An analytical estimation of the energy cost for legged locomotion

Legged locomotion requires the determination of a number of parameters such as stride period, stride length, order of leg movements, leg trajectory, etc. How are these parameters determined? It has been reported that the locomotor patterns of many legged animals exhibit common characteristics, which suggests that there exists a basic strategy for legged locomotion. In this study we derive an equation to estimate the cost of transport for legged locomotion and examine a criterion of the minimization of the transport cost as a candidate of the strategy. The obtained optimal locomotor pattern that minimizes the cost suitably represents many characteristics of the pattern observed in legged animals. This suggests that the locomotor pattern of legged animals is well optimized with regard to the energetic cost. The result also suggests that the existence of specific gait patterns and the phase transition between them could be the result due to optimization; they are induced by the change in the distribution of ground reaction forces for each leg during locomotion.     

Pendular mechanics and the kinematics and energetics of brachiating locomotion

Because brachiating locomotion is characterized by a pattern of swinging movements, brachiation has often been analogized to pendular motion, and aspects of the mechanics of pendular systems have been used to provide insight into both energetic and structural design aspects of this locomotor mode. However, there are several limitations to this approach. First, the motions of brachiating animals only approximate pendular motion, and therefore the energetics of these two systems are only roughly comparable. Second, the kinematic similarity between brachiation and pendular motion will be maximal at only one velocity, and the correspondence will be even less at greater or lesser speeds. Third, all forms of terrestrial locomotion that involve the use of limbs incorporate elements of pendular systems, and therefore brachiation is not unusual in this respect. Finally, it has been suggested that the mechanics of pendular motion will constrain the maximum attainable body size of brachiating animals and that this mechanical situation explains the lack of brachiating primates of greater than 30-kg body size; the present analysis provides evidence that the constraints on body size are far less strict than previously indicated and that extrinsic factors such as the geometry of the forest environment are more likely to dictate maximum body size for brachiators.     

The kangaroo's tail propels and powers pentapedal locomotion

When moving slowly, kangaroos plant their tail on the ground in sequence with their front and hind legs. To determine the tail''s role in this ‘pentapedal’ gait, we measured the forces the tail exerts on the ground and calculated the mechanical power it generates. We found that the tail is responsible for as much propulsive force as the front and hind legs combined. It also generates almost exclusively positive mechanical power, performing as much mass-specific mechanical work as does a human leg during walking at the same speed. Kangaroos use their muscular tail to support, propel and power their pentapedal gait just like a leg.     

Understanding sex differences in the cost of terrestrial locomotion

Little is known regarding the physiological consequences of the behavioural and morphological differences that result from sexual selection in birds. Male and female Svalbard rock ptarmigans (Lagopus muta hyperborea) exhibit distinctive behavioural differences during the breeding season. In particular, males continuously compete for and defend territories in order to breed successfully, placing large demands on their locomotor system. Here, we demonstrate that male birds have improved locomotor performance compared with females, showing both a lower cost of locomotion (CoL) and a higher top speed. We propose that the observed sex differences in locomotor capability may be due to sexual selection for improved male performance. While the mechanisms underlying these energetic differences are unclear, future studies should be wary when pooling male and female data.     

A moving topic: control and dynamics of animal locomotion

Animal locomotion arises from complex interactions among sensory systems, processing of sensory information into patterns of motor output, the musculo-skeletal dynamics that follow motor stimulation, and the interaction of appendages and body parts with the environment. These processes conspire to produce motions and forces that permit stunning manoeuvres with important ecological and evolutionary consequences. Thus, the habitats that animals may exploit, their ability to escape predators or attack prey, their capacity to manoeuvre and turn, or the use of their available energy all depend upon the processes that determine locomotion. Here, we summarize a series of 10 papers focused on this integrative research topic.     

