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.
Highlights
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
In conclusion: in the symmetric rebound, at low running speeds and in trotting, the step frequency equals the resonant frequency of the bouncing system, whereas in the on-off-ground asymmetric rebound, at high running speeds and in hopping, the step frequency is lower than the resonant frequency of the bouncing system
Summary
Locomotion results from the interaction of a motor, represented by the skeletal muscles, and a machine, the limb lever system (Figure 1). The muscles transform chemical energy of fuel ∆G into heat and positive mechanical work, Wm+, given by the product of muscular force and muscle shortening. The minimum, inevitable, work which has to be done to maintain the motion of any object in a surrounding, is given by the product of the resistance offered by the surrounding, the external frictional drag, times the distance covered during the motion. The overall efficiency of the locomotory apparatus may be expressed as the ratio between the minimum work necessary to maintain motion and the chemical energy transformed by the muscles, i.e., Overall efficiency = (Distancedrag)/∆G (1). ∆G/Distance = Drag/Overall efficiency showing that the chemical energy expenditure per unit of the distance covered during locomotion, the so called cost of transport, is greater the greater the external drag and the smaller the overall efficiency
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