Leg compliance is required to explain the ground reaction force patterns and speed ranges in different gaits

Abstract

Two simple models - vaulting over stiff legs and rebounding over compliant legs - are employed to describe the mechanics of legged locomotion. It is agreed that compliant legs are necessary for describing running and that legs are compliant while walking. Despite this agreement, stiff legs continue to be employed to model walking under the assumption that the compliance of the leg during walking is high enough to be considered stiff. Here we study gait choice and walk-to-run transition in a biped with compliance and show that the principles underlying gait choice and transition are completely different from stiff legs. Two findings underpin our conclusions: First, at the same speed, step length, and stance duration, multiple gaits that differ in the number of leg contraction cycles are possible. Among them, humans and other animals choose the (normal) gait with M-shaped vertical ground reaction forces (vGRF) not just because of energy considerations but also constraints from forces. Second, the transition from walking to running occurs because of three factors: vGRF minimum at mid-stance characteristic of normal walking, synchronization of horizontal and vertical motions during single support, and velocity redirection during the double support. The insight above required an analytical approximation of the double spring-loaded pendulum (DSLIP) model describing the intricate oscillatory dynamics that relate single and double support phases. Additionally, we also examined DSLIP as a quantitative model for locomotion and conclude that DSLIP speed-range is limited. However, insights gleaned from the analytical treatment of DSLIP are general and will inform the construction of more accurate models of walking.