The bounce of the body in hopping, running and trotting: different machines with the same motor

Abstract

The bouncing mechanism of human running is characterized by a shorter duration of the brake after ‘landing’ compared with a longer duration of the push before ‘takeoff’. This landing–takeoff asymmetry has been thought to be a consequence of the force–velocity relation of the muscle, resulting in a greater force exerted during stretching after landing and a lower force developed during shortening before takeoff. However, the asymmetric lever system of the human foot during stance may also be the cause. Here, we measure the landing–takeoff asymmetry in bouncing steps of running, hopping and trotting animals using diverse lever systems. We find that the duration of the push exceeds that of the brake in all the animals, indicating that the different lever systems comply with the basic property of muscle to resist stretching with a force greater than that developed during shortening. In addition, results show both the landing–takeoff asymmetry and the mass-specific vertical stiffness to be greater in small animals than in large animals. We suggest that the landing–takeoff asymmetry is an index of a lack of elasticity, which increases with increasing the role of muscle relative to that of tendon within muscle–tendon units.

Running backwards: soft landing–hard takeoff, a less efficient rebound

“…(a) Landing-takeoff asymmetry The landing -takeoff asymmetry described in running humans [2,10] and in running, hopping and trotting of other vertebrates [3] is characterized by: (i) a blunt attainment to the E cm (t) plateau at the end of the push and a sharp drop off the E cm (t) plateau at the start of the brake (black curve in figure 1); (ii) a peak The vertical bars indicate the standard deviation of the mean, the numbers near the symbols indicate the number of items in the mean and the asterisks indicate a significant difference between t push and t brake (p , 0.05). Lines (KALEIDAGRAPH 4.03 weighted fits) are just a guide for the eye and do not describe the underlying physical mechanism.…”

Symmetry and Asymmetry in Bouncing Gaits

“…From top to bottom: the mass of the animal, the positive work duration, t push , the negative work duration t brake , the landing-takeoff asymmetry, t push /t brake (mean of the ratios made at each speed), the mass specific vertical stiffness, k/M b , the resonant frequency of the bouncing system, f s =(1/2 ) k/M b , the step frequency, f step , the maximal upward acceleration, A v,mx, up , and the efficiency of doing external work, W ext /W metab . Note that: i) t push is greater than t brake (p < 0.05 in all animals except rams where p = 0.13), ii) t push /t brake is greater in small animals than in large animals (p < 0.05 in all animals except rams vs. monkey where p = 0.09), and iii) k/M b is greater in small animals than in large animals (p < 0.05) [89].…”

“…These animals use a machine (lever system) to promote locomotion, which differs from that of humans. The landingtakeoff asymmetry, i.e., the ratio t push /t brake was therefore measured in hopping, running and trotting animals to determine if it persists in spite of the different machines involved in these different types of locomotion [89]. In the elastic rebound of a spring-mass system, the mechanical energy of the center of mass at the equilibrium position during the descent equals the mechanical energy of the center of mass at the equilibrium position during the lift [32].…”

An analysis of the rebound of the body in backward human running

“…As during level running at a constant speed the momentum lost equals the momentum gained, the mean force exerted during the brake must be greater than that developed during the push, i.e. t brake <t push and F brake >F push ('hard landing and soft takeoff') (Cavagna et al, 2008b;Cavagna and Legramandi, 2009).…”