models are possible. The current work extends the current range of application 

of OpenSim models to high-intensity resistance training. Our work clearly indicates a need to extend the valid joint 

angle operating ranges for the Arnold lower body model. Specifically, the anatomical paths and wrapping surfaces of 

muscles in the model need to be further refined to allow knee angles up to 150° of flexion and hip angles up to 130° of 

flexion while minimizing any sign changes of muscle moment arms over the entire operating range of joint angles (i.e., 

agonist muscles should remain as agonists throughout the movements and vice versa for the antagonist muscles).

With regard to harness loading, the current work assumes that the kinematics do not change significantly between

loading schemes. Yet, harness loading will likely alter the amounts of lumbar, hip and knee flexion, when compared 

with bar loading. The extent to which this occurs must be tested in 1g, and possibly in 0g as well if the opportunity 
NASA/TM—2015-218852 77

presents itself. Kinematic changes will ultimately result in changes to the kinetic outcomes as well. Our work will 

quantify these changes.

This study currently does not include electromyography (EMG) data. Because static optimization is a severely 

under-constrained problem with an infinite solution set, EMG data can be used to increase the optimization constraints, 

guiding the muscle activation predictions to a more physiologically relevant solution. Alternatively, the EMG data can 

be used to validate the optimization results. Improving the optimization methodologies used and adding the capability 

to validate the muscle activation predictions will result in two benefits: 1) the ability to estimate individual muscle 

forces rather than aggregate muscle forces by group, and 2) the ability to estimate resultant joint forces more 

accurately since the loads on specific bones depend on specific individual muscles and their relative spatial 

relationships. Future work will include acquiring EMG data for all trials and re-incorporating the more complex 

Millard muscle model into the analyses.

The DAP project has acquired a full set of motion capture and loading data for the deadlift exercise on HULK.

Modeling efforts for the deadlift exercise will begin in Spring 2015 with the addition of a research fellow to the 

modeling team.

Finally, the data acquired to date have not fully explored all of the configurations in which subjects could perform 

the exercise. A rigorous set of testing combined with a thorough model sensitivity analysis would provide insight into 

the effects of cadence, stance, foot placement and the various parameters inherent in the models, e.g., muscle 

properties and analysis settings. The project will also explore these activities more fully in the coming year.

Conclusions

We have developed OpenSim models for three high-intensity lower-body resistance exercises (SQ, SLS and HR)

on the HULK device in 1g based on motion capture and measured external loading data. These models operate over a 

fuller range of motion and loading intensities than previously reported similar models. The models describe the 

subject’s kinematics during the movement, and they estimate average and peak values for joint torques, resultant joint

forces, and muscle forces by muscle group (not by individual muscle). We have identified the useful applications for 

these models, validated their outcomes against similar exercise studies previously reported, and identified their

inherent limitations.

NASA/TM—2015-218852 79

Appendix A.—Acronyms

AEC Advanced Exercise Concepts

ARED Advanced Resistive Exercise Device

BW body weight

COA center of application (of applied external force)

COP center of pressure (of GRF)

DAP Digital Astronaut Project

EMG electromyography

ExPC Exercise Physiology and Countermeasures

GRC NASA Glenn Research Center

GRF ground reaction force

H heavy

HHC Human Health and Countermeasures (Element)

HR heel raise

HRP Human Research Program

HULK Hybrid Ultimate Lifting Kit

ID inverse dynamics

IK inverse kinematics

ISS International Space Station

JSC NASA Johnson Space Center

L light

M medium

mocap motion capture

MPCV Multi-purpose Crew Vehicle

M&S models and simulations

NASA National Aeronautics and Space Administration

PF plantar flexor or patellofemoral

x RM x repetition maximum

RMS root mean square

RMSD root mean square difference

SE standard error

SLS single-leg squat

SO static optimization

SQ squat

SQD (deep) squat

SQP (parallel) squat

TF tibiofemoral

NASA/TM—2015-218852 81

Appendix B.—Model Parameters and Configurations

OpenSim Muscle Parameters

Muscle name OpenSim

muscle name

Muscle

type

Max isometric

force,

N

Optimal fiber

length,

m

Tendon slack

length,

m

Pennation

angle,

rad

Right Left Right Left Right Left Right Left

Adductor Brevis addbrev Millard 455 456 0.115 0.115 0.033 0.033 0.106 0.106

Adductor Longus addlong Millard 600 600 0.085 0.085 0.115 0.115 0.124 0.124

Adductor Magnus Distal addmagDist Millard 486 486 0.187 0.187 0.095 0.095 0.241 0.241

Adductor Magnus Ischium addmagIsch Schutte 486 486 0.165 0.165 0.229 0.228 0.208 0.208

Adductor Magnus Middle addmagMid Millard 486 486 0.140 0.140 0.052 0.052 0.257 0.257

