Biomechanics of quadrupedal walking: how do four-legged animals achieve inverted pendulum-like movements?

Walking involves a cyclic exchange of gravitational potential energy and kinetic energy of the center of mass. Our goal was to understand how the limbs of walking quadrupeds coordinate the vertical movements of the fore and hind quarters to produce these inverted pendulum-like movements. We collected kinematic and ground reaction force data from dogs walking over a range of speeds. We found that the fore and hind quarters of dogs behaved like two independent bipeds, each vaulting up and over its respective support limb. The center of mass moved up and down twice per stride, like a single walking biped, and up to 70% of the mechanical energy required to lift and accelerate the center of mass was recovered via the inverted pendulum mechanism. To understand how the limbs produce these center of mass movements, we created a simple model of two independent pendulums representing the movements of the fore and hind quarters. The model predicted that the fore and hind quarter movements would completely offset each other if the fore limb lagged the hind limb by 25% of the stride time and body mass was distributed equally between the fore and hind quarters. The primary reason that dogs did not walk with a flat trajectory of the center of mass was that each fore limb lagged its ipsilateral hind limb by only 15% of the stride time and thereby produced time periods when the fore and hind quarters moved up or down simultaneously. The secondary reason was that the fore limbs supported 63% of body mass. Consistent with these experimental results, the two-pendulum model predicts that the center of mass will undergo two fluctuations per stride cycle if limb phase is less than 25% and/or if the total mass is not distributed evenly between the fore or hind quarters.