Abstract
As part of its response to a perturbation, an animal often needs to reposition its body. Inertia acts to oppose the corrective motion, delaying the completion of the movement—we refer to this elapsed time as inertial delay. As animal size increases, muscle moment arms also increase, but muscles are proportionally weaker, and limb inertia is proportionally larger. Consequently, the scaling of inertial delays is complex. Our intent is to determine how quickly different sized animals can produce corrective movements when their muscles act at their force capacity, relative to the time within which those movements need to be performed. Here, we quantify inertial delay using two biomechanical models representing common scenarios in animal locomotion: a distributed mass pendulum approximating swing limb repositioning (swing task), and an inverted pendulum approximating whole body posture recovery (posture task). We parameterized the anatomical, muscular, and inertial properties of these models using literature scaling relationships, then determined inertial delay for each task across a large range of movement magnitudes and the full range of terrestrial mammal sizes. We found that inertial delays scaled with an average of M0.28 in the swing task and M0.35 in the posture task across movement magnitudes—larger animals require more absolute time to perform the same movement as small animals. The time available to complete a movement also increases with animal size, but less steeply. Consequently, inertial delays comprise a greater fraction of swing duration and other characteristic movement times in larger animals. We also compared inertial delays to the other component delays within the stimulus-response pathway. As movement magnitude increased, inertial delays exceeded these sensorimotor delays, and this occurred for smaller movements in larger animals. Inertial delays appear to be a challenge for motor control, particularly for bigger movements in larger animals.
Highlights
Independent of animal size, a fast response time is important to an animal’s survival
If muscles produce forces proportional to their mass, inertial delay will scale with the same exponent as characteristic movement times (Eqs 1 and 2), and relative delay would be independent of animal size
Varying the torque from half to four times its original value only increased the scaling exponent of inertial delay from M0.276 to M0.279. This indicates that our results for the scaling of inertial delay are robust to possible inaccuracies in our estimates for the torque produced by muscles that flex and extend the shoulder joint
Summary
Independent of animal size, a fast response time is important to an animal’s survival. It depends on the corrective movement task because the time to swing a limb to a new position, for example, may be different from that required to reject a push to the torso to avoid a fall This is because the two tasks involve different muscles, resulting in different force capacities, and different parts of the body, resulting in different inertial properties. Swing duration, fall duration, and pendulum period share a common scaling exponent providing us with some assurance that relative response time will not depend strongly on size as a consequence of our choice of the available movement time used to normalize the absolute response time. This system is an angular version of a sliding block model and can be analytically described as a double integrator—a simple and well-studied dynamical system [22,23]
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