Physiological, aerodynamic and geometric constraints of flapping account for bird gaits, and bounding and flap-gliding flight strategies

Aerodynamically economical flight is steady and level. The high-amplitude flapping and bounding flight style of many small birds departs considerably from any aerodynamic or purely mechanical optimum. Further, many large birds adopt a flap-glide flight style in cruising flight which is not consistent with purely aerodynamic economy. Here, an account is made for such strategies by noting a well-described, general, physiological cost parameter of muscle: the cost of activation. Small birds, with brief downstrokes, experience disproportionately high costs due to muscle activation for power during contraction as opposed to work. Bounding flight may be an adaptation to modulate mean aerodynamic force production in response to (1) physiological pressure to extend the duration of downstroke to reduce power demands during contraction; (2) the prevention of a low-speed downstroke due to the geometric constraints of producing thrust; (3) an aerodynamic cost to flapping with very low lift coefficients. In contrast, flap-gliding birds, which tend to be larger, adopt a strategy that reduces the physiological cost of work due both to activation and contraction efficiency. Flap-gliding allows, despite constraints to modulation of aerodynamic force lever-arm, (1) adoption of moderately large wing-stroke amplitudes to achieve suitable muscle strains, thereby reducing the activation costs for work; (2) reasonably quick downstrokes, enabling muscle contraction at efficient velocities, while being (3) prevented from very slow weight-supporting upstrokes due to the cost of performing ‘negative’ muscle work

The Muscle-Mechanical Compromise Framework: Implications for the Scaling of Gait and Posture

Many aspects of animal and human gait and posture cannot be predicted from purely mechanical work minimization or entirely based on optimizing muscle efficiency. Here, the Muscle-Mechanical Compromise Framework is introduced as a conceptual paradigm for considering the interactions and compromises between these two objectives. Current assumptions in implementing the Framework are presented. Implications of the compromise are discussed and related to the scaling of running mechanics and animal posture

Work minimization accounts for footfall phasing in slow quadrupedal gaits

Quadrupeds, like most bipeds, tend to walk with an even left/right footfall timing. However, the phasing between hind and forelimbs shows considerable variation. Here, we account for this variation by modeling and explaining the influence of hind-fore limb phasing on mechanical work requirements. These mechanics account for the different strategies used by: (1) slow animals (a group including crocodile, tortoise, hippopotamus and some babies); (2) normal medium to large mammals; and (3) (with an appropriate minus sign) sloths undertaking suspended locomotion across a range of speeds. While the unusual hind-fore phasing of primates does not match global work minimizing predictions, it does approach an only slightly more costly local minimum. Phases predicted to be particularly costly have not been reported in nature

Identification of mouse gaits using a novel force-sensing exercise wheel

The gaits that animals use can provide information on neurological and musculoskeletal disorders, as well as the biomechanics of locomotion. Mice are a common research model in many fields; however, there is no consensus in the literature on how (and if) mouse gaits vary with speed. One of the challenges in studying mouse gaits is that mice tend to run intermittently on treadmills or overground; this paper attempts to overcome this issue with a novel exercise wheel that measures vertical ground reaction forces. Unlike previous instrumented wheels, this wheel is able to measure forces continuously and can therefore record data from consecutive strides. By concatenating the maximum limb force at each time point, a force trace can be constructed to quantify and identify gaits. The wheel was three dimensionally printed, allowing the design to be shared with other researchers. The kinematic parameters measured by the wheel were evaluated using high-speed video. Gaits were classified using a metric called “3S” (stride signal symmetry), which quantifies the half wave symmetry of the force trace peaks. Although mice are capable of using both symmetric and asymmetric gaits throughout their speed range, the continuum of gaits can be divided into regions based on the frequency of symmetric and asymmetric gaits; these divisions are further supported by the fact that mice run less frequently at speeds near the boundaries between regions. The boundary speeds correspond to gait transition speeds predicted by the hypothesis that mice move in a dynamically similar fashion to other legged animals

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

Vaulting mechanics successfully predict decrease in walk-run transition speed with incline

