Interaction of leg stiffness and surface stiffness during human hopping

Abstract

When mammals run, the overall musculoskeletal system behaves as a single linear "leg spring". We used force platform and kinematic measurements to determine whether leg spring stiffness (k(leg)) is adjusted to accommodate changes in surface stiffness (ksurf) when humans hoop in place, a good experimental model for examining adjustments to k(leg) in bouncing gaits. We found that k(leg) was greatly increased to accommodate surfaces of lower stiffnesses. The series combination of k(leg) and ksurf [total stiffness (ktot)] was independent of ksurf at a given hopping frequency. For example, when humans hopped at a frequency of 2 Hz, they tripled their k(leg) on the least stiff surface (ksurf = 26.1 kN/m; k(leg) = 53.3 kN/m) compared with the most stiff surface (ksurf = 35,000 kN/m; k(leg) = 17.8 kN/m). Values for ktot were not significantly different on the least stiff surface (16.7 kN/m) and the most stiff surface (17.8 kN/m). Because of the k(leg) adjustment, many aspects of the hopping mechanics (e.g., ground-contact time and center of mass vertical displacement) remained remarkably similar despite a > 1,000-fold change in ksurf. This study provides insight into how k(leg) adjustments can allow similar locomotion mechanics on the variety of terrains encountered by runners in the natural world.

Running in the real world: adjusting leg stiffness for different surfaces

“…The magnitude of the increase in leg sti¡ness di¡ered among the subjects because leg sti¡ness and surface sti¡nesses were di¡erent for each subject. The relative magnitude of the leg sti¡ness adjustment necessary to maintain a constant vertical sti¡-ness depends on the ratio of surface sti¡ness to leg sti¡ness (Ferris & Farley 1997). When this ratio is lower, leg sti¡-ness is adjusted to a greater extent.…”

“…For a runner with a leg sti¡ness of 18 kN m 71 , a track sti¡ness of 195 kN m 71 , and a shoe sti¡ness of 200 kN m 71 (Alexander & Bennett 1989), leg sti¡ness would have to be increased by 22% to maintain a constant vertical sti¡-ness. The 18 kN m 71 re£ects the highest published leg sti¡ness value for a total of seven runners (He et al 1991;Farley & Gonzalez 1996), but it is likely that larger (Farley et al 1993) or stronger runners have even higher leg sti¡nesses and thus, greater adjustments (Ferris & Farley 1997).…”

“…However, recent studies have revealed that humans are capable of adjusting leg sti¡ness during bouncing gaits. Leg sti¡ness is adjusted to achieve di¡erent stride frequencies at the same speed (Farley et al 1991;Farley & Gonzalez 1996) or to accommodate di¡erences in surface sti¡ness during hopping in place at a designated frequency (Ferris & Farley 1997). Based on the ¢ndings from these studies, we hypothesized that runners would adjust leg sti¡ness to accommodate di¡erent surface sti¡-nesses, allowing them to run in a similar manner on all surfaces.…”

Long-term quadriceps femoris functional deficits following intramedullary nailing of isolated tibial fractures

“…Progressively increased weight bearing, impact force loading, and pace or cadence should be applied to functional tasks performed on surfaces of varying stiffness or friction [6], on stairs, and on uneven surfaces. Appropriate neuromuscular responses to sudden perturbations during these tasks is also essential to ensure adequate fall prevention capability.…”

An Investigation Into the Recovery Process of a Maximum Stretch-Shortening Cycle Fatigue Protocol on Drop and Rebound Jumps

“…A spring-mass model was used to analyze the control of vertical leg-spring stiffness, which has been defined as the ratio of the peak force in the spring, to the displacement of the spring at the instant that the leg spring is maximally compressed. Previous studies have shown that the peak GRF and the peak leg-spring displacement both occur simultaneously in the middle of the ground contact phase (17,21). Leg-spring stiffness measures were calculated by dividing the peak force by the displacement of the chair from initial contact with the force plate to the lowest point of the center of mass during recovery from each DJ.…”