Support polygons and symmetrical gaits in mammals

The symmetrical gaits of quadrupedal mammals are often described in terms of two variables: duty factor (S = the stanceperiod of one foot, as a percentage of the gait cycle) and diagonality(D = the percentage of the cycle period by which the left hind footfall precedes the left fore footfall). We show that support polygons are optimized during walking (i.e. the percentage of the locomotor cycle spent standing on only two feet is minimized) for: (1) the diagonal-sequence, diagonal-couplets walks characteristic of primates (50 < D < 75)when D = [hindlimb S]; (2) lateral-sequence, lateral-couplets walks (0 < D < 25)when D = [hindlimb S]- 50;(3) lateral-sequence, diagonal-couplets walks (25 < D < 50)when D = 100-[forelimb S]. To determine whether animal behaviour is optimal in this sense, we examined 346 symmetrical gait cycles in 45 mammal species. Ourempirical data show that mammalian locomotor behaviour approximates the theoretical optima. We suggest that diagonal-sequence walking may be adopted by primates as a means of ensuring that agrasping hindfoot is placed in a protracted position on a tested support at the moment when the contralateral forefoot strikes down on an untested support.