A unified theory for the energy cost of legged locomotion

Electrohydraulic musculoskeletal robotic leg for agile, adaptive, yet energy-efficient locomotion

Robotic locomotion in unstructured terrain demands an agile, adaptive, and energy-efficient architecture. To traverse such terrains, legged robots use rigid electromagnetic motors and sensorized drivetrains to adapt to the environment actively. These systems struggle to compete with animals that excel through their agile and effortless motion in natural environments. We propose a bio-inspired musculoskeletal leg architecture driven by antagonistic pairs of electrohydraulic artificial muscles. Our leg is mounted on a boom arm and can adaptively hop on varying terrain in an energy-efficient yet agile manner. It can also detect obstacles through capacitive self-sensing. The leg performs powerful and agile gait motions beyond 5 Hz and high jumps up to 40 % of the leg height. Our leg's tunable stiffness and inherent adaptability allow it to hop over grass, sand, gravel, pebbles, and large rocks using only open-loop force control. The electrohydraulic leg features a low cost of transport (0.73), and while squatting, it consumes only a fraction of the energy (1.2 %) compared to its conventional electromagnetic counterpart. Its agile, adaptive, and energy-efficient properties would open a roadmap toward a new class of musculoskeletal robots for versatile locomotion and operation in unstructured natural environments.

Relationship between metabolic cost, muscle moments and co-contraction during walking and running

BACKGROUND

The metabolic cost of locomotion is a key factor in walking and running performance. It has been studied by analysing the activation and co-activation of the muscles of the lower limbs. However, these measures do not comprehensively address muscle mechanics, in contrast to approaches using muscle moments and co-contraction.

RESEARCH QUESTION

What is the effect of speed and type of locomotion on muscle moments and co-contraction, and their relationship with metabolic cost during walking and running?

METHODS

Eleven recreational athletes (60.5 ± 7.1 kg; 169.0 ± 6.6 cm; 23.6 ± 3.3 years) walked and ran on a treadmill at different speeds, including a similar speed of 1.75 m.s-1. Metabolic cost was estimated from gas exchange measurements. Muscle moments and co-contraction of ankle and knee flexors and extensors during the stance and swing phases were estimated using an electromyographic-driven model.

RESULTS

Both the slowest and fastest walking speeds had significantly higher metabolic costs than intermediate ones (p < 0.05). The metabolic cost of walking was correlated with plantarflexors moment during swing phase (r = 0.62 at 0.5 m.s-1, r = 0.67 at 1,25 m.s-1), dorsiflexors moment during stance phase (r = 0.65 at 1.25 m.s-1, r = 0.67 at 1.5 and 1.75 m.s-1), and ankle co-contraction during the stance phase (r = 0.63 at 1.25 and 1.75 m.s-1). The metabolic cost of running at 3.25 m.s-1 during the swing phase was correlated with the dorsiflexors moment (r = 0.63), plantarflexors moment (r = 0.61) and ankle co-contraction (r = 0.60).

DISCUSSION AND CONCLUSION

Fluctuations in metabolic cost of walking and running could be explained, at least in part, by increased ankle antagonist moments and co-contraction.

Energy-based corridor identification for mammals between protected areas in Iran

Body mass plays a crucial role in determining the mass-specific energy expenditure during terrestrial locomotion across diverse animal taxa, affecting locomotion patterns. The energy landscape concept offers a framework to explore the relationship between landscape characteristics and energy expenditure, enhancing our understanding of animal movement. Although the energy landscape approach solely considers the topographic obstacles faced by animals, its suitability compared to previous methods for constructing resistance maps and delineating corridors has not been comprehensively examined. In this study, we utilized the enerscape R package to generate resistance maps in kilocalories (kcal) by incorporating digital elevation models (DEMs) and body size data (kg). We assigned body sizes ranging from 0.5 to 100 kg to encompass a wide range of small and large mammals in Iran, adjusting maximum dispersal distances accordingly from 50 to 200 km. By analyzing these scenarios, we produced four resistance maps for each body size. Next, we identified potential corridors between terrestrial protected areas in Iran using the Linkage Mapper toolkit and examined barriers and pinch-points along these paths. Our study revealed significant findings regarding the shared corridors between small and large mammals in Iran's landscape. Despite their differing body sizes and energy requirements, many corridors were found to be utilized by both small and large mammal species. For example, we identified 206 corridors for mammals weighing 500 g, which were also recognized as the least-cost paths for 100 kg mammals. Thus, embracing a comprehensive method in resistance map creation, one that incorporates species-specific traits and human infrastructure becomes imperative for accurately identifying least-cost paths and consequently pinpointing pinch points and barriers.

The work to swing limbs in humans versus chimpanzees and its relation to the metabolic cost of walking

Compared to their closest ape relatives, humans walk bipedally with lower metabolic cost (C) and less mechanical work to move their body center of mass (external mechanical work, WEXT). However, differences in WEXT are not large enough to explain the observed lower C: humans may also do less work to move limbs relative to their body center of mass (internal kinetic mechanical work, WINT,k). From published data, we estimated differences in WINT,k, total mechanical work (WTOT), and efficiency between humans and chimpanzees walking bipedally. Estimated WINT,k is ~ 60% lower in humans due to changes in limb mass distribution, lower stride frequency and duty factor. When summing WINT,k to WEXT, between-species differences in efficiency are smaller than those in C; variations in WTOT correlate with between-species, but not within-species, differences in C. These results partially support the hypothesis that the low cost of human walking is due to the concerted low WINT,k and WEXT.