Trunk orientation causes asymmetries in leg function in small bird terrestrial locomotion

In contrast to the upright trunk in humans, trunk orientation in most birds is almost horizontal (pronograde). It is conceivable that the orientation of the heavy trunk strongly influences the dynamics of bipedal terrestrial locomotion. Here, we analyse for the first time the effects of a pronograde trunk orientation on leg function and stability during bipedal locomotion. For this, we first inferred the leg function and trunk control strategy applied by a generalized small bird during terrestrial locomotion by analysing synchronously recorded kinematic (three-dimensional X-ray videography) and kinetic (three-dimensional force measurement) quail locomotion data. Then, by simulating quail gaits using a simplistic bioinspired numerical model which made use of parameters obtained in in vivo experiments with real quail, we show that the observed asymmetric leg function (left-skewed ground reaction force and longer leg at touchdown than at lift-off) is necessary for pronograde steady-state locomotion. In addition, steady-state locomotion becomes stable for specific morphological parameters. For quail-like parameters, the most common stable solution is grounded running, a gait preferred by quail and most of the other small birds. We hypothesize that stability of bipedal locomotion is a functional demand that, depending on trunk orientation and centre of mass location, constrains basic hind limb morphology and function, such as leg length, leg stiffness and leg damping.     

The metabolic and mechanical costs of step time asymmetry in walking

Animals use both pendular and elastic mechanisms to minimize energy expenditure during terrestrial locomotion. Elastic gaits can be either bilaterally symmetric (e.g. run and trot) or asymmetric (e.g. skip, canter and gallop), yet only symmetric pendular gaits (e.g. walk) are observed in nature. Does minimizing metabolic and mechanical power constrain pendular gaits to temporal symmetry? We measured rates of metabolic energy expenditure and calculated mechanical power production while healthy humans walked symmetrically and asymmetrically at a range of step and stride times. We found that walking with a 42 per cent step time asymmetry required 80 per cent (2.5 W kg⁻¹) more metabolic power than preferred symmetric gait. Positive mechanical power production increased by 64 per cent (approx. 0.24 W kg⁻¹), paralleling the increases we observed in metabolic power. We found that when walking asymmetrically, subjects absorbed more power during double support than during symmetric walking and compensated by increasing power production during single support. Overall, we identify inherent metabolic and mechanical costs to gait asymmetry and find that symmetry is optimal in healthy human walking.     

Dynamic arm swinging in human walking

Humans tend to swing their arms when they walk, a curious behaviour since the arms play no obvious role in bipedal gait. It might be costly to use muscles to swing the arms, and it is unclear whether potential benefits elsewhere in the body would justify such costs. To examine these costs and benefits, we developed a passive dynamic walking model with free-swinging arms. Even with no torques driving the arms or legs, the model produced walking gaits with arm swinging similar to humans. Passive gaits with arm phasing opposite to normal were also found, but these induced a much greater reaction moment from the ground, which could require muscular effort in humans. We therefore hypothesized that the reduction of this moment may explain the physiological benefit of arm swinging. Experimental measurements of humans (n = 10) showed that normal arm swinging required minimal shoulder torque, while volitionally holding the arms still required 12 per cent more metabolic energy. Among measures of gait mechanics, vertical ground reaction moment was most affected by arm swinging and increased by 63 per cent without it. Walking with opposite-to-normal arm phasing required minimal shoulder effort but magnified the ground reaction moment, causing metabolic rate to increase by 26 per cent. Passive dynamics appear to make arm swinging easy, while indirect benefits from reduced vertical moments make it worthwhile overall.     

Discontinuous ventilation and energetics of locomotion in the desert-dwelling female mutillid wasp, Dasymutilla gloriosa

Abstract. Data on the discontinuous ventilation cycle and cost of pedestrian locomotion in female Dasymutilla gloriosa (Sauss.), a desert-dwelling mutillid, are described and compared with equivalent data from other Hymenoptera. The discontinuous ventilation cycle was intermediate between that found in xeric and mesic hymenopterans, with the open phase being about 20% of the cycle. No noticeable flutter phase was observed. Thus D. gloriosa does not attempt to reduce respiratory water loss to the same extent as found in other desert dwelling Hymenoptera. The minimum cost of transport was significantly higher than that obtained for several ant species, indicating that ants are probably more efficient runners than any other Hymenoptera.     

