Abstract

Here, we present a simple stiff-limbed passive model of quadrupedal walking, compare mechanics predicted from the model with those observed from forceplate measurements of walking dogs and consider the implications of deviation from model predictions, especially with reference to collision mechanics. The model is based on the geometry of a 4-bar linkage consisting of a stiff hindleg, back, foreleg and the ground between the hind and front feet. It uses empirical morphological and kinematic inputs to determine the fluctuations in potential and kinetic energy, vertical and horizontal forces and energy losses associated with inelastic collisions at each foot placement. Using forceplate measurements to calculate centre of mass motions of walking dogs, we find that (1) dogs may, but are not required to, spend periods of double support (one hind- and one forefoot) agreeing with the passive model; (2) legs are somewhat compliant, and mechanical energy fluctuates during triple support, with mechanical energy being lost directly after hindfoot placement and replaced following forefoot placement. Footfall timings and timing of mechanical energy fluctuations are consistent with strategies to reduce collisional forces, analogous to the suggested role of ankle extension as an efficient powering mechanism in human walking.

Highlights

  • Walking with relatively stiff limbs, vaulting the hips over incompliant legs, presents a strategy for limiting the cost of locomotion

  • Mechanical energy forms interchange for ‘free’ – potential energy converts to kinetic as the centre of mass (COM) falls, and returns to potential as it rises again – so walking in bipeds is often described in terms of an ‘inverted pendulum’ (e.g. Cavagna et al, 1977)

  • While fluctuations in kinetic and potential energy of the COM are largely out of phase in walking quadrupeds (Cavagna et al, 1977) including dogs (Griffin et al, 2004), the mechanics of quadrupedal walking is generally less clear: kinetic and potential energy oscillations can be broadly out of phase, the degree to which limbs can be treated as stiff, inverted pendulums is uncertain

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Summary

Introduction

Walking with relatively stiff limbs, vaulting the hips (or hips and shoulders in the case of quadrupeds) over incompliant legs, presents a strategy for limiting the cost of locomotion. With this gait, mechanical energy forms interchange for ‘free’ – potential energy converts to kinetic as the centre of mass (COM) falls, and returns to potential as it rises again – so walking in bipeds is often described in terms of an ‘inverted pendulum’ We discuss some of the implications of minimising or managing collisions in quadrupedal walking and their potential use in accounting for observed footfall patterns and powering strategies

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