Patterns of mechanical energy change in tetrapod gait: pendula, springs and work

Abstract

Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.

The three-dimensional locomotor dynamics of African (Loxodonta africana) and Asian (Elephas maximus) elephants reveal a smooth gait transition at moderate speed

“…1.3 m s K1 ; figures 7 and 10), as mechanical energy recovery reaches its maximum ( figure 13a). This coincides with the observation that elephants' metabolic cost of transport ( J kg K1 m K1 ) is minimal at their normal moving speed (Langman et al 1995), consistent with the inference that they may use a passive inverted pendulum (and perhaps some elastic; Geyer et al 2006) mechanism(s) to conserve energy at their optimal speed, like most other terrestrial animals Blickhan & Full 1993;Farley & Ko 1997;Ahn et al 2004;Rubenson et al 2004;Biewener 2006;Biknevicius & Reilly 2006). Their maximal energy recovery may appear to be lower than that of typical walking quadrupeds (approx.…”

“…shift from vaulting to bouncing mechanics, e.g. Biewener 2006;Biknevicius & Reilly 2006) definitions normally lead to the same conclusion. However, when applied to the fast moving elephants, they are partly contradictory (Hutchinson et al 2006).…”

“…The second gait of elephants could be called an amble, intermediate gait or run (Muybridge 1899;Gambaryan 1974;Alexander et al 1979;Ahn et al 2004;Schmitt et al 2006), and raises the question of whether gaits may be better defined by individual limb dynamics (e.g. vaulting or bouncing of particular limbs) rather than whole-body CM dynamics (Biewener 2006;Biknevicius & Reilly 2006). However, we caution that the kinematic (Hutchinson et al 2003(Hutchinson et al , 2006 and kinetic (this study; especially figure 13) changes as elephants increase in speed are fairly continuous, perhaps involving a more gradual and subtle gait transition that blurs the distinction between seemingly discrete gaits (also see Ruina et al 2005;Geyer et al 2006).…”

Seroprevalence of Infectious Bursal Disease in Backyard Chickens of Six Districts of North Shewa Zones of Oromia and Amhara Regions, Ethiopia

“…In this way, limb and trunk spring compliance enables the storage and return of elastic energy to reduce the work of muscle contraction. Indeed, it is now generally accepted that the mass-spring elastic energy savings achieved during trotting by most quadrupeds are an evolutionary adaptation designed to minimize muscle work during steady level movement [17]. The T-score data from this study supports the mass-spring elastic energy model, in that a reduction in firing frequency with a change of pace from walk to trotting would serve to reduce and minimize muscle work during the steady level movement of trotting.…”

“…It has long been known that quadrupedal species convert potential energy and kinetic energy into elastic energy in spring elements of the limbs and trunk to regain some expended energy later during limb support [16,17]. In this way, limb and trunk spring compliance enables the storage and return of elastic energy to reduce the work of muscle contraction.…”