Energetic costs of feeding in 12 species of small-bodied primates

There are no comparative, empirical studies of the energetic costs of feeding in mammals. As a result, we lack physiological data to better understand the selection pressures on the mammalian feeding apparatus and the influence of variables such as food geometric and material properties. This study investigates interspecific scaling of the net energetic costs of feeding in relation to body size, jaw-adductor muscle mass and food properties in a sample of 12 non-human primate species ranging in size from 0.08 to 4.2 kg. Net energetic costs during feeding were measured by indirect calorimetry for a variety of pre-cut and whole raw foods varying in geometric and material properties. Net feeding costs were determined in two ways: by subtracting either the initial metabolic rate prior to feeding or subtracting the postprandial metabolic rate. Interspecific scaling relationships were evaluated using pGLS and OLS regression. Net feeding costs scale negatively relative to both body mass and jaw-adductor mass. Large animals incur relatively lower feeding costs indicating that small and large animals experience and solve mechanical challenges in relation to energetics in different ways. This article is part of the theme issue 'Food processing and nutritional assimilation in animals'.

The provisioned primate: patterns of obesity across lemurs, monkeys, apes and humans

Non-human primates are potentially informative but underutilized species for investigating obesity. I examined patterns of obesity across the Primate order, calculating the ratio of body mass in captivity to that in the wild. This index, relative body mass, for n = 40 non-human primates (mean ± s.d.: females: 1.28 ± 0.30, range 0.67-1.78, males: 1.24 ± 0.28, range 0.70-1.97) overlapped with a reference value for humans (women: 1.52, men: 1.44). Among non-human primates, relative body mass was unrelated to dietary niche, and was marginally greater among female cohorts of terrestrial species. Males and females had similar relative body masses, but species with greater sexual size dimorphism (male/female mass) in wild populations had comparatively larger female body mass in captivity. Provisioned populations in wild and free-ranging settings had similar relative body mass to those in research facilities and zoos. Compared to the wild, captive diets are unlikely to be low in protein or fat, or high in carbohydrate, suggesting these macronutrients are not driving overeating in captive populations. Several primate species, including chimpanzees, a sister-species to humans, had relative body masses similar to humans. Humans are not unique in the propensity to overweight and obesity. This article is part of a discussion meeting issue 'Causes of obesity: theories, conjectures and evidence (Part II)'.

The fire of evolution: energy expenditure and ecology in primates and other endotherms

Total energy expenditure (TEE) represents the total energy allocated to growth, reproduction and body maintenance, as well as the energy expended on physical activity. Early experimental work in animal energetics focused on the costs of specific tasks (basal metabolic rate, locomotion, reproduction), while determination of TEE was limited to estimates from activity budgets or measurements of subjects confined to metabolic chambers. Advances in recent decades have enabled measures of TEE in free-living animals, challenging traditional additive approaches to understanding animal energy budgets. Variation in lifestyle and activity level can impact individuals' TEE on short time scales, but interspecific differences in TEE are largely shaped by evolution. Here, we review work on energy expenditure across the animal kingdom, with a particular focus on endotherms, and examine recent advances in primate energetics. Relative to other placental mammals, primates have low TEE, which may drive their slow pace of life and be an evolved response to the challenges presented by their ecologies and environments. TEE variation among hominoid primates appears to reflect adaptive shifts in energy throughput and allocation in response to ecological pressures. As the taxonomic breadth and depth of TEE data expand, we will be able to test additional hypotheses about how energy budgets are shaped by environmental pressures and explore the more proximal mechanisms that drive intra-specific variation in energy expenditure.

Shorter muscle fascicle operating lengths increase the metabolic cost of cyclic force production

During locomotion, force-producing limb muscles are predominantly responsible for an animal's whole body metabolic energy expenditure. Animals can change the length of their force-producing muscle fascicles by altering body posture (e.g., joint angles), the structural properties of their biological tissues over time (e.g., tendon stiffness), or the body's kinetics (e.g., body weight). Currently, it is uncertain whether relative muscle fascicle operating lengths have a measurable effect on the metabolic energy expended during cyclic locomotion-like contractions. To address this uncertainty, we quantified the metabolic energy expenditure of human participants, as they cyclically produced two distinct ankle moments at three ankle angles (90°, 105°, and 120°) on a fixed-position dynamometer using their soleus. Overall, increasing participant ankle angle from 90° to 120° (more plantar flexion) reduced minimum soleus fascicle length by 17% (both moment levels, P < 0.001) and increased metabolic energy expenditure by an average of 208% across both moment levels (both P < 0.001). For both moment levels, the increased metabolic energy expenditure was not related to greater fascicle positive mechanical work (higher moment level, P = 0.591), fascicle force rate (both P ≥ 0.235), or model-estimated active muscle volume (both P ≥ 0.122). Alternatively, metabolic energy expenditure correlated with average relative soleus fascicle length (r = -0.72, P = 0.002) and activation (r = 0.51, P < 0.001). Therefore, increasing active muscle fascicle operating lengths may reduce metabolic energy expended during locomotion.NEW & NOTEWORTHY During locomotion, active muscles undergo cyclic length-changing contractions. In this study, we isolated confounding variables and revealed that cyclically producing force at relatively shorter fascicle lengths increases metabolic energy expenditure. Therefore, muscle fascicle operating lengths likely have a measurable effect on the metabolic energy expenditure during locomotion.

