The influence of speed and size on avian terrestrial locomotor biomechanics: Predicting locomotion in extinct theropod dinosaurs

Dynamic similarity and the peculiar allometry of maximum running speed

Animal performance fundamentally influences behaviour, ecology, and evolution. It typically varies monotonously with size. A notable exception is maximum running speed; the fastest animals are of intermediate size. Here we show that this peculiar allometry results from the competition between two musculoskeletal constraints: the kinetic energy capacity, which dominates in small animals, and the work capacity, which reigns supreme in large animals. The ratio of both capacities defines the physiological similarity index Γ, a dimensionless number akin to the Reynolds number in fluid mechanics. The scaling of Γ indicates a transition from a dominance of muscle forces to a dominance of inertial forces as animals grow in size; its magnitude defines conditions of "dynamic similarity" that enable comparison and estimates of locomotor performance across extant and extinct animals; and the physical parameters that define it highlight opportunities for adaptations in musculoskeletal "design" that depart from the eternal null hypothesis of geometric similarity. The physiological similarity index challenges the Froude number as prevailing dynamic similarity condition, reveals that the differential growth of muscle and weight forces central to classic scaling theory is of secondary importance for the majority of terrestrial animals, and suggests avenues for comparative analyses of locomotor systems.

What does climbing mean exactly? Assessing spatiotemporal gait characteristics of inclined locomotion in parrots

At what inclination does climbing begin? In this paper, we investigate the transition from walking to climbing in two species of parrot (Agapornis roseicollis and Nymphicus hollandicus) that are known to incorporate both their tail and their craniocervical system into the gait cycle during vertical climbing. Locomotor behaviors ranging in inclination were observed at angles between 0° and 90° for A. roseicollis, and 45°-85° degrees for N. hollandicus. Use of the tail in both species was observed at 45° inclination, and was joined at higher inclinations (> 65°) by use of the craniocervical system. Additionally, as inclination approached (but remained below) 90°, locomotor speeds were reduced while gaits were characterized by higher duty factors and lower stride frequency. These gait changes are consistent with those thought to increase stability. At 90°, A. roseicollis significantly increased its stride length, resulting in higher overall locomotor speed. Collectively these data demonstrate that the transition between horizontal walking and vertical climbing is gradual, incrementally altering several components of gait as inclinations increase. Such data underscore the need for further investigation into how exactly "climbing" is defined and the specific locomotor characteristics that differentiate this behavior from level walking.

Three toes and three modes: Dynamics of terrestrial, suspensory, and vertical locomotion in brown-throated three-toed sloths (Bradypodidae, Xenarthra)

Living sloths exhibit numerous anatomical specializations towards inverted quadrupedalism, however, previous studies have noted a more varied locomotor repertoire than previously anticipated. In this study, we present spatiotemporal gait characteristics and triaxial kinetic data from the brown-throated three-toed sloth (Bradypus variegatus) across three locomotor modes: terrestrial quadrupedal "crawling", suspensory walking, and vertical climbing. Compared to quadrupedal crawling and suspensory walking, B. variegatus adopted longer contact times and stride durations, larger duty factors, and greater speed during vertical climbing. Net fore-aft impulses were significantly greater during vertical climbing in both limb pairs than in quadrupedal crawling and suspensory walking. Functionally, during quadrupedal crawling and vertical climbing, both limb pairs served propulsive roles, while differentiation between a propulsive forelimb and braking hindlimb was observed during suspension. Net tangential forces differentiated vertical climbing kinetics from the other modes of locomotion, with the introduction of bidirectional pulling and pushing forces in the forelimb and hindlimb, respectively. The net mediolateral impulses were similar in vertical climbing and quadrupedal crawling as both limb pairs directed forces in one direction, whereas during suspensory walking, the laterally dominant forelimb was opposed by the medially dominant hindlimb. In total, this study provides novel data on the diverse locomotor dynamics in a slow-moving arboreal tetrapod and posits new testable hypotheses about the neuroplasticity and ease of transitioning between locomotor behaviors. The strikingly similar kinetic profiles of quadrupedal crawling and suspensory walking compared to vertical climbing suggest shared neuromuscular and mechanical demands between these mirrored locomotor modes.

