Northwestern University Feinberg School of Medicine

Northwestern University Prosthetics-Orthotics Center

Modeling of Able-bodied and Prosthetic Gait

Principal Investigators: Dudley S. Childress, PhD, and Steven A. Gard, PhD 

Project Director: Steven A. Gard, PhD 

Co-Investigator: Andrew H. Hansen, PhD

Student Investigator: Pinata H. Sessoms, MS

Funded by: National Institute on Disability and Rehabilitation Research (NIDRR), Department of Education, Grant # H133E030030

Status: Completed


There is a need for a firm theoretical foundation for walking in the field of rehabilitation and orthopaedics, because currently the biomechanics of gait are not sufficiently understood to allow quantification. Models and simulations of walking allow us to better understand different aspects of human movement and analyze motion in mathematical terms. Models of varying complexity can be compared to determine how each component in the model contributes to overall gait. Simulations can be run with these models, which are helpful for analyzing new design ideas (e.g., new prosthetic or orthotic components) or when data cannot be acquired experimentally. Some studies we are interested in using models and simulations include: studying the effects of changes in mass distribution in limb segments (i.e., to compare gait of able-bodied persons against those with lower limb amputations), consequences of varying shock absorption capabilities, and the effects of altering gait related parameters such as foot rocker mechanisms, step length or frequency, and kinematic parameters. The purpose of this project is to develop simple walking models for use in simulations of both able-bodied and prosthetic/orthotic gait in order to better understand the mechanics of, and the differences between, numerous gait styles.

Previous Work

There have been many different researchers that have used models to represent various forms of gait, from simple, single segment, inverted pendulum models (e.g., R. Alexander, G. Cavagna, T. McGeer, A. Kuo, J. Donelan, M. Garcia, and A. Ruina) to very complex, three-dimensional, multi-segment, multi-muscle models (e.g., S. Delp, F. Anderson, M. Pandy, L. Gilchrist, and M. Hardt). Early observations of human gait support a rocker representation of the foot [8] that was later defined by Perry [9] as made up of the rolling action of heel, ankle, and forefoot rockers. Addition of a rocker foot to an inverted pendulum model allows the leg to be effectively lengthened during walking [9] and creates more accurate equations relating step length, cadence, walking speed, and vertical excursion of the BCOM [1]. This simple model contradicts some of the original six determinants of gait theory by Saunders and Inman, showing that the vertical excursion of the BCOM is independent of pelvic obliquity [5] and stance-phase knee flexion [6] because these motions occur at a time in which they would not minimize the BCOM vertical excursion. This simple model is also able to predict certain gait parameters for constrained walking (i.e., fixed step length and cadence) which was confirmed with empirical data in our laboratory [2]. Issues with ambulation efficiency (relationships between forward kinetic and gravitational potential energy) have also been explored [7].

     footrocker_NURERC         invertedpendulum

Conceptual walking model that incorporates various aspects of the NU-RERC research (left) and the simple rocker based inverted pendulum model (right) in which we can analyze the relationship between foot rocker radius (r), step length (Sl), and vertical excursion of the body (h).


Second-generation gait models are being developed to further explore theoretical concepts of normal gait. We will incorporate and build upon the rocker based inverted pendulum models that our lab has used to study step length and vertical displacement of the body [1, 2], rocker radius and arc length for ankle-foot roll-over shapes [3]; spring stiffness, damping coefficient, and other factors relating to shock absorption during gait [4, 5, 6]; energy considerations of ambulation [1, 7]; and various leg adaptations to changing environmental conditions during gait [4]. The models will be used to increase understanding o f the scientific and engineering principles of human walking, which will aid in evaluating prosthetic and orthotic components, identifying the functional deficiencies of pathological gait, and designing new prosthetic and orthotic technology.

Second-generation gait models will include the addition of a pelvic link joining the two legs and allowance of rotations about the rocker heel and toe ("pivoting"), which will allow more events of gait to be modelled. These additions are important for modelling the double-support phase of gait (when both feet are in contact with the ground) which is the primary phase of gait where weight is shifted from one leg to the other and when the velocity of the BCOM is redirected from a downward trajectory back upwards for the next step [11]. Being able to model double-support phase may help us to have a better understanding of the energy required for walking and how this differs between able-bodied persons and persons with amputation. The ability to model pivoting will also allow us to determine it's effects on gait which may relate to "drop-off" seen in persons with amputation [12] and also pivoting seen in persons walking fast or taking long step lengths. Initial research in our laboratory indicates that "drop-off" can lead to higher impact forces on the leading limb. Additional components to the model may allow us to better explain certain aspects of walking, and may be added in the future, though more additions also increase the complexity of the model.

These models should provide us with a better understanding of foot-rocker mechanisms, shock absorption of the locomotor mechanism, energy considerations during ambulation, leg adaptations to changing environmental conditions during gait, and the importance of simple measures of walking.


[1] Gard and Childress (2001). What determines the vertical displacement of the body during normal walking? JPO: Journal of Prosthetics and Orthotics 13(3): 64-67.

[2] Miff et al. (2001). Vertical excursion of the trunk during gait is determined by step length. Gait and Posture 13(3): 258-259.

[3] Hansen et al. (2000). Prosthetic foot roll-over shapes with implications for alignment of trans-tibial prostheses. Prosthetics and Orthotics International 24(3): 205-215.

[4] Gard (1995). An investigation of foot clearance issues in normal and above-knee amputee gait. Biomedical Engineering. Evanston, Northwestern University.

[5] Childress and Gard (1997). Investigation of vertical motion of the human body during normal walking. Gait & Posture, 5(2): 161.

[6] Gard and Childress (1999). The influence of stance-phase knee flexion on the vertical displacement of the trunk during normal walking. Archives of Physical Medicine & Rehabilitation 80(1): 26-32.

[7] Miller (2003). Theories of human ambulation with applications to swing-through crutch gait. PhD Dissertation. Biomedical Engineering. Evanston, Northwestern University.

[8] Holmes (1863). The Human Wheel, Its Spokes and Felloes. The Atlantic Monthly, 11(67):567-580.

[9] Perry (1992). Gait Analysis: Normal and Pathological Function. Thorofare, NJ, SLACK Incorporated.

[10] Morawski and Wojcieszak (1978). "Miniwalker - a resonant model of human locomotion." In: Biomechanics VIA Int. Series on Biomechanics, Vol 2A, Proceedings of the 6th Int. Congress of Biomechanics. Edited by Asmussen, E. and Jorgensen, K. Baltimore: University Park Press, pp. 445-451.

[11] Kuo et al. (2005). Energetic consequences of walking like an inverted pendulum: step-to-step transitions. Exerc Sport Sci Rev 33(2): 88-97.

[12] Hansen et al (2004). Effects of prosthetic foot roll-over shape arc length on gait of trans-tibial prosthesis users. International Society of Prosthetics and Orthotics 11th World Congress, Wanchai, Hong Kong, Hong Kong National Society of The International Society for Prosthetics and Orthotics.