M1 Walking Inverted pendulum, GRF and energy recovery

Topic

The athlete's walking gait constitutes a mode of locomotion characterized by alternating double-leg support; within this movement, the center of mass—which defines the system's mechanical model—follows an inverted-pendulum trajectory. Specifically, the center of mass rises during the mid-stance phase and descends during the transfer phase between legs—a pattern of alternating support that serves as the criterion distinguishing walking from running.

The potential and kinetic energies of the center of mass remain out of phase throughout the walking cycle, allowing for a passive energy exchange that recovers a significant proportion of the cycle's final mechanical energy; this aligns with Cavagna’s inverted-pendulum model regarding the mechanical power of the center of mass.

The optimal walking speed minimizes the athlete's metabolic cost of transport—a metric defining the system's metabolic efficiency. If the athlete walks at a speed exceeding this optimum, the inverted-pendulum mechanism can no longer sustain the gait pattern; consequently, the athlete transitions to running precisely when their Froude number crosses the critical value associated with the walk-to-run transition.

The vertical ground reaction force during walking exhibits a double-peak profile with an intermediate minimum during the mid-stance phase—a temporal pattern distinct from the passive and active impact peaks characteristic of the athlete's running gait. Consequently, this model—characterized by the passive inverted-pendulum energy exchange introduced at the outset—distinguishes the athlete's final external mechanical work (performed to move the center of mass itself) from their internal mechanical work (performed to move individual body segments relative to that center of mass); this distinction mirrors the external and internal mechanical work defined by another model in this set. The final efficiency of the inverted-pendulum mechanism is thus quantified by the same energy recovery percentage established in another model within this set regarding the elastic recovery coefficient of a degenerated tendon. The fact that this walking gait achieves an even higher final energy recovery percentage results in an even greater final efficiency for the athlete's inverted-pendulum mechanism.

ID:1457