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 (Pmet) decreases compared with normal hopping (NH). Furthermore, humans retain near-constant total vertical stiffness ( ktot) when hopping with such an exoskeleton. To determine how spring stiffness profile affects Pmet 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 (DGexo), where stiffness, the slope of force vs. displacement, is initially high but decreases with greater displacement, linear spring stiffness (LNexo), where stiffness is constant, or progressive spring stiffness (PGexo), where stiffness is initially low but increases with greater displacement. Compared with NH, use of the DGexo, LNexo, and PGexo numerically resulted in 13–24% lower, 4–12% lower, and 0–8% higher Pmet, respectively, at 2.4–3.0 Hz. Hopping with the DGexo reduced Pmet compared with NH at 2.4–2.6 Hz ( P ≤ 0.0457) and reduced Pmet compared with the PGexo at 2.4–2.8 Hz ( P < 0.001). ktot 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 DGexo provided the greatest elastic energy return, followed by LNexo and PGexo ( P ≤ 0.001). Future full-leg, passive-elastic exoskeleton designs for hopping, and presumably running, should use a DGexo rather than an LNexo or a PGexo 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.

Evaluating the ‘cost of generating force’ hypothesis across frequency in human running and hopping

“…On the second day, participants performed five, 5-min stationary hopping trials, on both feet. To account for the effects of frequency on metabolic energy expenditure and given the similarity of frequencies that minimize metabolic energy expenditure during hopping and running (Allen and Grabowski, 2019;Cavagna et al, 1997;Farris and Sawicki, 2012;Grabowski and Herr, 2009;Kaneko et al, 1987), we instructed participants to hop in place while matching their step frequency to the audible metronome set to 85%, 92% 100%, 108% and 115% of their PSF from day 1. The order of the hopping trials was randomized, and we did not determine preferred hopping frequency.…”

“…Though the rate of force generation and active muscle volume well-explain metabolic energy expenditure across different running and hopping velocities, it is unknown if these biomechanical variables explain changes in metabolic energy expenditure across different stride and step frequencies, where a step equals ground contact and the subsequent aerial time and two steps comprise a stride. Previous studies have shown that humans have a preferred step frequency for running and hopping that minimizes metabolic energy expenditure, and deviating from the preferred step frequency increases metabolic energy expenditure (Allen and Grabowski, 2019;Cavagna et al, 1988;Cavanagh and Williams, 1982;Farris and Sawicki, 2012;Grabowski and Herr, 2009;Hӧgberg, 1952;Raburn et al, 2011;Swinnen et al, 2021); thus there is a U-shaped relationship between metabolic energy expenditure and step frequency (Doke and Kuo, 2007;Snyder and Farley, 2011;Swinnen et al, 2021). When considering the 'cost of generating force' hypothesis, Gutmann and Bertram (Gutmann and Bertram, 2017a;Gutmann and Bertram, 2017b) suggest that the rate of force production alone (Eqn.…”

Evaluating the “cost of generating force” hypothesis across frequency in human running and hopping

“…Though the rate of force generation and active muscle volume well-explain metabolic energy expenditure across different running and hopping velocities, it is unknown if these biomechanical variables explain changes in metabolic energy expenditure across different stride and step frequencies, where a step equals ground contact and the subsequent aerial time and two steps comprise a stride. Previous studies have shown that humans have a preferred step frequency for running and hopping that minimizes metabolic energy expenditure, and deviating from the preferred step frequency increases metabolic energy expenditure (Allen and Grabowski, 2019; Cavagna et al, 1988; Cavanagh and Williams, 1982; Farris and Sawicki, 2012; Grabowski and Herr, 2009; Högberg, 1952; Raburn et al, 2011; Swinnen et al, 2021); thus there is a U-shaped relationship between metabolic energy expenditure and step frequency (Doke and Kuo, 2007; Snyder and Farley, 2011; Swinnen et al, 2021). When considering the ‘cost of generating force’ hypothesis, Gutmann and Bertram (Gutmann and Bertram, 2017a; Gutmann and Bertram, 2017b) suggest that the rate of force production alone (Eqn.…”

Characterizing the Mechanical Stiffness of Passive-Dynamic Ankle-Foot Orthosis Struts

“…The spring stiffness profile refers to the slope of the force versus displacement or moment versus angle relationship. The stiffness profile of a spring within a passive-elastic exoskeleton in parallel with the legs affects elastic energy storage and return and metabolic cost during hopping ( 16 ). Specifically, use of this passive-elastic exoskeleton that had springs with a curvilinear stiffness profile, where stiffness decreased with compression (degressive), resulted in the greatest elastic energy return and lowest metabolic cost compared to springs with a linear stiffness profile and with a curvilinear stiffness profile where stiffness increased with compression.…”

“…Specifically, use of this passive-elastic exoskeleton that had springs with a curvilinear stiffness profile, where stiffness decreased with compression (degressive), resulted in the greatest elastic energy return and lowest metabolic cost compared to springs with a linear stiffness profile and with a curvilinear stiffness profile where stiffness increased with compression. Moreover, use of the exoskeleton with degressive stiffness springs reduced metabolic cost by 13–24% compared to hopping without an exoskeleton over a range of frequencies ( 16 ). Thus, use of a PD-AFO with a degressive strut stiffness profile, rather than a linear stiffness profile, may allow the user to run with a lower metabolic cost, which could ultimately improve their performance ( 17 ).…”