Symmetry and Asymmetry in Bouncing Gaits

Abstract

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.

Comprehensive mechanical power analysis in sprint running acceleration

“…The mono‐exponential fitting used in P horizontal (the simple method proposed by Samozino et al) does not account for the velocity oscillation that occurs at each foot contact, where the foot touches the ground in front of BCoM causing a braking/decelerating action. This occurs because, differently from moving on wheels, humans expose their BCoM to deceleration/acceleration sequences at each foot contact in their rimless‐spoked‐wheel locomotion . During running, this causes a velocity oscillation along the mean (monotonically) increasing velocity of the subject that deviates from the mono‐exponential fitting (Figure C).…”

“…This occurs because, differently from moving on wheels, humans expose their BCoM to deceleration/acceleration sequences at each foot contact in their rimless-spoked-wheel locomotion. 46 During running, this causes a velocity oscillation along the mean (monotonically) increasing velocity of the subject that deviates from the mono-exponential fitting ( Figure 6C). The difference between P f and P horizontal can thus be considered to represent the power for accelerating BCoM forward at each stance; this power difference is greater at the beginning of a sprint and becomes negligible at the end of the acceleration phase ( Figure 6C).…”

The implications of time on the ground on running economy: less is not always better

“…In addition, running biomechanics depend on the environment in which individuals run . For instance, an increase in running speed typically reduces t c and increases t a (Brughelli et al, 2011), while the braking ðt À c Þ and propulsion ðt þ c Þ times become more symmetrical ðt À c % t þ c Þ (Cavagna, 2006(Cavagna, , 2010 and align more closely with the spring-mass model as running speed increases. The storage and release of elastic energy could be enhanced at higher running speeds, with a short t c and high t a becoming more efficient (Cavagna et al, 2008a).…”

“…where i=c or a. The ratios Dz þ c /Δz c and t þ c /t c as well as Dz þ a /z a and t þ a /t a were also calculated to explore upward and downward movement symmetries (Cavagna, 2010).…”

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

“…Factors that determine the more economic choice of step frequency in forward running are: (i) tuning the step frequency to the natural frequency of the bouncing system, and (ii) choosing a step frequency that minimizes the total aerobic-limited step average power within the limits set by the anaerobic-limited push average power (Cavagna, 2010). The first strategy is usually adopted at low running speeds and abandoned for the second strategy at high running speeds by increasing the average upward acceleration above 1g during the lower part of the vertical oscillation of the centre of mass.…”