The effect of asymmetrical body-mass distribution on the stability and dynamics of quadruped bounding

The effect of asymmetrical body-mass distribution on the stability and dynamics of two-degree-of-freedom quadruped bounding in place is investigated in this study. An analytical stability criterion for bounding of quadrupeds with asymmetrical mass distribution is developed. Bounding is found to be passively stable in the Hamiltonian sense when the dimensionless pitch moment of inertia of the body is less than 1-beta², where beta is a dimensionless measure of the asymmetry. The criterion is derived under the assumptions of infinite leg stiffness and no energy loss. With energy dissipation modeled as linear damping in the legs, simulation results show that the criterion is independent of the value of leg stiffness and a conservative estimate of the critical inertia value. Body symmetry appears to be more favorable to stable bounding than asymmetry, but only slightly so in practicality. The results show that asymmetry offers some advantages when the dynamic characteristics of bounding are compared for symmetrical and asymmetrical models. Lower stride frequency, larger vertical displacement, and smaller duty factor are obtained with this more animal-like model