A model of scale effects in mammalian quadrupedal running
2002
SUMMARY Although the effects of body size on mammalian locomotion are well
documented, the underlying mechanisms are not fully understood. Here, we
present a computational model of the 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 animals9 are
made up of rigid segments (head, trunk and four legs) linked by joints and are
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 that are 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) is 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.
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