Distorting limb design for dynamically similar locomotion

Sharon R. Bullimore , Jeremy F. Burn

Abstract

Terrestrial mammals of different sizes tend to move in a dynamically similar manner when travelling at speeds corresponding to equal values of the Froude number. This means that certain dimensionless locomotor parameters, including peak vertical ground reaction force relative to body weight, stride length relative to leg length and duty factor, are independent of animal size. The Froude number is consequently used to define equivalent speeds for mammals of different sizes. However, most musculoskeletal–tissue properties, including tendon elastic modulus, do not scale in a dynamically similar manner. Therefore, mammals could not be completely dynamically similar, even if perfectly geometrically similar. We argue that, for mammals to move in a dynamically similar manner, they must exhibit systematic ‘distortions’ of limb structure with size that compensate for the size independence of the tendon elastic modulus. An implication of this is that comparing mammals at equal Froude numbers cannot remove all size–dependent effects. We show that the previously published allometry of limb moment arms is sufficient to compensate for size–independent tendon properties. This suggests that it is an important factor in allowing mammals of different sizes to move in a dynamically similar manner.