Adductor Magnus Proximal addmagProx Millard 486 486 0.105 0.105 0.047 0.047 0.387 0.387

Biceps Femoris Long Head bflh Millard 1058 1058 0.090 0.090 0.341 0.340 0.202 0.202

Biceps Femoris Short Head bfsh Millard 474 474 0.117 0.117 0.105 0.105 0.215 0.215

Extensor Digitorum Longus edl Millard 518 518 0.077 0.077 0.408 0.410 0.188 0.188

Extensor Hallucis Longus ehl Millard 248 248 0.082 0.083 0.365 0.367 0.164 0.164

Flexor Digitorum Longus fdl Millard 412 412 0.049 0.049 0.412 0.413 0.237 0.237

Flexor Hallucis Longus fhl Millard 655 655 0.057 0.057 0.385 0.386 0.295 0.295

Gastrocnemius Lateral gaslat Millard 910 910 0.060 0.060 0.444 0.447 0.209 0.209

Gastrocnemius Medial gasmed Millard 1962 1962 0.100 0.100 0.435 0.435 0.173 0.173

Gemellus gem Millard 164 164 0.027 0.027 0.044 0.044 0.000 0.000

Gluteus Maximus 1 glmax1 Millard 819 819 0.170 0.170 0.051 0.051 0.382 0.382

Gluteus Maximus 2 glmax2 Millard 1171 1171 0.180 0.180 0.075 0.075 0.382 0.382

Gluteus Maximus 3 glmax3 Millard 789 789 0.200 0.200 0.074 0.074 0.382 0.382

Gluteus Medius 1 glmed1 Millard 1322 1322 0.085 0.085 0.057 0.057 0.358 0.358

Gluteus Medius 2 glmed2 Millard 925 925 0.090 0.090 0.069 0.069 0.358 0.358

Gluteus Medius 3 glmed3 Millard 1053 1053 0.130 0.130 0.060 0.049 0.358 0.358

Gluteus Minimus 1 glmin1 Millard 270 270 0.090 0.090 0.016 0.017 0.175 0.175

Gluteus Minimus 2 glmin2 Millard 285 285 0.070 0.070 0.027 0.027 0.000 0.000

Gluteus Minimus 3 glmin3 Millard 323 323 0.060 0.060 0.054 0.054 0.017 0.017

Gracilis grac Millard 206 206 0.244 0.244 0.178 0.178 0.143 0.143

Iliacus iliacus Millard 933 933 0.109 0.109 0.080 0.080 0.250 0.250

Patellar Ligament patlig Schutte 2 2 0.057 0.058 0.006 0.006 0.000 0.000

Pectineus pect Millard 266 266 0.105 0.105 0.001 0.011 0.000 0.000

Peroneus Brevis perbrev Millard 459 459 0.052 0.052 0.169 0.170 0.201 0.201

Peroneus Longus perlong Millard 980 980 0.057 0.057 0.374 0.376 0.246 0.246

Peroneus Tertius pertert Millard 135 135 0.090 0.090 0.113 0.114 0.227 0.227

Piriformis piri Millard 444 444 0.050 0.050 0.124 0.124 0.175 0.175

Psoas psoas Millard 720 720 0.119 0.119 0.099 0.099 0.187 0.187

Quadratus Femoris quadfem Millard 381 381 0.061 0.061 0.027 0.027 0.000 0.000

Rectus Femoris recfem Millard 1273 1273 0.060 0.060 0.345 0.345 0.243 0.243

Sartorius sart Millard 170 170 0.400 0.400 0.117 0.117 0.023 0.023

Semimembranosus semimem Millard 1744 1744 0.060 0.060 0.360 0.330 0.264 0.264
NASA/TM—2015-218852 82

OpenSim Muscle Parameters

Muscle name OpenSim

muscle name

Muscle

type

Max isometric

force,

N

Optimal fiber

length,

m

Tendon slack

length,

m

Pennation

angle,

rad

Right Left Right Left Right Left Right Left

Semitendinosus semiten Millard 453 453 0.207 0.207 0.262 0.263 0.225 0.225

Soleus soleus Millard 5379 5379 0.060 0.060 0.375 0.375 0.494 0.494

Tensor Fasciae Latae tfl Millard 233 233 0.092 0.092 0.453 0.469 0.052 0.052

Tibialis Anterior tibant Millard 1011 1011 0.078 0.079 0.275 0.277 0.168 0.168

Tibialis Posterior tibpost Millard 1358 1358 0.043 0.044 0.323 0.325 0.239 0.239

Vastus Intermedius vasint Millard 1536 1536 0.140 0.140 0.112 0.111 0.079 0.079

Vastus Lateralis vaslat Millard 3383 3383 0.140 0.140 0.137 0.137 0.321 0.321

Vastus Medialis vasmed Millard 2166 2166 0.140 0.140 0.118 0.118 0.517 0.517

Erector Spinae ercspn aThelen 2500 2500 0.141 0.141 0.035 0.035 0.000 0.000

Abdominal Internal Oblique intobl aThelen 900 900 0.116 0.116 0.116 0.116 0.000 0.000

