Connecting the legs with a spring improves human running economy

Abstract

Human running is inefficient. For every 10 calories burned, less than 1 is needed to maintain a constant forward velocity - the remaining energy is, in a sense, wasted. The majority of this wasted energy is expended to support the bodyweight and redirect the center of mass during the stance phase of gait. An order of magnitude less energy is expended to brake and accelerate the swinging leg. Accordingly, most devices designed to increase running efficiency have targeted the costlier stance phase of gait. An alternative approach is seen in nature: spring-like tissues in some animals and humans are believed to assist leg swing. While it has been assumed that such a spring simply offloads the muscles that swing the legs, thus saving energy, this mechanism has not been experimentally investigated. Here, we show that a spring, or 'exotendon', connecting the legs of a human reduces the energy required for running by 6.4±2.8%, and does so through a complex mechanism that produces savings beyond those associated with leg swing. The exotendon applies assistive forces to the swinging legs, increasing the energy optimal stride frequency. Runners then adopt this frequency, taking faster and shorter strides, and reduce the joint mechanical work to redirect their center of mass. Our study shows how a simple spring improves running economy through a complex interaction between the changing dynamics of the body and the adaptive strategies of the runner, highlighting the importance of considering each when designing systems that couple human and machine.

Keywords: Assistive device; Biomechanics; Energetic cost; Gait; Metabolic cost; Stride frequency.

Conflict of interest statement

Competing interestsThe authors declare no competing or financial interests.

© 2019. Published by The Company of Biologists Ltd.

Figures

Fig. 1.

Energetics and mechanics in running animals. (A) Cost of transport (COT) as a function of body mass (Full, 1989; Minetti et al., 2013; Schmidt-Nielsen, 1972) shows that running (gray circles) is less efficient than swimming (dark blue squares) and flying (light blue triangles). (B) Only a small fraction of the energy expended in running does useful work on the environment to move against air resistance (Davies, 1980; Pugh, 1970); the remainder is expended primarily to accelerate the center of mass, both vertically and fore–aft, during stance. Much less is used to swing the legs (Arellano and Kram, 2014; Marsh et al., 2004; Modica and Kram, 2005). (C) Elastic tissues are hypothesized to reduce the energy required to swing the mass (m) of the limbs. (D) A pendular model of limb oscillation showing that a parallel spring (elastic tissue) can store energy during braking and return energy during acceleration, reducing required muscle moments.

Fig. 2.

Exotendon hypothesized mechanism of savings. (A) Runners choose an energetically optimal stride frequency (dark red circle), which results from a combination of processes that require more energy with increasing stride frequency, such as leg swing (dark red thin line), and those that require less energy with increasing stride frequency, such as the work performed to redirect the center of mass (COM) during stance (black thin line). We hypothesize that the exotendon shifts the leg swing curve rightward (light red thin line), increasing the optimal stride frequency, and reduces total energy expenditure (including expenditure associated with work on the center of mass). (B) Note that at this new optimal stride frequency, the costs associated with performing work on the center of mass can be reduced by an amount that is comparable to, or even exceeds, reductions associated with swinging the legs.

Fig. 3.

Time-lapse photographs of a runner using the exotendon. The length of the exotendon is tuned so that the device is long enough that it does not apply forces when the feet cross each other and does not break when the feet are far apart, yet short enough that it does not become entangled when the feet pass each other. Images span one complete gait cycle.

Fig. 4.

Reduced energy expenditure during exotendon running. (A) On day 1, runners initially showed no change in energy expenditure (trial 1), yet showed reductions after running with the exotendon for 15–20 min (trial 2). Runners retained these savings across days (trial 3). After a total of 35–40 min of experience with the exotendon across both days, the greatest reductions in energy expenditure were evident (trial 4), with all runners (n=12) showing improved economy and average savings of 6.4±2.8%. Error bars represent 1 s.d. Asterisks indicate statistical significance after Holm–Šidák correction with confidence level α=0.05. (B) By the final trial, participants took shorter, faster strides with the exotendon, increasing stride frequency by an average of 8% above that measured during natural running (P=1.1×10−5, two-tailed paired t-test, n=12).

Fig. 5.

Exotendon mechanism of savings. (A) In experiments, the exotendon increased the energetically optimal stride frequency (8.1%, P=3.7×10−3, paired t-test, n=4). Shaded regions show the 95% confidence interval of curve fits. (B) Biological moments during swing were reduced, likely due to the assistance of the exotendon, and biological moments during stance were reduced, possibly due to the increased stride frequency. Note that horizontal forces applied by the exotendon to the stance foot likely do not affect the joint moments of that leg, because they are opposed by frictional forces with the ground. However, the exotendon forces applied to the swing leg may indirectly affect the joint moments of the stance leg through the hips. (C) Force–time plot of the exotendon throughout the stride for one participant (n=1). The tension in the exotendon peaked at around 30 N at the extents of the stride, and was zero whenever the feet were closer together than the slack length of the device.

Fig. 6.

Average joint-level kinetics. Comparisons of average, absolute joint moments and power across stance and swing for the participants from experiment 3 (n=4). We compared moments and power produced during natural running (dark red) with those produced during exotendon running. Average kinetics during exotendon runs were separated into the exotendon contribution (blue) and the biological contribution (light red). We report the P-values resulting from two-tailed paired t-tests comparing biological contributions to kinetics in natural and exotendon running below the axes (light red text) and comparing total kinetics in natural and exotendon runs above the bars (light blue). Asterisks indicate comparisons that were significant after Holm–Šidák correction (α=0.05). When running with the exotendon, during swing, hip, knee and ankle biological moments were reduced compared with natural running, as was knee power. During stance, hip and knee biological moments were reduced, along with knee and ankle power.