3D geometric morphometric analysis of the distal radius insertion sites of the palmar radiocarpal ligaments indicates a relationship between wrist anatomy and unique locomotor behavior in hylobatids

OBJECTIVES

The objective of this study is to explore the anatomical differences in the insertion sites of the palmar radiocarpal ligaments between hylobatids and other hominoids that may be related to their different locomotor behaviors.

MATERIALS AND METHODS

The morphology of the insertion sites of the palmar radiocarpal ligaments was analyzed with three-dimensional geometric morphometrics (3D GM) in the distal radial epiphysis of 44 hylobatids, 25 Pan, 31 Gorilla and 15 Pongo.

RESULTS

Relative to other hominoids, hylobatid insertion sites of the palmar radiocarpal ligaments were relatively larger and the insertion site of the short radiolunate ligament had a palmar orientation.

DISCUSSION

Larger palmar radiocarpal ligaments in hylobatids can help stabilize the wrist during the radial and ulnar displacement that occurs in ricochetal brachiation, the characteristic locomotor behavior of hylobatids, and compensate for the large traction loads on the wrist during extended-elbow vertical climbing.

Balancing growth, reproduction, maintenance, and activity in evolved energy economies

Economic models predominate in life history research, which investigates the allocation of an organism's resources to growth, reproduction, and maintenance. These approaches typically employ a heuristic Y model of resource allocation, which predicts trade-offs among tasks within a fixed budget. The common currency among tasks is not always specified, but most models imply that metabolic energy, either from food or body stores, is the critical resource. Here, we review the evidence for metabolic energy as the common currency of growth, reproduction, and maintenance, focusing on studies in humans and other vertebrates. We then discuss the flow of energy to competing physiological tasks (physical activity, maintenance, and reproduction or growth) and its effect on life history traits. We propose a Ψ model of energy flow to these tasks, which provides an integrative framework for examining the influence of environmental factors and the expansion and contraction of energy budgets in the evolution of life history strategies.

Stride frequency or length? A phylogenetic approach to understand how animals regulate locomotor speed

Speed regulation in animals involves stride frequency and stride length. While the relationship between these variables has been well documented, it remains unresolved whether animals primarily modify stride frequency or stride length to increase speed. In this study, we explored the interrelationships between these three variables across a sample of 103 tetrapods and assessed whether speed regulation strategy is influenced by mechanical, allometric, phylogenetic or ecological factors. We observed that crouched terrestrial species tend to regulate speed through stride frequency. Such a strategy is energetically costly, but results in greater locomotor maneuverability and greater stability. In contrast, regulating speed through stride length is closely tied to larger arboreal animals with relatively extended limbs. Such movements reduce substrate oscillations on thin arboreal supports and/or helps to reduce swing phase costs. The slope of speed on frequency is lower in small crouched animals than in large-bodied erect species. As a result, substantially more rapid limb movements are matched with only small speed increases in crouched, small-bodied animals. Furthermore, the slope of speed on stride length was inversely proportional to body mass. As such, small changes in stride length can result in relatively rapid speed increases for small-bodied species. These results are somewhat counterintuitive, in that larger species, which have longer limbs and take longer strides, do not appear to gain as much speed increase out of lengthening their stride. Conversely, smaller species that cycle their limbs rapidly do not gain as much speed out of increasing stride frequency as do larger species.

Insect-Inspired Robots: Bridging Biological and Artificial Systems

This review article aims to address common research questions in hexapod robotics. How can we build intelligent autonomous hexapod robots that can exploit their biomechanics, morphology, and computational systems, to achieve autonomy, adaptability, and energy efficiency comparable to small living creatures, such as insects? Are insects good models for building such intelligent hexapod robots because they are the only animals with six legs? This review article is divided into three main sections to address these questions, as well as to assist roboticists in identifying relevant and future directions in the field of hexapod robotics over the next decade. After an introduction in section (1), the sections will respectively cover the following three key areas: (2) biomechanics focused on the design of smart legs; (3) locomotion control; and (4) high-level cognition control. These interconnected and interdependent areas are all crucial to improving the level of performance of hexapod robotics in terms of energy efficiency, terrain adaptability, autonomy, and operational range. We will also discuss how the next generation of bioroboticists will be able to transfer knowledge from biology to robotics and vice versa.

Determinants of climbing energetic costs in humans

Previous studies in primates and other animals have shown that mass-specific cost of transport (J kg-1 m-1) for climbing is independent of body size across species, but little is known about within-species allometry of climbing costs or the effects of difficulty and velocity. Here, we assessed the effects of velocity, route difficulty and anatomical variation on the energetic cost of climbing within humans. Twelve experienced rock climbers climbed on an indoor wall over a range of difficulty levels and velocities, with energy expenditure measured via respirometry. We found no effect of body mass or limb proportions on mass-specific cost of transport among subjects. Mass-specific cost of transport was negatively correlated with climbing velocity. Increased route difficulty was associated with slower climbing velocities and thus higher costs, but there was no statistically significant effect of route difficulty on energy expenditure independent of velocity. Finally, human climbing costs measured in this study were similar to published values for other primates, suggesting arboreal adaptations have a negligible effect on climbing efficiency.

Positive allometry of sexually selected traits: Do metabolic maintenance costs play an important role?