Orangutans use compliant branches to lower the energetic cost of locomotion

Within the forest canopy, the shortest gaps between tree crowns lie between slender terminal branches. While the compliance of these supports has previously been shown to increase the energetic cost of gap crossing in arboreal animals (e.g. Alexander 1991 Z. Morphol. Anthropol. 78, 315-320; Demes et al. 1995 Am. J. Phys. Anthropol. 96, 419-429), field observations suggest that some primates may be able to use support compliance to increase the energetic efficiency of locomotion. Here, we calculate the energetic cost of alternative methods of gap crossing in orangutans (Pongo abelii). Tree sway (in which orangutans oscillate a compliant tree trunk with increasing magnitude to bridge a gap) was found to be less than half as costly as jumping, and an order of magnitude less costly than descending the tree, walking to the vine and climbing it. Observations of wild orangutans suggest that they actually use support compliance in many aspects of their locomotor behaviour. This study seems to be the first to show that elastic compliance in arboreal supports can be used to reduce the energetic cost of gap crossing.     

Functional diversification within and between muscle synergists during locomotion

Locomotion arises from the complex and coordinated function of limb muscles. Yet muscle function is dynamic over the course of a single stride and between strides for animals moving at different speeds or on variable terrain. While it is clear that motor unit recruitment can vary between and within muscles, we know little about how work is distributed within and between muscles under in vivo conditions. Here we show that the lateral gastrocnemius (LG) of helmeted guinea fowl (Numida meleagris) performs considerably more work than its synergist, the medial gastrocnemius (MG) and that the proximal region of the MG (pMG) performs more work than the distal region (dMG). Positive work done by the LG was approximately twice that of the proximal MG when the birds walked at 0.5 ms -1, and four times when running at 2.0 m s-1. This is probably due to different moments at the knee, as well as differences in motor unit recruitment. The dMG performed less work than the pMG because its apparent dynamic stiffness was greater, and because it exhibited a greater recruitment of slow-twitch fibres. The greater compliance of the pMG leads to increased stretch of its fascicles at the onset of force, further enhancing force production. Our results demonstrate the capacity for functional diversity between and within muscle synergists, which increases with changes in gait and speed.     

Evidence for energy savings from aerial running in the Svalbard rock ptarmigan (Lagopus muta hyperborea)

Svalbard rock ptarmigans were walked and run upon a treadmill and their energy expenditure measured using respirometry. The ptarmigan used three different gaits: a walking gait at slow speeds (less than or equal to 0.75 m s(-1)), grounded running at intermediate speeds (0.75 m s(-1) < U < 1.67 m s(-1)) and aerial running at high speeds (greater than or equal to 1.67 m s(-1)). Changes of gait were associated with reductions in the gross cost of transport (COT; J kg(-1) m(-1)), providing the first evidence for energy savings with gait change in a small crouched-postured vertebrate. In addition, for the first time (excluding humans) a decrease in absolute metabolic energy expenditure (rate of O(2) consumption) in aerial running when compared with grounded running was identified. The COT versus U curve varies between species and the COT was cheaper during aerial running than grounded running, posing the question of why grounded running should be used at all. Existing explanations (e.g. stability during running over rocky terrain) amount to just so stories with no current evidence to support them. It may be that grounded running is just an artefact of treadmill studies. Research investigating the speeds used by animals in the field is sorely needed.     