Abdominal External Oblique extobl aThelen 900 900 0.138 0.138 0.161 0.161 0.000 0.000 aReference 48
NASA/TM—2015-218852 83

Appendix C.—Measured External Force Data

C.1 Squat Exercise

(a)

Figure 31.—External force data as measured during deep and parallel squats. Average and peak (a) ground reaction forces in the 

normal (Y) direction, (b) resultant ground reaction forces in the shear direction, and (c) cable tension forces on the bar reported by 

the HULK device.
NASA/TM—2015-218852 84

(a)

Figure 31.—Continued. External force data as measured during deep and parallel squats. Average and peak (a) ground reaction 

forces in the normal (Y) direction, (b) resultant ground reaction forces in the shear direction, and (c) cable tension forces on the 

bar reported by the HULK device.
NASA/TM—2015-218852 85

(b)

Figure 31.—Continued. External force data as measured during deep and parallel squats. Average and peak (a) ground reaction 

forces in the normal (Y) direction, (b) resultant ground reaction forces in the shear direction, and (c) cable tension forces on the 

bar reported by the HULK device.
NASA/TM—2015-218852 86

(b)

Figure 31.—Continued. External force data as measured during deep and parallel squats. Average and peak (a) ground reaction 

forces in the normal (Y) direction, (b) resultant ground reaction forces in the shear direction, and (c) cable tension forces on the 

bar reported by the HULK device.
NASA/TM—2015-218852 87

(c)

Figure 31.—Continued. External force data as measured during deep and parallel squats. Average and peak (a) ground reaction 

forces in the normal (Y) direction, (b) resultant ground reaction forces in the shear direction, and (c) cable tension forces on the 

bar reported by the HULK device.
NASA/TM—2015-218852 88

(c)

Figure 31.—Concluded. External force data as measured during deep and parallel squats. Average and peak (a) ground reaction 

forces in the normal (Y) direction, (b) resultant ground reaction forces in the shear direction, and (c) cable tension forces on the 

bar reported by the HULK device.
NASA/TM—2015-218852 89

C.2 Single-Leg Squat Exercise

Figure 32.—External force data as measured during single-leg squats. Average and peak ground reaction forces in the normal (Y) 

and shear directions for the SLS and average and peak cable tension forces on the bar reported by the HULK device.
NASA/TM—2015-218852 90

C.3 Heel Raise Exercise

Figure 33.—External force data as measured during heel raises. Average and peak ground reaction forces in the normal (Y) and 

shear directions for the SLS and average and peak cable tension forces on the bar reported by the HULK device.
NASA/TM—2015-218852 91

Appendix D.—Marker Set Used For Data Collection

Figure 34.—Modified plug-in gait marker set used for motion capture data collection

NASA/TM—2015-218852 93

Appendix E.—Procedure For Producing External Force Files

From Device Load and Ground Reaction Force Data

How to make External loads files (*.MOT) by combining GRF and device load data

1. Determine the precise start and stop times and duration for each rep in the set from the TRC files. Plot the 

LBAR_Y and RBAR_Y marker positions and find the peaks and valleys of the bar displacement for each 

exercise to determine the start of each rep in the lift from the kinematic sense. You must do this for each load 

case individually! Record the data in a note or spreadsheet we can share.

2. Open the corresponding device load file in Matlab and select the Time, RForce, LForce and BarDisp columns 

and make them Matlab variables. Convert RForce and LForce from pounds to Newtons by multiplying them 

by 4.44822.

RForce = RForce .* 4.44822; LForce = LForce .* 4.44822;

3. Define a new Time_Resamp variable in Matlab that spans from the start time of the MOT file for GRF’s 

(usually 0.000) and spans to the end time of the GRF MOT file in 0.004 sec increments, e.g.,

Time = 0.000 : 0.004 : 10.912;

4. Use the interp1 function to resample the device load and bar displacement data onto the new Time variable, 

e.g.,

RForce_Resamp = interp1(Time, RForce, TimeSamp);

LForce_Resamp = interp1(Time, LForce, TimeSamp);

BarDisp_Resamp = interp1(Time, BarDisp, TimeSamp);

Now find the corresponding start and end of each rep in the BarDisp_Resamp data. Determine the relative time 

offset in order to sync the bar displacement with the marker kinematics in step 1. Eliminate the time difference 

from the beginning of each Force variable so that the force data is synchronized with the kinematics data. Also 

trim the back end of the force variables so that the data length exactly matches that of the kinematics. Redefine 

the time variables so that they also exactly match the kinematics.