Sexual selection drives the evolution of some of the most exaggerated traits in nature. Studies on sexual selection often focus on the size of these traits relative to body size, but few focus on energetic maintenance costs of the tissues that compose them, and the ways in which these costs vary with body size. The relationships between energy use and body size have consequences that may allow large individuals to invest disproportionally more in sexually selected structures, or lead to the reduced per-gram maintenance cost of enlarged structures. Although sexually selected traits can incur energetic maintenance costs, these costs are not universally high; they are dependent on the relative mass and metabolic activity of tissues associated with them. Energetic costs of maintenance may play a pervasive yet little-explored role in shaping the relative scaling of sexually selected traits across diverse taxa. Also see the video abstract here: https://youtu.be/JyuoQIeA33Q.

Cyclically producing the same average muscle-tendon force with a smaller duty increases metabolic rate

Ground contact duration and stride frequency each affect muscle metabolism and help scientists link walking and running biomechanics to metabolic energy expenditure. While these parameters are often used independently, the product of ground contact duration and stride frequency (i.e. duty factor) may affect muscle contractile mechanics. Here, we sought to separate the metabolic influence of the duration of active force production, cycle frequency and duty factor. Human participants produced cyclic contractions using their soleus (which has a relatively homogeneous fibre type composition) at prescribed cycle-average ankle moments on a fixed dynamometer. Participants produced these ankle moments over short, medium and long durations while maintaining a constant cycle frequency. Overall, decreased duty factor did not affect cycle-average fascicle force (p ≥ 0.252) but did increase net metabolic power (p ≤ 0.022). Mechanistically, smaller duty factors increased maximum muscle-tendon force (p < 0.001), further stretching in-series tendons and shifting soleus fascicles to shorter lengths and faster velocities, thereby increasing soleus total active muscle volume (p < 0.001). Participant soleus total active muscle volume well-explained net metabolic power (r = 0.845; p < 0.001). Therefore, cyclically producing the same cycle-average muscle-tendon force using a decreased duty factor increases metabolic energy expenditure by eliciting less economical muscle contractile mechanics.

Differences in muscle mechanics underlie divergent optimality criteria between feeding and locomotor systems

Tetrapod musculoskeletal diversity is usually studied separately in feeding and locomotor systems. However, direct comparisons between these systems promise important insight into how natural selection deploys the same basic musculoskeletal toolkit-connective tissues, bones, nerves, and skeletal muscle-to meet the differing performance criteria of feeding and locomotion. Recent studies using this approach have proposed that the feeding system is optimized for precise application of high forces and the locomotor system is optimized for wide and rapid joint excursions for minimal energetic expenditure. If this hypothesis is correct, then it stands to reason that other anatomical and biomechanical variables within the feeding and locomotor systems should reflect these diverging functions. To test this hypothesis, we compared muscle moment arm lengths, mechanical advantages, and force vector orientations of two jaw elevator muscles (m. temporalis and m. superficial masseter), an elbow flexor (m. brachialis) and extensor (m. triceps- lateral head), and a knee flexor (m. biceps femoris-short head) and extensor (m. vastus lateralis) across 18 species of primates. Our results show that muscles of the feeding system are more orthogonally oriented relative to the resistance arm (mandible) and operate at relatively large moment arms and mechanical advantages. Moreover, these variables show relatively little change across the range of jaw excursion. In contrast, the representative muscles of the locomotor system have much smaller mechanical advantages and, depending on joint position, smaller muscle moment arm lengths and almost parallel orientations relative to the resistance arm. These patterns are consistent regardless of phylogeny, body mass, locomotor mode, and feeding specialization. We argue that these findings reflect fundamental functional dichotomies between tetrapod locomotor and feeding systems. By organizing muscles in a manner such that moment arms and mechanical advantage are relatively small, the locomotor system can produce broad joint excursions and high angular velocities with only small muscular contraction. As such, the anatomical organization of muscles within the limbs allows striding animals to move relatively rapidly and with minimal energetic expenditure. In contrast, the anatomical configuration of muscles in the feeding system, at least m. superficial masseter and m. temporalis, favors their force-producing capacity at the expense of excursion and velocity.

Variation in limb loading magnitude and timing in tetrapods

Comparative analyses of locomotion in tetrapods reveal two patterns of stride cycle variability. Tachymetabolic tetrapods (birds and mammals) have lower inter-cycle variation in stride duration than bradymetabolic tetrapods (amphibians, lizards, turtles and crocodilians). This pattern has been linked to the fact that birds and mammals share enlarged cerebella, relatively enlarged and heavily myelinated Ia afferents, and γ-motoneurons to their muscle spindles. Both tachymetabolic tetrapod lineages also possess an encapsulated Golgi tendon morphology, thought to provide more spatially precise information on muscle tension. The functional consequence of this derived Golgi tendon morphology has never been tested. We hypothesized that one advantage of precise information on muscle tension would be lower and more predictable limb bone stresses, achieved in tachymetabolic tetrapods by having less variable substrate reaction forces than bradymetabolic tetrapods. To test this hypothesis, we analyzed hindlimb substrate reaction forces during locomotion of 55 tetrapod species in a phylogenetic comparative framework. Variation in species means of limb loading magnitude and timing confirm that, for most of the variables analyzed, variance in hindlimb loading and timing is significantly lower in species with encapsulated versus unencapsulated Golgi tendon organs. These findings suggest that maintaining predictable limb loading provides a selective advantage for birds and mammals by allowing energy savings during locomotion, lower limb bone safety factors and quicker recovery from perturbations. The importance of variation in other biomechanical variables in explaining these patterns, such as posture, effective mechanical advantage and center-of-mass mechanics, remains to be clarified.

