Symmetry 2010, 2(3), 1270-1321; doi:10.3390/sym2031270
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Symmetry and Asymmetry in Bouncing Gaits

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Received: 16 December 2009; in revised form: 18 June 2010 / Accepted: 24 June 2010 / Published: 25 June 2010
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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Abstract: 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.
Keywords: locomotion; running; hopping; trotting; on-off-ground and landing-takeoff asymmetry; muscle force-velocity relation; stretch-shorten cycle; muscle-tendon units
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Cavagna, G.A. Symmetry and Asymmetry in Bouncing Gaits. Symmetry 2010, 2, 1270-1321.

AMA Style

Cavagna GA. Symmetry and Asymmetry in Bouncing Gaits. Symmetry. 2010; 2(3):1270-1321.

Chicago/Turabian Style

Cavagna, Giovanni A. 2010. "Symmetry and Asymmetry in Bouncing Gaits." Symmetry 2, no. 3: 1270-1321.


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