Do we all walk the walk? A comparison of walking behaviors across tetrapods

A walking gait has been identified in a range of vertebrate species with different body plans, habitats, and life histories. With increased application of this broad umbrella term, it has become necessary to assess the physical characteristics, analytical approaches, definitions, and diction used to describe walks. To do this, we reviewed studies of slow speed locomotion across a range of vertebrates to refine the parameters used to define walking, evaluate analytical techniques, and propose approaches to maximize consistency across subdisciplines. We summarize nine key parameters used to characterize walking behaviors in mammals, birds, reptiles, amphibians, and fishes. After identifying consistent patterns across groups, we propose a comprehensive definition for a walking gait. A walk is a form of locomotion where the majority of the forward propulsion of the animal comes from forces generated by the appendages interacting with the ground. During a walk, an appendage must be out of phase with the opposing limb in the same girdle and there is always at least one limb acting as ground-support (no suspension phase). Additionally, walking occurs at dimensionless speeds <1 v* and the duty factor of the limbs is always >0.5. Relative to other gaits used by the same species, the stance duration of a walk is long, the cycle frequency is low, and the cycle distance is small. Unfortunately, some of these biomechanical parameters, while effectively describing walks, may also characterize other, non-walking gaits. Inconsistent methodology likely contributes to difficulties in comparing data across many groups of animals; consistent application of data collection and analytical techniques in research methodology can improve these comparisons. Finally, we note that the kinetics of quadrupedal movements are still poorly understood and much work remains to be done to understand the movements of small, exothermic tetrapods.

Patterns of single limb forces during terrestrial and arboreal locomotion in rosy-faced lovebirds (Psittaciformes: Agapornis roseicollis)

The biomechanical demands of arboreal locomotion are generally thought to necessitate specialized kinetic and kinematic gait characteristics. While such data has been widely collected across arboreal quadrupeds, no study has yet explored how arboreal substrates influence the locomotor behavior of birds. Parrots - an ancient arboreal lineage that exhibit numerous anatomical specializations towards life in the trees - represent an ideal model group within which to examine this relationship. Here, we quantify limb loading patterns within the rosy-faced lovebird (Agapornis roseicollis) across a range of experimental conditions to define under which circumstances arboreal gaits are triggered, and how, during arboreal walking, gait patterns change across substrates of varying diameter. In so doing, we address longstanding questions as to how the challenges associated with arboreality affect gait parameters. Arboreal locomotion was associated with the adoption of a sidling gait, which was employed exclusively on the small- and medium-poles but not terrestrially. When sidling, the hindlimbs are decoupled into a distinct leading limb (which imparts exclusively braking forces) and trailing limb (which generates only propulsive forces). Sidling was also associated with relatively low pitching forces, even on the smallest substrate. Indeed, these forces were significantly lower than mediolateral forces experienced during striding on terrestrial and large-diameter substrates. We propose that the adoption of sidling gaits is a consequence of avian foot morphology and represents a novel form of arboreal locomotion where inversion/eversion is impossible. Such movement mechanics is likely widespread among avian taxa and may also typify patterns of arboreal locomotion in humans.

