Symmetry and Asymmetry in Bouncing Gaits
In running, hopping and trotting gaits, the center of mass of the body oscillates each step below and above an equilibrium position where the vertical force on the ground equals body weight. In trotting and low speed human running, the average vertical acceleration of the center of mass during the l...
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doaj-7f3d91af5ce54a929f82d317b26a00ef2020-11-24T20:46:23ZengMDPI AGSymmetry2073-89942010-06-01231270132110.3390/sym2031270Symmetry and Asymmetry in Bouncing GaitsGiovanni A. CavagnaIn running, hopping and trotting gaits, the center of mass of the body oscillates each step below and above an equilibrium position where the vertical force on the ground equals body weight. In trotting and low speed human running, the average vertical acceleration of the center of mass during the lower part of the oscillation equals that of the upper part, the duration of the lower part equals that of the upper part and the step frequency equals the resonant frequency of the bouncing system: we define this as on-offground symmetric rebound. In hopping and high speed human running, the average vertical acceleration of the center of mass during the lower part of the oscillation exceeds that of the upper part, the duration of the upper part exceeds that of the lower part and the step frequency is lower than the resonant frequency of the bouncing system: we define this as on-off-ground asymmetric rebound. Here we examine the physical and physiological constraints resulting in this on-off-ground symmetry and asymmetry of the rebound. Furthermore, the average force exerted during the brake when the body decelerates downwards and forwards is greater than that exerted during the push when the body is reaccelerated upwards and forwards. This landing-takeoff asymmetry, which would be nil in the elastic rebound of the symmetric spring-mass model for running and hopping, suggests a less efficient elastic energy storage and recovery during the bouncing step. During hopping, running and trotting the landing-takeoff asymmetry and the mass-specific vertical stiffness are smaller in larger animals than in the smaller animals suggesting a more efficient rebound in larger animals. http://www.mdpi.com/2073-8994/2/3/1270/locomotionrunninghoppingtrottingon-off-ground and landing-takeoff asymmetrymuscle force-velocity relationstretch-shorten cyclemuscle-tendon units |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Giovanni A. Cavagna |
spellingShingle |
Giovanni A. Cavagna Symmetry and Asymmetry in Bouncing Gaits Symmetry locomotion running hopping trotting on-off-ground and landing-takeoff asymmetry muscle force-velocity relation stretch-shorten cycle muscle-tendon units |
author_facet |
Giovanni A. Cavagna |
author_sort |
Giovanni A. Cavagna |
title |
Symmetry and Asymmetry in Bouncing Gaits |
title_short |
Symmetry and Asymmetry in Bouncing Gaits |
title_full |
Symmetry and Asymmetry in Bouncing Gaits |
title_fullStr |
Symmetry and Asymmetry in Bouncing Gaits |
title_full_unstemmed |
Symmetry and Asymmetry in Bouncing Gaits |
title_sort |
symmetry and asymmetry in bouncing gaits |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2010-06-01 |
description |
In running, hopping and trotting gaits, the center of mass of the body oscillates each step below and above an equilibrium position where the vertical force on the ground equals body weight. In trotting and low speed human running, the average vertical acceleration of the center of mass during the lower part of the oscillation equals that of the upper part, the duration of the lower part equals that of the upper part and the step frequency equals the resonant frequency of the bouncing system: we define this as on-offground symmetric rebound. In hopping and high speed human running, the average vertical acceleration of the center of mass during the lower part of the oscillation exceeds that of the upper part, the duration of the upper part exceeds that of the lower part and the step frequency is lower than the resonant frequency of the bouncing system: we define this as on-off-ground asymmetric rebound. Here we examine the physical and physiological constraints resulting in this on-off-ground symmetry and asymmetry of the rebound. Furthermore, the average force exerted during the brake when the body decelerates downwards and forwards is greater than that exerted during the push when the body is reaccelerated upwards and forwards. This landing-takeoff asymmetry, which would be nil in the elastic rebound of the symmetric spring-mass model for running and hopping, suggests a less efficient elastic energy storage and recovery during the bouncing step. During hopping, running and trotting the landing-takeoff asymmetry and the mass-specific vertical stiffness are smaller in larger animals than in the smaller animals suggesting a more efficient rebound in larger animals. |
topic |
locomotion running hopping trotting on-off-ground and landing-takeoff asymmetry muscle force-velocity relation stretch-shorten cycle muscle-tendon units |
url |
http://www.mdpi.com/2073-8994/2/3/1270/ |
work_keys_str_mv |
AT giovanniacavagna symmetryandasymmetryinbouncinggaits |
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