5. Look for the Bluetooth dropouts in the data. If data for one foot exists but not the other, copy the good data 

onto the other and assume they are equal over that time interval. At the end of this, you will have the force 

magnitudes for Left and Right on the bar, but you still need to define the center of application (COA) and the 

directional components of force.

6. Now open the corresponding *.TRC marker data file and select the X, Y and Z positions of RBAR, RPLT, 

LBAR, and LPLT as Matlab variables over the same time interval as you used for the GRF MOT files. That is 

12 variables in total. Remember TRC files are in mm not meters, and so are the COP locations in the MOT file 

to be created.
NASA/TM—2015-218852 94

7. Compute the COA positions of RBAR and LBAR. First convert the marker positions (in mm) to meters by 

dividing by 1000. Add the strap offset (0.03 m) to each X marker position to get the COA’s and use the same 

Y and Z. Remember to subtract 0.03 m from LBAR_X, not add it.

RBar_Force_px = RBAR_X/1000 + 0.03;

RBar_Force_py = RBAR_Y/1000;

RBar_Force_pz = RBAR_Z/1000;

LBar_Force_px = LBAR_X/1000 - 0.03;

LBar_Force_py = LBAR_Y/1000;

LBar_Force_pz = LBAR_Z/1000;

8. Now compute the direction cosines for each axis based on the vectors defined by RBAR-RPLT and LBARLPLT.

RVec = [RPLT_X - RBAR_X RPLT_Y - RBAR_Y RPLT_Z - RBAR_Z];

LVec = [LPLT_X - LBAR_X LPLT_Y - LBAR_Y LPLT_Z - LBAR_Z];

MagRVec = sqrt(RVec(:, 1).^2 + RVec(:, 2).^2 + RVec(:, 3).^2);

MagLVec = sqrt(LVec(:, 1).^2 + LVec(:, 2).^2 + LVec(:, 3).^2);

DirCos_RVec = [RVec(:, 1) ./ MagRVec, RVec(:, 2) ./ MagRVec, RVec(:, 3) ./ MagRVec];

DirCos_LVec = [LVec(:, 1) ./ MagLVec, LVec(:, 2) ./ MagLVec, LVec(:, 3) ./ MagLVec];

9. Now, compute the directional components of the Force on the bar.

RBar_Force_vx = RForce_Resamp .* DirCos_RVec(:,1);

RBar_Force_vy = RForce_Resamp .* DirCos_RVec(:,2);

RBar_Force_vz = RForce_Resamp .* DirCos_RVec(:,3);

LBar_Force_vx = LForce_Resamp .* DirCos_LVec(:,1);

LBar_Force_vy = LForce_Resamp .* DirCos_LVec(:,2);

LBar_Force_vz = LForce_Resamp .* DirCos_LVec(:,3);

10. And finally, append 12 new columns into the *.MOT file for GRF and save it under a new name with the 

suffix “ExtFor” (e.g., HULK_S10_HR_M150_ExtFor.MOT). Remember to change the number of columns 

from 19 to 31!

RBar_Force_vx RBar_Force_vy RBar_Force_vz RBar_Force_px RBar_Force_py RBar_Force_pz 

LBar_Force_vx LBar_Force_vy LBar_Force_vz LBar_Force_px LBar_Force_py LBar_Force_pz

11. In the GRF Setup files for Inverse Dynamics, RRA and Static Optimization, you need to specify how these 

forces get applied to the model. Make sure you are using a model with the bar connected to the torso by a free 
NASA/TM—2015-218852 95

joint (6 DOF). Make sure the RBAR, RPLT, LBAR and LPLT markers are also in the model. Run IK to get 

the true position of the bar versus time. Our upper body model is low fidelity, so the bar will appear to impale 

the neck—go with it, don’t try to fix it.

12. Compute the midpoint of the bar as the midpoint of the two markers in ground coordinates:

[x, y,z] = [(LBAR_X-RBAR_X)/2, (LBAR_Y-RBAR_Y)/2, (LBAR_Z-RBAR_Z)/2]

Place a new marker here in the OpenSim GUI referenced to ground. Now change the body reference of the 

new marker to Bar and save those coordinates. Then change the body reference of the marker to torso and save 

those coordinates.

13. Add a point constraint to the model between the bar (child) and torso (parent). Use the point coordinates saved 

above to define the location of the point constraint in each body. Rerun IK.

14. When you go to run ID and you make your GRF setup file, you need to specify the new forces on the ID setup 

dialog, External loads tab. Click on the edit icon to the far right. Add the new forces as show in the series of 

dialogs below, but use the filenames that are appropriate to your specific exercise.
NASA/TM—2015-218852 96

Remember! When you save from the ID External Loads tab, you save the XML file for External Loads setup.

When you save from the Main Settings tab, you save the XML file for ID Setup.
NASA/TM—2015-218852 97

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