Whole-limb scaling of muscle mass and force-generating capacity in amniotes

Skeletal muscle mass, architecture and force-generating capacity are well known to scale with body size in animals, both throughout ontogeny and across species. Investigations of limb muscle scaling in terrestrial amniotes typically focus on individual muscles within select clades, but here this question was examined at the level of the whole limb across amniotes generally. In particular, the present study explored how muscle mass, force-generating capacity (measured by physiological cross-sectional area) and internal architecture (fascicle length) scales in the fore- and hindlimbs of extant mammals, non-avian saurians (‘reptiles’) and bipeds (birds and humans). Sixty species spanning almost five orders of magnitude in body mass were investigated, comprising previously published architectural data and new data obtained via dissections of the opossum Didelphis virginiana and the tegu lizard Salvator merianae. Phylogenetic generalized least squares was used to determine allometric scaling slopes (exponents) and intercepts, to assess whether patterns previously reported for individual muscles or functional groups were retained at the level of the whole limb, and to test whether mammals, reptiles and bipeds followed different allometric trajectories. In general, patterns of scaling observed in individual muscles were also observed in the whole limb. Reptiles generally have proportionately lower muscle mass and force-generating capacity compared to mammals, especially at larger body size, and bipeds exhibit strong to extreme positive allometry in the distal hindlimb. Remarkably, when muscle mass was accounted for in analyses of muscle force-generating capacity, reptiles, mammals and bipeds almost ubiquitously followed a single common scaling pattern, implying that differences in whole-limb force-generating capacity are principally driven by differences in muscle mass, not internal architecture. In addition to providing a novel perspective on skeletal muscle allometry in animals, the new dataset assembled was used to generate pan-amniote statistical relationships that can be used to predict muscle mass or force-generating capacity in extinct amniotes, helping to inform future reconstructions of musculoskeletal function in the fossil record.

Fast-running theropods tracks from the Early Cretaceous of La Rioja, Spain

Theropod behaviour and biodynamics are intriguing questions that paleontology has been trying to resolve for a long time. The lack of extant groups with similar bipedalism has made it hard to answer some of the questions on the matter, yet theoretical biomechanical models have shed some light on the question of how fast theropods could run and what kind of movement they showed. The study of dinosaur tracks can help answer some of these questions due to the very nature of tracks as a product of the interaction of these animals with the environment. Two trackways belonging to fast-running theropods from the Lower Cretaceous Enciso Group of Igea (La Rioja) are presented here and compared with other fast-running theropod trackways published to date. The Lower Cretaceous Iberian fossil record and some features present in these footprints and trackways suggest a basal tetanuran, probably a carcharodontosaurid or spinosaurid, as a plausible trackmaker. Speed analysis shows that these trackways, with speed ranges of 6.5-10.3 and 8.8-12.4 ms^-1, testify to some of the top speeds ever calculated for theropod tracks, shedding light on the question of dinosaur biodynamics and how these animals moved.

Are they arboreal? Climbing abilities and mechanics in the red-backed salamander (Plethodon cinereus)

While red-backed salamanders (Plethodon cinereus) are most often observed in terrestrial forested areas, several studies report arboreal substrate use and climbing behavior. However, salamanders do not have any of the anatomical features commonly observed in specialized climbing species (e.g., claws, setae, suction cups). Instead, salamanders cling to surfaces using the shear and adhesive properties of their mucous layer. In this study, we explore the capabilities and spatiotemporal gait patterns of arboreal locomotion in the red-backed salamander as they move across twelve substrate conditions ranging in diameter, orientation, and roughness. On arboreal substrates, red-backed salamanders decreased locomotor speed, stride frequency, phase and stride length, and increased duty factor and stride duration. Such responses have been observed in other non-salamander species and are posited to increase arboreal stability. Furthermore, these findings indicate that amphibian locomotion, or at least the locomotor behavior of the red-backed salamander, is not stereotyped and that some locomotor plasticity is possible in response to the demands of the external environment. However, red-backed salamanders were unable to locomote on any small-diameter or vertically-oriented coarse substrates. This finding provides strong evidence that the climbing abilities of red-backed salamanders are attributable solely to mucous adhesion and that this species is unable to produce the necessary external "gripping" forces to achieve fine-branch arboreal locomotion or scale substrates where adhesion is not possible. The red-backed salamander provides an ideal model for arboreal locomotor performance of anatomically-unspecialized amphibians and offers insight into transitionary stages in the evolution of arborealism in this lineage.