Limitations imposed by wearing armour on Medieval soldiers' locomotor performance

In Medieval Europe, soldiers wore steel plate armour for protection during warfare. Armour design reflected a trade-off between protection and mobility it offered the wearer. By the fifteenth century, a typical suit of field armour weighed between 30 and 50 kg and was distributed over the entire body. How much wearing armour affected Medieval soldiers' locomotor energetics and biomechanics is unknown. We investigated the mechanics and the energetic cost of locomotion in armour, and determined the effects on physical performance. We found that the net cost of locomotion (C(met)) during armoured walking and running is much more energetically expensive than unloaded locomotion. C(met) for locomotion in armour was 2.1-2.3 times higher for walking, and 1.9 times higher for running when compared with C(met) for unloaded locomotion at the same speed. An important component of the increased energy use results from the extra force that must be generated to support the additional mass. However, the energetic cost of locomotion in armour was also much higher than equivalent trunk loading. This additional cost is mostly explained by the increased energy required to swing the limbs and impaired breathing. Our findings can predict age-associated decline in Medieval soldiers' physical performance, and have potential implications in understanding the outcomes of past European military battles.     

Utilization of granular solidification during terrestrial locomotion of hatchling sea turtles

Biological terrestrial locomotion occurs on substrate materials with a range of rheological behaviour, which can affect limb-ground interaction, locomotor mode and performance. Surfaces like sand, a granular medium, can display solid or fluid-like behaviour in response to stress. Based on our previous experiments and models of a robot moving on granular media, we hypothesize that solidification properties of granular media allow organisms to achieve performance on sand comparable to that on hard ground. We test this hypothesis by performing a field study examining locomotor performance (average speed) of an animal that can both swim aquatically and move on land, the hatchling Loggerhead sea turtle (Caretta caretta). Hatchlings were challenged to traverse a trackway with two surface treatments: hard ground (sandpaper) and loosely packed sand. On hard ground, the claw use enables no-slip locomotion. Comparable performance on sand was achieved by creation of a solid region behind the flipper that prevents slipping. Yielding forces measured in laboratory drag experiments were sufficient to support the inertial forces at each step, consistent with our solidification hypothesis.     

Rain increases the energy cost of bat flight

Similar to insects, birds and pterosaurs, bats have evolved powered flight. But in contrast to other flying taxa, only bats are furry. Here, we asked whether flight is impaired when bat pelage and wing membranes get wet. We studied the metabolism of short flights in Carollia sowelli, a bat that is exposed to heavy and frequent rainfall in neotropical rainforests. We expected bats to encounter higher thermoregulatory costs, or to suffer from lowered aerodynamic properties when pelage and wing membranes catch moisture. Therefore, we predicted that wet bats face higher flight costs than dry ones. We quantified the flight metabolism in three treatments: dry bats, wet bats and no rain, wet bats and rain. Dry bats showed metabolic rates predicted by allometry. However, flight metabolism increased twofold when bats were wet, or when they were additionally exposed to rain. We conclude that bats may not avoid rain only because of sensory constraints imposed by raindrops on echolocation, but also because of energetic constraints.     

Muscle power attenuation by tendon during energy dissipation

An important function of skeletal muscle is deceleration via active muscle fascicle lengthening, which dissipates movement energy. The mechanical interplay between muscle contraction and tendon elasticity is critical when muscles produce energy. However, the role of tendon elasticity during muscular energy dissipation remains unknown. We tested the hypothesis that tendon elasticity functions as a mechanical buffer, preventing high (and probably damaging) velocities and powers during active muscle fascicle lengthening. We directly measured lateral gastrocnemius muscle force and length in wild turkeys during controlled landings requiring rapid energy dissipation. Muscle-tendon unit (MTU) strain was measured via video kinematics, independent of muscle fascicle strain (measured via sonomicrometry). We found that rapid MTU lengthening immediately following impact involved little or no muscle fascicle lengthening. Therefore, joint flexion had to be accommodated by tendon stretch. After the early contact period, muscle fascicles lengthened and absorbed energy. This late lengthening occurred after most of the joint flexion, and was thus mainly driven by tendon recoil. Temporary tendon energy storage led to a significant reduction in muscle fascicle lengthening velocity and the rate of energy absorption. We conclude that tendons function as power attenuators that probably protect muscles against damage from rapid and forceful lengthening during energy dissipation.