Hopping with degressive spring stiffness in a full-leg exoskeleton lowers metabolic cost compared with progressive spring stiffness and hopping without assistance

Abstract

When humans hop with a passive-elastic exoskeleton with springs in parallel with both legs, net metabolic power (P_met) decreases compared with normal hopping (NH). Furthermore, humans retain near-constant total vertical stiffness (k_tot) when hopping with such an exoskeleton. To determine how spring stiffness profile affects P_met and biomechanics, 10 subjects hopped on both legs normally and with three full-leg exoskeletons that each used a different spring stiffness profile at 2.4, 2.6, 2.8, and 3.0 Hz. Each subject hopped with an exoskeleton that had a degressive spring stiffness (DG_exo), where stiffness, the slope of force vs. displacement, is initially high but decreases with greater displacement, linear spring stiffness (LN_exo), where stiffness is constant, or progressive spring stiffness (PG_exo), where stiffness is initially low but increases with greater displacement. Compared with NH, use of the DG_exo, LN_exo, and PG_exo numerically resulted in 13-24% lower, 4-12% lower, and 0-8% higher P_met, respectively, at 2.4-3.0 Hz. Hopping with the DG_exo reduced P_met compared with NH at 2.4-2.6 Hz (P ≤ 0.0457) and reduced P_met compared with the PG_exo at 2.4-2.8 Hz (P < 0.001). k_tot while hopping with each exoskeleton was not different compared with NH, suggesting that humans adjust leg stiffness to maintain overall stiffness regardless of the spring stiffness profile in an exoskeleton. Furthermore, the DG_exo provided the greatest elastic energy return, followed by LN_exo and PG_exo (P ≤ 0.001). Future full-leg, passive-elastic exoskeleton designs for hopping, and presumably running, should use a DG_exo rather than an LN_exo or a PG_exo to minimize metabolic demand.NEW & NOTEWORTHY When humans hop at 2.4-3.0 Hz normally and with an exoskeleton with different spring stiffness profiles in parallel to the legs, net metabolic power is lowest when hopping with an exoskeleton with degressive spring stiffness. Total vertical stiffness is constant when using an exoskeleton with linear or nonlinear spring stiffness compared with normal hopping. In-parallel spring stiffness influences net metabolic power and biomechanics and should be considered when designing passive-elastic exoskeletons for hopping and running.

Keywords: assistive device; bouncing gaits; energetics; spring rate; spring-mass model.