Predictive simulations of running gait reveal a critical dynamic role for the tail in bipedal dinosaur locomotion

Locomotion has influenced the ecology, evolution, and extinction of species throughout history, yet studying locomotion in the fossil record is challenging. Computational biomechanics can provide novel insight by mechanistically relating observed anatomy to whole-animal function and behavior. Here, we leverage optimal control methods to generate the first fully predictive, three-dimensional, muscle-driven simulations of locomotion in an extinct terrestrial vertebrate, the bipedal non-avian theropod dinosaur Coelophysis. Unexpectedly, our simulations involved pronounced lateroflexion movements of the tail. Rather than just being a static counterbalance, simulations indicate that the tail played a crucial dynamic role, with lateroflexion acting as a passive, physics-based mechanism for regulating angular momentum and improving locomotor economy, analogous to the swinging arms of humans. We infer this mechanism to have existed in many other bipedal non-avian dinosaurs as well, and our methodology provides new avenues for exploring the functional diversity of dinosaur tails in the future.

Gait mechanics of a blind echolocating rodent: Implications for the locomotion of small arboreal mammals and proto-bats

Arboreal mammals have evolved a range of biomechanical adaptations that allow them to navigate trees effectively. One such feature that has received considerable attention is the importance of vision that helps arboreal animals assess gap distances, assure proper foot placement, and inspect potential risks. While there is considerable debate about the relative importance of the visual system specifics, there is little doubt that the ability to at least see the environment must confer some level of safety when navigating arboreal substrates. In this study, we explore spatiotemporal and kinematic patterns of arboreal locomotion in the Vietnamese pygmy dormouse (Typhlomys chapensis), a blind rodent that uses ultrasonic echolocation to navigate in tree canopies. We compare these data with five other species of arboreal rodents and primates. Spatiotemporal gait characteristics are largely similar between the Vietnamese pygmy dormouse and other small-bodied arboreal species analyzed. Most notable is the tendency for relatively high-speed asymmetrical gaits on large-diameter substrates and slower symmetrical lateral-sequence gaits on small-diameter substrates. Furthermore, for all species speed is primarily regulated by increasing stride frequency rather than length. Kinematics of the Vietnamese pygmy dormouse changed little in response substrate size and were primarily driven by speed. These findings suggest that the information gathered during ultrasonic scanning is sufficient to allow effective quadrupedal locomotion while moving on arboreal supports. The Vietnamese pygmy dormouse may serve as a model for the quadrupedal nocturnal ancestor of bats, which had started developing ultrasonic echolocation and reducing vision while likely occupying an arboreal niche.

Computational modelling of muscle fibre operating ranges in the hindlimb of a small ground bird (Eudromia elegans), with implications for modelling locomotion in extinct species

The arrangement and physiology of muscle fibres can strongly influence musculoskeletal function and whole-organismal performance. However, experimental investigation of muscle function during in vivo activity is typically limited to relatively few muscles in a given system. Computational models and simulations of the musculoskeletal system can partly overcome these limitations, by exploring the dynamics of muscles, tendons and other tissues in a robust and quantitative fashion. Here, a high-fidelity, 26-degree-of-freedom musculoskeletal model was developed of the hindlimb of a small ground bird, the elegant-crested tinamou (Eudromia elegans, ~550 g), including all the major muscles of the limb (36 actuators per leg). The model was integrated with biplanar fluoroscopy (XROMM) and forceplate data for walking and running, where dynamic optimization was used to estimate muscle excitations and fibre length changes throughout both gaits. Following this, a series of static simulations over the total range of physiological limb postures were performed, to circumscribe the bounds of possible variation in fibre length. During gait, fibre lengths for all muscles remained between 0.5 to 1.21 times optimal fibre length, but operated mostly on the ascending limb and plateau of the active force-length curve, a result that parallels previous experimental findings for birds, humans and other species. However, the ranges of fibre length varied considerably among individual muscles, especially when considered across the total possible range of joint excursion. Net length change of muscle-tendon units was mostly less than optimal fibre length, sometimes markedly so, suggesting that approaches that use muscle-tendon length change to estimate optimal fibre length in extinct species are likely underestimating this important parameter for many muscles. The results of this study clarify and broaden understanding of muscle function in extant animals, and can help refine approaches used to study extinct species.

