8. Bouncing Gaits: Running, Trotting and Hopping

This chapter describes the mechanism of running, hopping and trotting. In these gaits, opposite to walking, kinetic energy of forward motion and gravitational potential energies of the center of mass of the body oscillate in phase during the step. The step period is divided into ‘effective’ contact time, t _ce, and aerial time, t _ae, corresponding to a vertical force exerted on the ground greater respectively lower than body weight. At low running speeds and in trotting t _ce = t _ae, the rebound is on-off-ground symmetric, and the step frequency equals the resonant frequency of the bouncing system. At high running speeds and in hopping t _ce < t _ae, the rebound is on-off-ground asymmetric, and the step frequency is lower than the resonant frequency of the bouncing system. Furthermore, in all bouncing gaits (from turkeys to humans) the duration of the brake following impact on the ground is shorter than the duration of the subsequent push, i.e., t _brake < t _push, which is expression of a landing-takeoff asymmetry: hard landing-soft takeoff. The landing-takeoff asymmetry implies that the average force exerted during the brake, when the muscles are stretched, is greater than that exerted during the push when the muscles shorten. This means that very different machines (lever systems) comply with the basic characteristics of the motor (muscle), unchanged from frog to humans, to resist stretching with a force greater than that exerted during shortening. When the operation of the machine is reversed, as in backward running, the resulting soft landing-hard takeoff results in a decreased efficiency.