A mathematical model for the dynamics of human locomotion

Abstract

The problem of developing a model to describe and study human gait was undertaken using Lagrangian mechanics. The approach is that of the initial value problem, i.e. starting with the initial conditions which are the limb angles and velocities, and the system inputs which are the applied joint moments, the system response is found. Seven segments are used to model the human body with complete three segment lower limbs, and the head arms and trunk included as one segment. There are six joints, two each at the hips, knees, and ankles. To show the behavior of the developed model a set of initial conditions and moment histories were obtained from measurements in a gait laboratory. Using these data with minor modifications, it is shown that the model progresses through the normal walking cycle, or with minor perturbations, atypical gait patterns can be demonstrated. It is hoped that this model will provide further insight into human gait. For example, alterations of the time histories of the joint moments can be used to predict how certain muscle groups affect gait. Thus the teaching of the complexities of gait will be facilitated. Ultimately, predictions concerning the results of therapy and surgery might be made using this model as a diagnostic tool. The emphasis in this paper is on the development of the mathematical model and not on numerical results.