Directionally compliant legs influence the intrinsic pitch behaviour of a trotting quadruped

Limb design is well conserved among quadrupeds, notably, the knees point forward (i.e. cranial inclination of femora) and the elbows point back (i.e. caudal inclination of humeri). This study was undertaken to examine the effects of joint orientation on individual leg forces and centre of mass dynamics. Steady-speed trotting was simulated in two quadrupedal models. Model I had the knee and elbow orientation of a quadruped and model II had a reversed leg configuration in which knees point back and elbows point forward. The model's legs showed directional compliance determined by the orientation of the knee/elbow. In both models, forward pointing knees/elbows produced a propulsive force bias, while rearward pointing knees/elbows produced a braking force bias. Hence, model I showed the same pattern of hind-leg propulsion and fore-leg braking observed in trotting animals. Simulations revealed minimal pitch oscillations during steady-speed trotting of model I, but substantially greater and more irregular pitch oscillations of model II. The reduced pitch oscillation of model I was a result of fore-leg and hind-leg forces that reduced pitching moments during early and late stance, respectively. This passive mechanism for reducing pitch oscillations was an emergent property of directionally compliant legs with the fore-hind configuration of model I. Such intrinsic stability resulting from mechanical design can simplify control tasks and lead to more robust running machines.