Why are the fastest runners of intermediate size? Contrasting scaling of mechanical demands and muscle supply of work and power

The fastest land animals are of intermediate size. Cheetah, antelope, greyhounds and racehorses have been measured running much faster than reported for elephants or elephant shrews. Can this be attributed to scaling of physical demands and explicit physiological constraints to supply? Here, we describe the scaling of mechanical work demand each stride, and the mechanical power demand each stance. Unlike muscle stress, strain and strain rate, these mechanical demands cannot be circumvented by changing the muscle gearing with minor adaptations in bone geometry or trivial adjustments to limb posture. Constraints to the capacity of muscle to supply work and power impose fundamental limitations to maximum speed. Given an upper limit to muscle work capacity each contraction, maximum speeds in big animals are constrained by the mechanical work demand each step. With an upper limit to instantaneous muscle power production, maximal speeds in small animals are limited by the high power demands during brief stance periods. The high maximum speed of the cheetah may therefore be attributed as much to its size as to its other anatomical and physiological adaptations.

The Possibility of Zero Limb-Work Gaits in Sprawled and Parasagittal Quadrupeds: Insights from Linkages of the Industrial Revolution

Animal legs are diverse, complex, and perform many roles. One defining requirement of legs is to facilitate terrestrial travel with some degree of economy. This could, theoretically, be achieved without loss of mechanical energy if the body could take a continuous horizontal path supported by vertical forces only-effectively a wheel-like translation, and a condition closely approximated by walking tortoises. If this is a potential strategy for zero mechanical work cost among quadrupeds, how might the structure, posture, and diversity of both sprawled and parasagittal legs be interpreted? In order to approach this question, various linkages described during the industrial revolution are considered. Watt's linkage provides an analogue for sprawled vertebrates that uses diagonal limb support and shows how vertical-axis joints could enable approximately straight-line horizontal translation while demanding minimal mechanical power. An additional vertical-axis joint per leg results in the wall-mounted pull-out monitor arm and would enable translation with zero mechanical work due to weight support, without tipping or toppling. This is consistent with force profiles observed in tortoises. The Peaucellier linkage demonstrates that parasagittal limbs with lateral-axis joints could also achieve the zero-work strategy. Suitably tuned four-bar linkages indicate this is feasibly approximated for flexed, biologically realistic limbs. Where "walking" gaits typically show out of phase fluctuation in center of mass kinetic and gravitational potential energy, and running, hopping or trotting gaits are characterized by in-phase energy fluctuations, the zero limb-work strategy approximated by tortoises would show zero fluctuations in kinetic or potential energy. This highlights that some gaits, perhaps particularly those of animals with sprawled or crouched limbs, do not fit current kinetic gait definitions; an additional gait paradigm, the "zero limb-work strategy" is proposed.

The scaling or ontogeny of human gait kinetics and walk-run transition: The implications of work vs. peak power minimization

A simple model is developed to find vertical force profiles and stance durations that minimize either limb mechanical work or peak power demands during bipedal locomotion. The model predicts that work minimization is achieved with a symmetrical vertical force profile, consistent with previous models and observations of adult humans, and data for 487 participants (predominantly 11–18 years old) required to walk at a range of speeds at a Science Fair. Work minimization also predicts the discrete walk-run transition, familiar for adult humans. In contrast, modeled peak limb mechanical power demands are minimized with an early skew in vertical ground reaction force that increases with speed, and stance durations that decrease steadily with speed across the work minimizing walk-run transition speed. The peak power minimization model therefore predicts a continuous walk-run gait transition that is quantitatively consistent with measurements of younger children (1.1–4.7 years) required to locomote at a range of speeds but free to select their own gaits.

The human foot and heel-sole-toe walking strategy: a mechanism enabling an inverted pendular gait with low isometric muscle force?

Mechanically, the most economical gait for slow bipedal locomotion requires walking as an ‘inverted pendulum’, with: I, an impulsive, energy-dissipating leg compression at the beginning of stance; II, a stiff-limbed vault; and III, an impulsive, powering push-off at the end of stance. The characteristic ‘M’-shaped vertical ground reaction forces of walking in humans reflect this impulse–vault–impulse strategy. Humans achieve this gait by dissipating energy during the heel-to-sole transition in early stance, approximately stiff-limbed, flat-footed vaulting over midstance and ankle plantarflexion (powering the toes down) in late stance. Here, we show that the ‘M’-shaped walking ground reaction force profile does not require the plantigrade human foot or heel–sole–toe stance; it is maintained in tip–toe and high-heel walking as well as in ostriches. However, the unusual, stiff, human foot structure—with ground-contacting heel behind ankle and toes in front—enables both mechanically economical inverted pendular walking and physiologically economical muscle loading, by producing extreme changes in mechanical advantage between muscles and ground reaction forces. With a human foot, and heel–sole–toe strategy during stance, the shin muscles that dissipate energy, or calf muscles that power the push-off, need not be loaded at all—largely avoiding the ‘cost of muscle force’—during the passive vaulting phase.