The interplay between habitat use, morphology and locomotion in subterranean crustaceans of the genus Niphargus

Locomotion is an important, fitness-related functional trait. Environment selects for type of locomotion and shapes the morphology of locomotion-related traits such as body size and appendages. In subterranean aquatic arthropods, these traits are subjected to multiple, at times opposing selection pressures. Darkness selects for enhanced mechano- and chemosensory systems and hence elongation of appendages. Conversely, water currents have been shown to favor short appendages. However, no study has addressed the variation in locomotion of invertebrates inhabiting cave streams and cave lakes, or questioned the relationship between species' morphology and locomotion. To fill this knowledge gap, we studied the interplay between habitat use, morphology and locomotion in amphipods of the subterranean genus Niphargus. Previous studies showed that lake and stream species differ in morphology. Namely, lake species are large, stout and long-legged, whereas stream species are small, slender and short-legged. We here compared locomotion mode and speed between three lake and five stream species. In addition, we tested whether morphology predicts locomotion. We found that the stream species lie on their body sides and move using slow crawling or tail-flipping. The species inhabiting lakes move comparably faster, and use a variety of locomotion modes. Noteworthy, one of the lake species almost exclusively moves in an upright or semi-upright position that resembles walking. Body size and relative length of appendages predict locomotion mode and speed in all species. We propose that integrating locomotion in the studies of subterranean species might improve our understanding of their morphological evolution.

Terrestrial locomotion energy costs vary considerably between species: no evidence that this is explained by rate of leg force production or ecology

Inter-specifically, relative energy costs of terrestrial transport vary several-fold. Many pair-wise differences of locomotor costs between similarly-sized species are considerable, and are yet to be explained by morphology or gait kinematics. Foot contact time, a proxy for rate of force production, is a strong predictor of locomotor energy costs across species of different size and might predict variability between similarly sized species. We tested for a relationship between foot contact time and metabolic rate during locomotion from published data. We investigated the phylogenetic correlation between energy expenditure rate and foot contact time, conditioned on fixed effects of mass and speed. Foot contact time does not explain variance in rate of energy expenditure during locomotion, once speed and body size are accounted for. Thus, perhaps surprisingly, inter-specific differences in the mass-independent net cost of terrestrial transport (NCOT) are not explained by rates of force production. We also tested for relationships between locomotor energy costs and eco-physiological variables. NCOT did not relate to any of the tested eco-physiological variables; we thus conclude either that interspecific differences in transport cost have no influence on macroecological and macrophysiological patterns, or that NCOT is a poor indicator of animal energy expenditure beyond the treadmill.

Joint angular excursions during cyclical behaviors differ between tetrapod feeding and locomotor systems

Tetrapod musculoskeletal diversity is usually studied separately in feeding and locomotor systems. However, comparisons between these systems promise important insight into how natural selection deploys the same basic musculoskeletal toolkit—connective tissues, bones, nerves and skeletal muscle—to meet the differing performance criteria of feeding and locomotion. In this study, we compare average joint angular excursions during cyclic behaviors– chewing, walking and running–in a phylogenetic context to explore differences in the optimality criteria of these two systems. Across 111 tetrapod species, average limb-joint angular excursions during cyclic locomotion are greater and more evolutionarily labile than those of the jaw joint during cyclic chewing. We argue that these findings reflect fundamental functional dichotomies between tetrapod locomotor and feeding systems. Tetrapod chewing systems are optimized for precise application of force over a narrower, more controlled and predictable range of displacements, the principal aim being to fracture the substrate, the size and mechanical properties of which are controlled at ingestion and further reduced and homogenized (respectively) by the chewing process. In contrast, tetrapod limbed locomotor systems are optimized for fast and energetically efficient application of force over a wider and less predictable range of displacements, the principal aim being to move the organism at varying speeds relative to a substrate whose geometry and mechanical properties need not become more homogenous as locomotion proceeds. Hence, the evolution of tetrapod locomotor systems has been accompanied by an increasing diversity of limb-joint excursions, as tetrapods have expanded across a range of locomotor substrates and environments.

Elite swimmers do not exhibit a body mass index trade-off across a wide range of event distances

There is a trade-off reflected in the contrasting phenotypes of elite long-distance runners, who are typically leaner, and elite sprinters, who are usually more heavily muscled. It is unclear, however, whether and how swimmers' bodies vary across event distances from the 50 m swim, which is about a 20-30 s event, to the 10 000 m marathon swim, which is about a 2 h event. We examined data from the 2012 Olympics to test whether swimmers' phenotypes differed across event distances. We show that across all swimming event distances, from the 50 m sprint to the 10 000 m marathon, swimmers converge on a single optimal body mass index (BMI) in men's and women's events, in marked contrast with the strong inverse relationship between BMI and event distance found in runners. The absence of a speed-endurance trade-off in the body proportions of swimmers indicates a fundamental difference in design pressures and performance capability in terrestrial versus aquatic environments.