Musculoskeletal modelling of the Nile crocodile (Crocodylus niloticus) hindlimb: Effects of limb posture on leverage during terrestrial locomotion

We developed a three-dimensional, computational biomechanical model of a juvenile Nile crocodile (Crocodylus niloticus) pelvis and hindlimb, composed of 47 pelvic limb muscles, to investigate muscle function. We tested whether crocodiles, which are known to use a variety of limb postures during movement, use limb orientations (joint angles) that optimise the moment arms (leverages) or moment-generating capacities of their muscles during different limb postures ranging from a high walk to a sprawling motion. We also describe the three-dimensional (3D) kinematics of the crocodylian hindlimb during terrestrial locomotion across an instrumented walkway and a treadmill captured via X-ray Reconstruction of Moving Morphology (biplanar fluoroscopy; 'XROMM'). We reconstructed the 3D positions and orientations of each of the hindlimb bones and used dissection data for muscle lines of action to reconstruct a focal, subject-specific 3D musculoskeletal model. Motion data for different styles of walking (a high, crouched, bended and two types of sprawling motion) were fed into the 3D model to identify whether any joints adopted near-optimal poses for leverage across each of the behaviours. We found that (1) the hip adductors and knee extensors had their largest leverages during sprawling postures and (2) more erect postures typically involved greater peak moment arms about the hip (flexion-extension), knee (flexion) and metatarsophalangeal (flexion) joints. The results did not fully support the hypothesis that optimal poses are present during different locomotory behaviours because the peak capacities were not always reached around mid-stance phase. Furthermore, we obtained few clear trends for isometric moment-generating capacities. Therefore, perhaps peak muscular leverage in Nile crocodiles is instead reached either in early/late stance or possibly during swing phase or other locomotory behaviours that were not studied here, such as non-terrestrial movement. Alternatively, our findings could reflect a trade-off between having to execute different postures, meaning that hindlimb muscle leverage is not optimised for any singular posture or behaviour. Our model, however, provides a comprehensive set of 3D estimates of muscle actions in extant crocodiles which can form a basis for investigating muscle function in extinct archosaurs.

Limb work and joint work minimization reveal an energetic benefit to the elbows-back, knees-forward limb design in parasagittal quadrupeds

Quadrupedal animal locomotion is energetically costly. We explore two forms of mechanical work that may be relevant in imposing these physiological demands. Limb work, due to the forces and velocities between the stance foot and the centre of mass, could theoretically be zero given vertical limb forces and horizontal centre of mass path. To prevent pitching, skewed vertical force profiles would then be required, with forelimb forces high in late stance and hindlimb forces high in early stance. By contrast, joint work-the positive mechanical work performed by the limb joints-would be reduced with forces directed through the hip or shoulder joints. Measured quadruped kinetics show features consistent with compromised reduction of both forms of work, suggesting some degree of, but not perfect, inter-joint energy transfer. The elbows-back, knees-forward design reduces the joint work demand of a low limb-work, skewed, vertical force profile. This geometry allows periods of high force to be supported when the distal segment is near vertical, imposing low moments about the elbow or knee, while the shoulder or hip avoids high joint power despite high moments because the proximal segment barely rotates-translation over this period is due to rotation of the distal segment.

Survey of biomechanical aspects of arthropod terrestrialisation - Substrate bound legged locomotion

Arthropods are the most diverse clade on earth with regard to both species number and variability of body plans. Their general body plan is characterised by variable numbers of legs, and many-legged locomotion is an essential aspect of many aquatic and terrestrial arthropod species. Moreover, arthropods belong to the first groups of animals to colonise subaerial habitats, and they did so repeatedly and independently in a couple of clades. Those arthropod clades that colonised land habitats were equipped with highly variable body plans and locomotor apparatuses. Proceeding from their respective specific anatomies, they were challenged with strongly changing environmental conditions as well as altered physical and physiological constraints. This review explores the transitions from aquatic to terrestrial habitats across the different arthropod body plans and explains the major mechanisms and principles that constrain design and function of a range of locomotor apparatuses. Important aspects of movement physiology addressed here include the effects of different numbers of legs, different body sizes, miniaturisation and simplification of body plans and different ratios of inertial and damping forces. The article's focus is on continuous legged locomotion, but related ecological and behavioural aspects are also taken into account.

