Lee, D. V.: Relating limb geometry to ground reaction force in running quadrupeds: A design for stability?

A defining characteristic of legged locomotion is forward movement of the body over the feet, which remain more-or-less fixed with respect to the ground. This mandates that, in quadrupeds, the limbs retract about their proximal joints (i.e., hip or shoulder) during the entire stance. I used a simple, planar model to investigate the mechanical consequences of this kinematic constraint. The model consisted of a rigid body and two massless limbs (a fore- and hindlimb). The proximal segments were joined to distal portions of the limbs by rotational springs and were oriented either anteriorly or posteriorly. The distal portions acted as compression springs. Two basic assumptions were made in the simulation: 1) limb excursions are symmetrical with respect to a transverse plane through the proximal joint, and 2) the limbs retract with a constant angular velocity that produces no net acceleration or deceleration during stance. Given these neutral criteria, proximal segment orientation was found to produce substantial directional biases in ground reaction force during simulated trotting. A knee-forward, elbow-back geometry emulated the hindlimb acceleration bias and forelimb deceleration bias observed in trotting quadrupeds. This limb geometry, which is common to nearly all quadrupeds, may provide intrinsic mechanical stability during running.