Exploring the mechanical basis for acceleration: pelvic limb locomotor function during accelerations in racing greyhounds (Canis familiaris)

Animals in their natural environments are confronted with a regular need to perform rapid accelerations (for example when escaping from predators or chasing prey). Such acceleration requires net positive mechanical work to be performed on the centre of mass by skeletal muscle. Here we determined how pelvic limb joints contribute to the mechanical work and power that are required for acceleration in galloping quadrupeds. In addition, we considered what, if any, biomechanical strategies exist to enable effective acceleration to be achieved. Simultaneous kinematic and kinetic data were collected for racing greyhounds undergoing a range of low to high accelerations. From these data, joint moments and joint powers were calculated for individual hindlimb joints. In addition, the mean effective mechanical advantage (EMA) of the limb and the ;gear ratio' of each joint throughout stance were calculated. Greatest increases in joint work and power with acceleration appeared at the hip and hock joints, particularly in the lead limb. Largest increases in absolute positive joint work occurred at the hip, consistent with the hypothesis that quadrupeds power locomotion by torque about the hip. In addition, hindlimb EMA decreased substantially with increased acceleration - a potential strategy to increase stance time and thus ground impulses for a given peak force. This mechanism may also increase the mechanical advantage for applying the horizontal forces necessary for acceleration.

Low speed maneuvering flight of the rose-breasted cockatoo (Eolophus roseicapillus). II. Inertial and aerodynamic reorientation

The reconfigurable, flapping wings of birds allow for both inertial and aerodynamic modes of reorientation. We found evidence that both these modes play important roles in the low speed turning flight of the rose-breasted cockatoo Eolophus roseicapillus. Using three-dimensional kinematics recorded from six cockatoos making a 90 degrees turn in a flight corridor, we developed predictions of inertial and aerodynamic reorientation from estimates of wing moments of inertia and flapping arcs, and a blade-element aerodynamic model. The blade-element model successfully predicted weight support (predicted was 88+/-17% of observed, N=6) and centripetal force (predicted was 79+/-29% of observed, N=6) for the maneuvering cockatoos and provided a reasonable estimate of mechanical power. The estimated torque from the model was a significant predictor of roll acceleration (r(2)=0.55, P<0.00001), but greatly overestimated roll magnitude when applied with no roll damping. Non-dimensional roll damping coefficients of approximately -1.5, 2-6 times greater than those typical of airplane flight dynamics (approximately -0.45), were required to bring our estimates of reorientation due to aerodynamic torque back into conjunction with the measured changes in orientation. Our estimates of inertial reorientation were statistically significant predictors of the measured reorientation within wingbeats (r(2) from 0.2 to 0.37, P<0.0005). Components of both our inertial reorientation and aerodynamic torque estimates correlated, significantly, with asymmetries in the activation profile of four flight muscles: the pectoralis, supracoracoideus, biceps brachii and extensor metacarpi radialis (r(2) from 0.27 to 0.45, P<0.005). Thus, avian flight maneuvers rely on production of asymmetries throughout the flight apparatus rather than in a specific set of control or turning muscles.

The mechanics of jumping versus steady hopping in yellow-footed rock wallabies

The goal of our study was to explore the mechanical power requirements associated with jumping in yellow-footed rock wallabies and to determine how these requirements are achieved relative to steady-speed hopping mechanics. Whole body power output and limb mechanics were measured in yellow-footed rock wallabies during steady-speed hopping and moving jumps up to a landing ledge 1.0 m high (approximately 3 times the animals' hip height). High-speed video recordings and ground reaction force measurements from a runway-mounted force platform were used to calculate whole body power output and to construct a limb stiffness model to determine whole limb mechanics. The combined mass of the hind limb extensor muscles was used to estimate muscle mass-specific power output. Previous work suggested that a musculoskeletal design that favors elastic energy recovery, like that found in tammar wallabies and kangaroos, may impose constraints on mechanical power generation. Yet rock wallabies regularly make large jumps while maneuvering through their environment. As jumping often requires high power, we hypothesized that yellow-footed rock wallabies would be able to generate substantial amounts of mechanical power. This was confirmed, as we found net extensor muscle power outputs averaged 155 W kg(-1) during steady hopping and 495 W kg(-1) during jumping. The highest net power measured reached nearly 640 W kg(-1). As these values exceed the maximum power-producing capability of vertebrate skeletal muscle, we suggest that back, trunk and tail musculature likely play a substantial role in contributing power during jumping. Inclusion of this musculature yields a maximum power output estimate of 452 W kg(-1) muscle. Similar to human high-jumpers, rock wallabies use a moderate approach speed and relatively shallow leg angle of attack (45-55 degrees) during jumps. Additionally, initial leg stiffness increases nearly twofold from steady hopping to jumping, facilitating the transfer of horizontal kinetic energy into vertical kinetic energy. Time of contact is maintained during jumping by a substantial extension of the leg, which keeps the foot in contact with the ground.