Date of Award

Spring 1996

Document Type


Degree Name

Master of Science in Biomedical Engineering - (M.S.)


Biomedical Engineering Committee

First Advisor

H. Michael Lacker

Second Advisor

Peter Engler

Third Advisor

David S. Kristol


A mathematical model of the swing phase, toe-off and heel strike is presented in this paper and is mathematically represented as a two dimensional, simple coupled pendulum system with three degrees of freedom. Lagange equations of motion are used to solve this highly idealized system. The model consists of three segments which represent the stance leg, thigh and shank. During the swing phase it is assumed that the only external forces acting on the system are gravity and viscous dissipative terms proportional to joint angular velocities. It is assumed that muscle forces act only to establish the initial limb segment configuration and velocities at the start of the swing and toe-off.

The mechanical energy of this system is examined to determine optimum gait parameters that minimize mechanical energy losses.

Theoretical results from this model are compared to collected experimental data obtained from clinical trials, for each experimental trial the mass and centers of mass of the limb segments is altered by attaching known fixed weights to the experimental subject. The altered gait patterns that result are recorded .and compared to theoretical predictions of the model.

Numerical analysis is used to minimize the error that occurs in the model, thus verification of model and gait parameter identification is examined. Findings suggest that the model predictions agree with experimental data, however, the model is sensitive to parameter changes and finding values which minimize residual error in the model need further investigation. It is hopeful that eventually this model will be used as a clinical tool for optimizing gait mechanics and prosthetic design.