A Model of Scale Effects in
Mammalian Quadrupedal Running.

Although the effects of body size on mammalian locomotion are well documented, the underlying mechanisms are not fully understood. The Biomechatronics group has developed a computational model of animal mechanics, control, and energetics that unifies some well-known scale effects in running quadrupeds. The model consists of dynamic, physics-based simulations of six running mammals ranging in size from a chipmunk to a horse (0.115-676 kg). The 'virtual animals' are made up of rigid segments (head, trunk, and four legs), linked by joints and similar in morphology to particular species. In the model, each stance limb acts as a spring operating within a narrow range of stiffness, forward motion is powered and controlled by active hip and shoulder torques, and metabolic cost is predicted from the time course of supporting body weight. Model parameters important for stability (joint stiffnesses, limb-retraction times, and target positions and velocities of the limbs) are selected such that (i) running kinematics (aerial height, forward speed, and body pitch) are smooth and periodic; and (ii) overall leg stiffness is in agreement with published data. Both trotting and galloping gaits are modeled, and comparisons across size are made at speeds that are physiologically similar among species. Model predictions are in agreement with data on vertical stiffness, limb angles, metabolic cost of transport, stride frequency, peak force, and duty factor. This work supports the idea that a single, integrative model can predict important features of running across size by employing simple strategies to control overall leg stiffness. More broadly, the model provides a quantitative framework for testing hypotheses that relate limb control, stability, and metabolic cost.

Publication
Herr H, Huang G, McMahon T. A Model of Scale Effects in Mammalian Quadrupedal Running. J. Exp.Biol. 2002;
205:959-67. Download PDF.