Dynamic Principles of Center of Mass in Human Walking

TL;DR

This paper analytically and numerically investigates how the timing of initial foot contact influences ground reaction forces and center of mass dynamics in human walking, revealing optimal timing conditions and a least-action principle.

Contribution

It introduces a novel analysis linking initial contact timing with physical quantities of gait and establishes a least-action principle in human walking.

Findings

Physical quantities reach extrema when initial contact occurs mid-cycle.

Dispersion analysis reveals optimal contact timing for minimal action.

The least-action principle is validated in gait dynamics.

Abstract

We present results of an analytic and numerical calculation that studies the relationship between the time of initial foot contact and the ground reaction force of human gait and explores the dynamic principle of center of mass. Assuming the ground reaction force of both feet to be the same in the same phase of a stride cycle, we establish the relationships between the time of initial foot contact and the ground reaction force, acceleration, velocity, displacement and average kinetic energy of center of mass. We employ the dispersion to analyze the effect of the time of the initial foot contact that imposes upon these physical quantities. Our study reveals that when the time of one foot's initial contact falls right in the middle of the other foot's stride cycle, these physical quantities reach extrema. An action function has been identified as the dispersion of the physical quantities and optimized analysis used to prove the least-action principle in gait. In addition to being very significant to the research domains such as clinical diagnosis, biped robot's gait control, the exploration of this principle can simplify our understanding of the basic properties of gait.