Scaling of avian bipedal locomotion reveals independent effects of body mass and leg posture on gait

Birds provide an interesting opportunity to study the relationships between body size, limb morphology and bipedal locomotor function. Birds are ecologically diverse and span a large range of body size and limb proportions, yet all use their hindlimbs for bipedal terrestrial locomotion, for at least some part of their life history. Here, we review the scaling of avian striding bipedal gaits to explore how body mass and leg morphology influence walking and running. We collate literature data from 21 species, spanning a 2500× range in body mass from painted quail to ostriches. Using dynamic similarity theory to interpret scaling trends, we find evidence for independent effects of body mass, leg length and leg posture on gait. We find no evidence for scaling of duty factor with body size, suggesting that vertical forces scale with dynamic similarity. However, at dynamically similar speeds, large birds use relatively shorter stride lengths and higher stride frequencies compared with small birds. We also find that birds with long legs for their mass, such as the white stork and red-legged seriema, use longer strides and lower swing frequencies, consistent with the influence of high limb inertia on gait. We discuss the observed scaling of avian bipedal gait in relation to mechanical demands for force, work and power relative to muscle actuator capacity, muscle activation costs related to leg cycling frequency, and considerations of stability and agility. Many opportunities remain for future work to investigate how morphology influences gait dynamics among birds specialized for different habitats and locomotor behaviors.

What determines the metabolic cost of human running across a wide range of velocities?

The cost of generating force hypothesis proposes that the metabolic rate during running is determined by the rate of muscle force development (1/tc, tc=contact time) and the volume of active leg muscle. A previous study assumed a constant recruited muscle volume and reported that the rate of force development alone explained ∼70% of the increase in metabolic rate for human runners across a moderate velocity range (2-4 m s−1). We hypothesized that over a wider range of velocities, the effective mechanical advantage (EMA) of the lower limb joints would overall decrease, necessitating a greater volume of active muscle recruitment. Ten high-caliber male human runners ran on a force-measuring treadmill at 8, 10, 12, 14, 16 and 18 km hr−1 while we analyzed their expired air to determine metabolic rates. We measured ground reaction forces and joint kinematics to calculate contact time and estimate active muscle volume. From 8 to 18 km hr−1, metabolic rate increased 131% from 9.28 to 21.44 W kg−1. Contact time (tc) decreased from 0.280 sec to 0.190 sec, and thus the rate of force development (1/tc) increased by 48%. Ankle EMA decreased by 19.7±11%, knee EMA increased by 11.1±26.9% and hip EMA decreased by 60.8±11.8%. Estimated active muscle volume per leg increased 52.8% from 1663±152 cm3 to 2550±169 cm3. Overall, 98% of the increase in metabolic rate across the velocity range was explained by just two factors: the rate of generating force and the volume of active leg muscle.

An anatomical and mechanical analysis of the douc monkey (genus Pygathrix), and its role in understanding the evolution of brachiation

OBJECTIVES

Pygathrix is an understudied Asian colobine unusual among the Old World monkeys for its use of arm-swinging. Little data exists on the anatomy and mechanics of brachiation in this genus. Here, we consider this colobine to gain insight into the parallel evolution of suspensory behavior in primates.

MATERIALS AND METHODS

This study compares axial and appendicular morphological variables of Pygathrix with other Asian colobines. Additionally, to assess the functional consequences of Pygathrix limb anatomy, kinematic and kinetic data during arm-swinging are included to compare the douc monkey to other suspensory primates (Ateles and Hylobates).

RESULTS

Compared to more pronograde species, Pygathrix and Nasalis share morphology consistent with suspensory locomotion such as its narrower scapulae and elongated clavicles. More distally, Pygathrix displays a gracile humerus, radius, and ulna, and shorter olecranon process. During suspensory locomotion, Pygathrix, Ateles, and Hylobates all display mechanical convergence in limb loading and movements of the shoulder and elbow, but Pygathrix uses pronated wrist postures that include substantial radial deviation during arm-swinging.

DISCUSSION

The adoption of arm-swinging represents a major shift within at least three anthropoid clades and little data exist about its transition. Across species, few mechanical differences are observed during arm-swinging. Apparently, there are limited functional solutions to the challenges associated with moving bimanually below branches, especially in more proximal forelimb regions. Morphological data support this idea that the Pygathrix distal forelimb differs from apes more than its proximal end. These results can inform other studies of ape evolution, the pronograde to orthograde transition, and the convergent ways in which suspensory locomotion evolved in primates.

The evolution of vertical climbing in primates: evidence from reaction forces

Vertical climbing is an essential behavior for arboreal animals, yet limb mechanics during climbing are poorly understood and rarely compared with those observed during horizontal walking. Primates commonly engage in both arboreal walking and vertical climbing, and this makes them an ideal taxa in which to compare these locomotor forms. Additionally, primates exhibit unusual limb mechanics compared with most other quadrupeds, with weight distribution biased towards the hindlimbs, a pattern that is argued to have evolved in response to the challenges of arboreal walking. Here we test an alternative hypothesis that functional differentiation between the limbs evolved initially as a response to climbing. Eight primate species were recorded locomoting on instrumented vertical and horizontal simulated arboreal runways. Forces along the axis of, and normal to, the support were recorded. During walking, all primates displayed forelimbs that were net braking, and hindlimbs that were net propulsive. In contrast, both limbs served a propulsive role during climbing. In all species, except the lorisids, the hindlimbs produced greater propulsive forces than the forelimbs during climbing. During climbing, the hindlimbs tends to support compressive loads, while the forelimb forces tend to be primarily tensile. This functional disparity appears to be body-size dependent. The tensile loading of the forelimbs versus the compressive loading of the hindlimbs observed during climbing may have important evolutionary implications for primates, and it may be the case that hindlimb-biased weight support exhibited during quadrupedal walking in primates may be derived from their basal condition of climbing thin branches.