There is an ongoing debate about the reasons underlying gait transition in terrestrial locomotion. In bipedal locomotion, the ‘compass gait’, a reductionist model of inverted pendulum walking, predicts the boundaries of speed and step length within which walking is feasible. The stance of the compass gait is energetically optimal—at walking speeds—owing to the absence of leg compression/extension; completely stiff limbs perform no work during the vaulting phase. Here, we extend theoretical compass gait vaulting to include inclines, and find good agreement with previous observations of changes in walk–run transition speed (approx. 1% per 1% incline). We measured step length and frequency for humans walking either on the level or up a 9.8 per cent incline and report preferred walk–run, walk–compliant-walk and maximum walk–run transition speeds. While the measured ‘preferred’ walk–run transition speed lies consistently below the predicted maximum walking speeds, and ‘actual’ maximum walking speeds are clearly above the predicted values, the onset of compliant walking in level as well as incline walking occurs close to the predicted values. These findings support the view that normal human walking is constrained by the physics of vaulting, but preferred absolute walk–run transition speeds may be influenced by additional factors

Minimalist analogue robot discovers animal-like walking gaits

Robots based on simplified or abstracted biomechanical concepts can be a useful tool for investigating how and why animals move the way they do. In this paper we present an extremely simple quadruped robot, which is able to walk with no form of software or controller. Instead, individual leg movements are triggered directly by switches on each leg which detect leg loading and unloading. As the robot progresses, pitching and rolling movements of its body result in a gait emerging with a consistent leg movement order, despite variations in stride and stance time. This gait has similarities to the gaits used by walking primates and grazing livestock, and is close to the gait which was recently theorised to derive from animal body geometry. As well as presenting the design and construction of the robot, we present experimental measurements of the robot's gait kinematics and ground reaction forces determined using high speed video and a pressure mat, and compare these to gait parameters of animals taken from literature. Our results support the theory that body geometry is a key determinant of animal gait at low speeds, and also demonstrate that steady state locomotion can be achieved with little to no active control

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 grazing gait, and implications of toppling table geometry for primate footfall sequences

Many medium and large herbivores locomote forwards very slowly and intermittently when grazing. While the footfall order during grazing is the same as for walking, the relative fore–hind timing—phasing—is quite different. Extended periods of static stability are clearly required during grazing; however, stability requirements are insufficient to account for the timing. Aspects of relatively rapid rolling and pitching—toppling due to the resistance of the back to bending and twisting—can be included in a simplifying geometric model to explain the observation that, in grazing livestock, a step forward with a forefoot is consistently and immediately followed by a step forward from the hind; but not vice versa. The same principles and geometry, but applied to the footfall pattern of walking primates, show that toppling would occur at a different point in the gait cycle. This provides a potential account for the distinctive diagonal-sequence footfall pattern of primates, as it prevents the instant of toppling from being at forefoot placement. Careful and controlled hand positioning would thus be facilitated, presumably beneficial to walking on top of branches, despite a slight energetic cost compared with the usual lateral sequence pattern of horses

Matching times of leading and following suggest cooperation through direct reciprocity during V-formation flight in ibis

One conspicuous feature of several larger bird species is their annual migration in V-shaped or echelon formation. When birds are flying in these formations, energy savings can be achieved by using the aerodynamic up-wash produced by the preceding bird. As the leading bird in a formation cannot profit from this up-wash, a social dilemma arises around the question of who is going to fly in front? To investigate how this dilemma is solved, we studied the flight behavior of a flock of juvenile Northern bald ibis (Geronticus eremita) during a human-guided autumn migration. We could show that the amount of time a bird is leading a formation is strongly correlated with the time it can itself profit from flying in the wake of another bird. On the dyadic level, birds match the time they spend in the wake of each other by frequent pairwise switches of the leading position. Taken together, these results suggest that bald ibis cooperate by directly taking turns in leading a formation. On the proximate level, we propose that it is mainly the high number of iterations and the immediacy of reciprocation opportunities that favor direct reciprocation. Finally, we found evidence that the animals' propensity to reciprocate in leading has a substantial influence on the size and cohesion of the flight formations