Compliant leg behaviour explains basic dynamics of walking and running

Abstract

The basic mechanics of human locomotion are associated with vaulting over stiff legs in walking and rebounding on compliant legs in running. However, while rebounding legs well explain the stance dynamics of running, stiff legs cannot reproduce that of walking. With a simple bipedal spring-mass model, we show that not stiff but compliant legs are essential to obtain the basic walking mechanics; incorporating the double support as an essential part of the walking motion, the model reproduces the characteristic stance dynamics that result in the observed small vertical oscillation of the body and the observed out-of-phase changes in forward kinetic and gravitational potential energies. Exploring the parameter space of this model, we further show that it not only combines the basic dynamics of walking and running in one mechanical system, but also reveals these gaits to be just two out of the many solutions to legged locomotion offered by compliant leg behaviour and accessed by energy or speed.

The three-dimensional locomotor dynamics of African (Loxodonta africana) and Asian (Elephas maximus) elephants reveal a smooth gait transition at moderate speed

“…1.3 m s K1 ; figures 7 and 10), as mechanical energy recovery reaches its maximum ( figure 13a). This coincides with the observation that elephants' metabolic cost of transport ( J kg K1 m K1 ) is minimal at their normal moving speed (Langman et al 1995), consistent with the inference that they may use a passive inverted pendulum (and perhaps some elastic; Geyer et al 2006) mechanism(s) to conserve energy at their optimal speed, like most other terrestrial animals Blickhan & Full 1993;Farley & Ko 1997;Ahn et al 2004;Rubenson et al 2004;Biewener 2006;Biknevicius & Reilly 2006). Their maximal energy recovery may appear to be lower than that of typical walking quadrupeds (approx.…”

“…vaulting or bouncing of particular limbs) rather than whole-body CM dynamics (Biewener 2006;Biknevicius & Reilly 2006). However, we caution that the kinematic (Hutchinson et al 2003(Hutchinson et al , 2006 and kinetic (this study; especially figure 13) changes as elephants increase in speed are fairly continuous, perhaps involving a more gradual and subtle gait transition that blurs the distinction between seemingly discrete gaits (also see Ruina et al 2005;Geyer et al 2006). Although this strays dangerously into semantic issues, the shift from vaulting to bouncing hindlimb mechanics we have inferred from slow to fast speeds in elephants is a major change of locomotor function that was not suspected or as thoroughly demonstrated in previous studies, and hence we view it as a distinct gait.…”

“…Hence, some energy-saving mechanism (very likely pendulum-like walking; although elastic mechanisms may contribute even in walking, e.g. Geyer et al 2006) must be utilized by elephants at their energetically optimal speed. However, as speed increases, elephants should change their locomotor pattern at least in a biomechanical sense, as inverted pendulum-like walking (i.e.…”

Biomechanics and energetics of walking on uneven terrain

“…It can thus produce both higher positive work at one joint and a greater negative work at the other, yet experience a smaller change in actual muscle work. In addition, some joint work may be performed passively through elastic energy storage and return by tendon, as has been implicated most strongly for the ankle (Sawicki et al, 2009) but also in the knee and hip (Doke and Kuo, 2007;Geyer et al, 2006). It is therefore likely that positive joint work is an overestimate of actual muscle work, which could explain the relatively high ΔEff.…”

Trajectory generation of straightened knee walking for humanoid robot iCub

“…Lately, Geyer [14] showed that the compliant rather than the stiff legs are essential to obtain the basic walking mechanics, such as ground reaction force (GRF) pattern, and introduced a spring-mass model for walking as well as running. In this paper, inspired by Geyer's study of the compliant legs, we incorporate the virtual spring-damper model into the conventional cart-table model to obtain a more straightened knee walking which is more energy efficient and more comparable to humans.…”