Energetic cost of walking in fossil hominins

OBJECTIVE

Many biomechanical studies consistently show that a broader pelvis increases the reaction forces and bending moments across the femoral shaft, increasing the energetic costs of unloaded locomotion. However, a biomechanical model does not provide the real amount of metabolic energy expended in walking. The aim of this study is to test the influence of pelvis breadth on locomotion cost and to evaluate the locomotion efficiency of extinct Pleistocene hominins.

MATERIAL AND METHODS

The current study measures in vivo the influence of pelvis width on the caloric cost of locomotion, integrating anthropometry, body composition and indirect calorimetry protocols in a sample of 46 subjects of both sexes.

RESULTS

We show that a broader false pelvis is substantially more efficient for locomotion than a narrower one and that the influence of false pelvis width on the energetic cost is similar to the influence of leg length. Two models integrating body mass, femur length and bi-iliac breadth are used to estimate the net and gross energetic costs of locomotion in a number of extinct hominins. The results presented here show that the locomotion of Homo was not energetically more efficient than that of Australopithecus and that the locomotion of extinct Homo species was not less efficient than that of modern Homo sapiens.

DISCUSSION

The changes in the anatomy of the pelvis and lower limb observed with the appearance of Homo ergaster probably did not fully offset the increased expenditure resulting from a larger body mass. Moreover, the narrow pelvis in modern humans does not contribute to greater efficiency of locomotion.

Measuring the Energy of Ventilation and Circulation during Human Walking using Induced Hypoxia

Energy expenditure (EE) during walking includes energy costs to move and support the body and for respiration and circulation. We measured EE during walking under three different oxygen concentrations. Eleven healthy, young, male lowlanders walked on a treadmill at seven gait speeds (0.67–1.83 m s⁻¹) on a level gradient under normobaric normoxia (room air, 21% O₂), moderate hypoxia (15% O₂), and severe hypoxia (11% O₂). By comparing the hypoxia-induced elevation in heart rate (HR [bpm]), ventilation (V_E [L min⁻¹]) with the change in energy expenditure (EE [W]) at each speed, we were able to determine circulatory and respiratory costs. In a multivariate model combining HR and V_E, respiratory costs were 0.44 ± 0.15 W per each L min⁻¹ increase in V_E, and circulatory costs were 0.24 ± 0.05 W per each bpm increase in HR (model adjusted r² = 0.97, p < 0.001). These V_E costs were substantially lower than previous studies that ignored the contribution of HR to cardiopulmonary work. Estimated HR costs were consistent with, although somewhat higher than, measures derived from catheterization studies. Cardiopulmonary costs accounted for 23% of resting EE, but less than 5% of net walking costs (i.e., with resting EE subtracted).

Gait changes in a line of mice artificially selected for longer limbs

In legged terrestrial locomotion, the duration of stance phase, i.e., when limbs are in contact with the substrate, is positively correlated with limb length, and negatively correlated with the metabolic cost of transport. These relationships are well documented at the interspecific level, across a broad range of body sizes and travel speeds. However, such relationships are harder to evaluate within species (i.e., where natural selection operates), largely for practical reasons, including low population variance in limb length, and the presence of confounding factors such as body mass, or training. Here, we compared spatiotemporal kinematics of gait in Longshanks, a long-legged mouse line created through artificial selection, and in random-bred, mass-matched Control mice raised under identical conditions. We used a gait treadmill to test the hypothesis that Longshanks have longer stance phases and stride lengths, and decreased stride frequencies in both fore- and hind limbs, compared with Controls. Our results indicate that gait differs significantly between the two groups. Specifically, and as hypothesized, stance duration and stride length are 8–10% greater in Longshanks, while stride frequency is 8% lower than in Controls. However, there was no difference in the touch-down timing and sequence of the paws between the two lines. Taken together, these data suggest that, for a given speed, Longshanks mice take significantly fewer, longer steps to cover the same distance or running time compared to Controls, with important implications for other measures of variation among individuals in whole-organism performance, such as the metabolic cost of transport.

Body size and lower limb posture during walking in humans

We test whether locomotor posture is associated with body mass and lower limb length in humans and explore how body size and posture affect net joint moments during walking. We acquired gait data for 24 females and 25 males using a three-dimensional motion capture system and pressure-measuring insoles. We employed the general linear model and commonality analysis to assess the independent effect of body mass and lower limb length on flexion angles at the hip, knee, and ankle while controlling for sex and velocity. In addition, we used inverse dynamics to model the effect of size and posture on net joint moments. At early stance, body mass has a negative effect on knee flexion (p < 0.01), whereas lower limb length has a negative effect on hip flexion (p < 0.05). Body mass uniquely explains 15.8% of the variance in knee flexion, whereas lower limb length uniquely explains 5.4% of the variance in hip flexion. Both of the detected relationships between body size and posture are consistent with the moment moderating postural adjustments predicted by our model. At late stance, no significant relationship between body size and posture was detected. Humans of greater body size reduce the flexion of the hip and knee at early stance, which results in the moderation of net moments at these joints.