Low leg compliance permits grounded running at speeds where the inverted pendulum model gets airborne

Animals typically switch from grounded (no flight phases) to aerial running at dimensionless speeds u^ < 1. But some birds use grounded running far above u^ = 1, which puzzles biologists because the inverted pendulum becomes airborne at this speed. Here, we combine computer experiments using the spring-mass model with locomotion data from small birds, macaques and humans to understand the relationship between leg function (stiffness, angle of attack), locomotion speed and gait. With our model, we found three-humped ground reaction force profiles for slow grounded running speeds. The minimal single-humped grounded running speed is u^ = 0.4. This speed value roughly coincides with the transition speed from vaulting to bouncing mechanics in bipeds. Maximal grounded running speed in the model is not limited. In experiments, animals changed from grounded to aerial running at dimensionless contact time around 1. Considering these real-world contact times reduces the solution space drastically, but experimental data fit well. The model still predicts maximal grounded running speed  u^ > 1 for low stiffness values used by birds but decreases below u^ = 1 for increasing stiffness. For stiffer legs used in human walking and running, periodic grounded running vanishes. At speeds at which birds and macaques change to aerial running, we found periodic aerial running to intersect grounded running. This could explain why animals can alternate between grounded and aerial running at the same speed and identical leg parameters. Compliant legs enable different gaits and speeds with similar leg parameters, stiff legs require parameter adaptations.

The fast and the frugal: Divergent locomotory strategies drive limb lengthening in theropod dinosaurs

Limb length, cursoriality and speed have long been areas of significant interest in theropod paleobiology, since locomotory capacity, especially running ability, is critical in the pursuit of prey and to avoid becoming prey. The impact of allometry on running ability, and the limiting effect of large body size, are aspects that are traditionally overlooked. Since several different non-avian theropod lineages have each independently evolved body sizes greater than any known terrestrial carnivorous mammal, ~1000kg or more, the effect that such large mass has on movement ability and energetics is an area with significant implications for Mesozoic paleoecology. Here, using expansive datasets that incorporate several different metrics to estimate body size, limb length and running speed, we calculate the effects of allometry on running ability. We test traditional metrics used to evaluate cursoriality in non-avian theropods such as distal limb length, relative hindlimb length, and compare the energetic cost savings of relative hindlimb elongation between members of the Tyrannosauridae and more basal megacarnivores such as Allosauroidea or Ceratosauridae. We find that once the limiting effects of body size increase is incorporated there is no significant correlation to top speed between any of the commonly used metrics, including the newly suggested distal limb index (Tibia + Metatarsus/ Femur length). The data also shows a significant split between large and small bodied theropods in terms of maximizing running potential suggesting two distinct strategies for promoting limb elongation based on the organisms’ size. For small and medium sized theropods increased leg length seems to correlate with a desire to increase top speed while amongst larger taxa it corresponds more closely to energetic efficiency and reducing foraging costs. We also find, using 3D volumetric mass estimates, that the Tyrannosauridae show significant cost of transport savings compared to more basal clades, indicating reduced energy expenditures during foraging and likely reduced need for hunting forays. This suggests that amongst theropods, hindlimb evolution was not dictated by one particular strategy. Amongst smaller bodied taxa the competing pressures of being both a predator and a prey item dominant while larger ones, freed from predation pressure, seek to maximize foraging ability. We also discuss the implications both for interactions amongst specific clades and Mesozoic paleobiology and paleoecological reconstructions as a whole.

