Mathematical Model of Human Walking: A Theoretical Study Based on Anthropometric Data

Background. Walking is a fundamental human activity, vital for daily living, social connection, employment, etc. Methods. In the current study, we present a mathematical model of it, based on the planar double pendulum system influenced by gravity. For parameters of the pendulum, i.e., the characteristic of the limbs (thigh + shank), we use realistic mass–inertial parameters. The model incorporates anthropometric and inertial data specific to the average Bulgarian, Russian, German, and American male, including segment masses, centres of mass, as well as densities of the segments taken from experimental studies. Results. We derive the corresponding nonlinear differential equations governing the model. We solve them analytically, when possible, and, in the general case, numerically. For moderate initial angles (from the frontal plane) and angular velocities of the thigh and shank, the pendulum exhibits motion closely resembling natural human gait. The results for all nationalities considered are very close to each other. For comparatively slow walking speeds, the model provides realistic results. Conclusions. Our approach highlights how a relatively simple biomechanical model can capture essential features of human locomotion and provides a foundation for further refinement and comparison with more complex gait modelling techniques. Such modifications are outlined.