Instantaneous Metabolic Cost of Walking: Joint-Space Dynamic Model with Subject-Specific Heat Rate

A subject-specific model of instantaneous cost of transport (ICOT) is introduced from the joint-space formulation of metabolic energy expenditure using the laws of thermodynamics and the principles of multibody system dynamics. Work and heat are formulated in generalized coordinates as functions of joint kinematic and dynamic variables. Generalized heat rates mapped from muscle energetics are estimated from experimental walking metabolic data for the whole body, including upper-body and bilateral data synchronization. Identified subject-specific energetic parameters-mass, height, (estimated) maximum oxygen uptake, and (estimated) maximum joint torques-are incorporated into the heat rate, as opposed to the traditional in vitro and subject-invariant muscle parameters. The total model metabolic energy expenditure values are within 5.7 ± 4.6% error of the measured values with strong (R2 > 0.90) inter- and intra-subject correlations. The model reliably predicts the characteristic convexity and magnitudes (0.326-0.348) of the experimental total COT (0.311-0.358) across different subjects and speeds. The ICOT as a function of time provides insights into gait energetic causes and effects (e.g., normalized comparison and sensitivity with respect to walking speed) and phase-specific COT, which are unavailable from conventional metabolic measurements or muscle models. Using the joint-space variables from commonly measured or simulated data, the models enable real-time and phase-specific evaluations of transient or non-periodic general tasks that use a range of (aerobic) energy pathway similar to that of steady-state walking.

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.

Phylogenetic comparisons of pedestrian locomotion costs: confirmations and new insights

The energetic costs for animals to locomote on land influence many aspects of their ecology. Size accounts for much of the among-species variation in terrestrial transport costs, but species of similar body size can still exhibit severalfold differences in energy expenditure. We compiled measurements of the (mass-specific) minimum cost of pedestrian transport (COT_min, mL/kg/m) for 201 species - by far the largest sample to date - and used phylogenetically informed comparative analyses to investigate possible eco-evolutionary differences in COT_min between various groupings of those species. We investigated number of legs, ectothermy and endothermy, waddling, and nocturnality specifically in lizards. Thus, our study primarily revisited previous theories about variations in COT_min between species, testing them with much more robust analyses. Having accounted for mass, while residual COT_min did not differ between bipedal and other species, specifically waddling bipeds were found to have relatively high COT_min. Furthermore, nocturnal lizards have relatively low COT_min although temperature does not appear to affect COT_min in ectotherms. Previous studies examining across-species variation in COT_min from a biomechanical perspective show that the differences between waddling birds and nonwaddling species, and between nocturnal lizards and other ecotherms, are likely to be attributable to differences in ground reaction forces, posture, and effective limb length.

A different angle: comparative analyses of whole-animal transport costs running uphill

Comparative work on animals' costs of terrestrial locomotion has focussed on the underpinning physiology and biomechanics. Often, much of an animal's energy budget is spent on moving around thus there is also value in interpreting such data from an ecological perspective. When animals move through their environment they encounter topographical variation, and this is a key factor that can dramatically affect their energy expenditure. We collated published data on the costs for birds and mammals to locomote terrestrially on inclines, and investigated the scaling relationships using a phylogenetically informed approach. We show that smaller animals have a greater mass-specific cost of transport on inclines across the body mass range analysed. We also demonstrate that the increase in cost for smaller animals to run up a slope relative to along a flat surface is comparatively low. Heavier animals show larger absolute and relative increases in energy cost to travel uphill. Consideration of all aspects of the cost of incline locomotion – absolute, relative, and mass-specific – provides a fuller understanding of the interactions between transport costs, body mass, incline gradient and phylogeny, and enables us to consider their ecological implications, which we couch within the context of the ‘energy landscape‘.

Comparative locomotor costs of domestic dogs reveal energetic economy of wolf-like breeds

The broad diversity in morphology and geographic distribution of the 35 free-ranging members of the family Canidae is only rivaled by that of the domesticated dog, Canis lupus familiaris. Considered to be among nature's most elite endurance athletes, both domestic and wild canids provide a unique opportunity to examine the variability in mammalian aerobic exercise performance and energy expenditure. To determine the potential effects of domestication and selective breeding on locomotor gait and economy in canids, we measured the kinematics and mass-specific metabolism of three large (&gt;20 kg) dog breed groups (northern breeds, retrievers, and hounds) of varying morphological and genomic relatedness to their shared progenitor, the gray wolf. By measuring all individuals moving in preferred steady-state gaits along a level transect and on a treadmill, we found distinct biomechanical, kinematic, and energetic patterns for each breed group. While all groups exhibited reduced total cost of transport (COT) at faster speeds, the total COT and net COT during trotting and galloping were significantly lower for northern breed dogs (3.0 and 2.1 J∙kg−1∙m−1, respectively) relative to hound (4.2 and 3.4 J∙kg−1∙m−1, respectively) and retriever dogs (3.8 and 3.0 J∙kg−1∙m−1, respectively) of comparable mass. Similarly, northern breeds expended less energy per stride (3.47 J∙kg−1∙stride−1) than hounds or retrievers (4.97 and 4.02 J∙kg−1∙stride−1, respectively). These results suggest that, in addition to their close genetic and morphological ties to gray wolves, northern breed dogs have retained highly cursorial kinematic and physiological traits that promote economical movement across the landscape.