Trunk pitch oscillations for energy trade-offs in bipedal running birds and robots

Bipedal animals have diverse morphologies and advanced locomotion abilities. Terrestrial birds, in particular, display agile, efficient, and robust running motion, in which they exploit the interplay between the body segment masses and moment of inertias. On the other hand, most legged robots are not able to generate such versatile and energy-efficient motion and often disregard trunk movements as a means to enhance their locomotion capabilities. Recent research investigated how trunk motions affect the gait characteristics of humans, but there is a lack of analysis across different bipedal morphologies. To address this issue, we analyze avian running based on a spring-loaded inverted pendulum model with a pronograde (horizontal) trunk. We use a virtual point based control scheme and modify the alignment of the ground reaction forces to assess how our control strategy influences the trunk pitch oscillations and energetics of the locomotion. We derive three potential key strategies to leverage trunk pitch motions that minimize either the energy fluctuations of the center of mass or the work performed by the hip and leg. We suggest how these strategies could be used in legged robotics.

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.

Spring-loaded inverted pendulum goes through two contraction-extension cycles during the single-support phase of walking

Despite the overall complexity of legged locomotion, the motion of the center of mass (COM) itself is relatively simple, and can be qualitatively described by simple mechanical models. In particular, walking can be qualitatively modeled by a simple model in which each leg is described by a spring-loaded inverted pendulum (SLIP). However, SLIP has many limitations and is unlikely to serve as a quantitative model. As a first step to obtaining a quantitative model for walking, we explored the ability of SLIP to model the single-support phase of walking, and found that SLIP has two limitations. First, it predicts larger horizontal ground reaction forces (GRFs) than empirically observed. A new model – angular and radial spring-loaded inverted pendulum (ARSLIP) – can overcome this deficit. Second, although the leg spring (surprisingly) goes through contraction-extension-contraction-extensions (CECEs) during the single-support phase of walking and can produce the characteristic M-shaped vertical GRFs, modeling the single-support phase requires active elements. Despite these limitations, SLIP as a model provides important insights. It shows that the CECE cycling lengthens the stance duration allowing the COM to travel passively for longer, and decreases the velocity redirection between the beginning and end of a step.

Summary: We quantitatively evaluate a simple model for human walking based on two-spring and find that this model describes many features of human walking.

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.

Cancellous bone and theropod dinosaur locomotion. Part I-an examination of cancellous bone architecture in the hindlimb bones of theropods

This paper is the first of a three-part series that investigates the architecture of cancellous ('spongy') bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and has previously been used to infer locomotor biomechanics in extinct tetrapod vertebrates, especially primates. Despite great promise, cancellous bone architecture has remained little utilized for investigating locomotion in many other extinct vertebrate groups, such as dinosaurs. Documentation and quantification of architectural patterns across a whole bone, and across multiple bones, can provide much information on cancellous bone architectural patterns and variation across species. Additionally, this also lends itself to analysis of the musculoskeletal biomechanical factors involved in a direct, mechanistic fashion. On this premise, computed tomographic and image analysis techniques were used to describe and analyse the three-dimensional architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs for the first time. A comprehensive survey across many extant and extinct species is produced, identifying several patterns of similarity and contrast between groups. For instance, more stemward non-avian theropods (e.g. ceratosaurs and tyrannosaurids) exhibit cancellous bone architectures more comparable to that present in humans, whereas species more closely related to birds (e.g. paravians) exhibit architectural patterns bearing greater similarity to those of extant birds. Many of the observed patterns may be linked to particular aspects of locomotor biomechanics, such as the degree of hip or knee flexion during stance and gait. A further important observation is the abundance of markedly oblique trabeculae in the diaphyses of the femur and tibia of birds, which in large species produces spiralling patterns along the endosteal surface. Not only do these observations provide new insight into theropod anatomy and behaviour, they also provide the foundation for mechanistic testing of locomotor hypotheses via musculoskeletal biomechanical modelling.

Cancellous bone and theropod dinosaur locomotion. Part II-a new approach to inferring posture and locomotor biomechanics in extinct tetrapod vertebrates

This paper is the second of a three-part series that investigates the architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and therefore has the potential to provide insight into locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part II, a new biomechanical modelling approach is outlined, one which mechanistically links cancellous bone architectural patterns with three-dimensional musculoskeletal and finite element modelling of the hindlimb. In particular, the architecture of cancellous bone is used to derive a single 'characteristic posture' for a given species-one in which bone continuum-level principal stresses best align with cancellous bone fabric-and thereby clarify hindlimb locomotor biomechanics. The quasi-static approach was validated for an extant theropod, the chicken, and is shown to provide a good estimate of limb posture at around mid-stance. It also provides reasonable predictions of bone loading mechanics, especially for the proximal hindlimb, and also provides a broadly accurate assessment of muscle recruitment insofar as limb stabilization is concerned. In addition to being useful for better understanding locomotor biomechanics in extant species, the approach hence provides a new avenue by which to analyse, test and refine palaeobiomechanical hypotheses, not just for extinct theropods, but potentially many other extinct tetrapod groups as well.

Cancellous bone and theropod dinosaur locomotion. Part III-Inferring posture and locomotor biomechanics in extinct theropods, and its evolution on the line to birds

This paper is the last of a three-part series that investigates the architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is highly sensitive to its prevailing mechanical environment, and may therefore help further understanding of locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part III, the biomechanical modelling approach derived previously was applied to two species of extinct, non-avian theropods, Daspletosaurus torosus and Troodon formosus. Observed cancellous bone architectural patterns were linked with quasi-static, three-dimensional musculoskeletal and finite element models of the hindlimb of both species, and used to derive characteristic postures that best aligned continuum-level principal stresses with cancellous bone fabric. The posture identified for Daspletosaurus was largely upright, with a subvertical femoral orientation, whilst that identified for Troodon was more crouched, but not to the degree observed in extant birds. In addition to providing new insight on posture and limb articulation, this study also tested previous hypotheses of limb bone loading mechanics and muscular control strategies in non-avian theropods, and how these aspects evolved on the line to birds. The results support the hypothesis that an upright femoral posture is correlated with bending-dominant bone loading and abduction-based muscular support of the hip, whereas a crouched femoral posture is correlated with torsion-dominant bone loading and long-axis rotation-based muscular support. Moreover, the results of this study also support the inference that hindlimb posture, bone loading mechanics and muscular support strategies evolved in a gradual fashion along the line to extant birds.

Bipedal gait versatility in the Japanese macaque (Macaca fuscata)

It was previously believed that, among primates, only humans run bipedally. However, there is now growing evidence that at least some non-human primates can not only run bipedally but can also generate a running gait with an aerial phase. Japanese macaques trained for bipedal performances have been known to exhibit remarkable bipedal locomotion capabilities, but no aerial-phase running has previously been reported. In the present study, we investigated whether Japanese macaques could run with an aerial phase by collecting bipedal gait sequences from three macaques on a level surface at self-selected speeds (n = 188). During our experiments, body kinematics and ground reaction forces were recorded by a motion-capture system and two force plates installed within a wooden walkway. Our results demonstrated that macaques were able to utilize a variety of bipedal gaits including grounded running, skipping, and even running with an aerial phase. The self-selected bipedal locomotion speed of the macaques was fast, with Froude speed ranging from 0.4 to 1.3. However, based on congruity, no single trial that could be categorized as a pendulum-like walking gait was observed. The parameters describing the temporal, kinematic, and dynamic characteristics of macaque bipedal running gaits follow the patterns previously documented for other non-human primates and terrestrial birds that use running gaits, but are different from those of humans and from birds' walking gaits. The present study confirmed that when a Japanese macaque engages in bipedal locomotion, even without an aerial phase, it generally utilizes a spring-like running mechanism because the animals have a limited ability to stiffen their legs. That limitation is due to anatomical restrictions determined by the morphology and structure of the macaque musculoskeletal system. The general adoption of grounded running in macaques and other non-human primates, along with its absence in human bipedal locomotion, suggests that abandonment of compliant gait was a critical transition in the evolution of human obligatory bipedalism.

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.