Differential leg and trunk operation during skipping without and with hurdles in bipedal Japanese macaque.

When locomoting bipedally at higher speeds, macaques preferred unilateral skipping (galloping). The same skipping pattern was maintained while hurdling across two low obstacles at the distance of a stride within our experimental track. The present study investigated leg and trunk joint rotations and leg joint moments, with the aim of clarifying the differential leg and trunk operation during skipping in bipedal macaques. Especially at the hip, the range of joint rotation and extension at lift off was larger in the leading than in the trailing leg. The flexing knee absorbed energy and the extending ankle generated work during each step. The trunk showed only minor deviations from symmetry. Hurdling amplified the differences and notably resulted in a quasi-elastic use of the leading knee and in an asymmetric operation of the trunk.

Skipping without and with hurdles in bipedal macaque: global mechanics.

Macaques trained to perform bipedally used running gaits across a wide range of speeds. At higher speeds they preferred unilateral skipping (galloping). The same asymmetric stepping pattern was used while hurdling across two low obstacles placed at the distance of a stride within our experimental track. In bipedal macaques during skipping, we expected a differential use of the trailing and leading legs. The present study investigated global properties of the effective and virtual leg, the location of the virtual pivot point (VPP), and the energetics of the center of mass (CoM), with the aim of clarifying the differential leg operation during skipping in bipedal macaques. When skipping, macaques displayed minor double support and aerial phases during one stride. Asymmetric leg use was indicated by differences in leg kinematics. Axial damping and tangential leg work did not influence the indifferent peak ground reaction forces and impulses, but resulted in a lift of the CoM during contact of the leading leg. The aerial phase was largely due to the use of the double support. Hurdling amplified the differential leg operation. Here, higher ground reaction forces combined with increased double support provided the vertical impulse to overcome the hurdles. Following CoM dynamics during a stride, skipping and hurdling represented bouncing gaits. The elevation of the VPP of bipedal macaques resembled that of human walking and running in the trailing and leading phases, respectively. Because of anatomical restrictions, macaque unilateral skipping differs from that of humans, and may represent an intermediate gait between grounded and aerial running.

Positioning of pivot points in quadrupedal locomotion: limbs global dynamics in four different dog breeds.

Dogs (Canis familiaris) prefer the walk at lower speeds and the more economical trot at speeds ranging from 0.5 Fr up to 3 Fr. Important works have helped to understand these gaits at the levels of the center of mass, joint mechanics, and muscular control. However, less is known about the global dynamics for limbs and if these are gait or breed-specific. For walk and trot, we analyzed dogs' global dynamics, based on motion capture and single leg kinetic data, recorded from treadmill locomotion of French Bulldog (N = 4), Whippet (N = 5), Malinois (N = 4), and Beagle (N = 5). Dogs' pelvic and thoracic axial leg functions combined compliance with leg lengthening. Thoracic limbs were stiffer than the pelvic limbs and absorbed energy in the scapulothoracic joint. Dogs' ground reaction forces (GRF) formed two virtual pivot points (VPP) during walk and trot each. One emerged for the thoracic (fore) limbs (VPPTL) and is roughly located above and caudally to the scapulothoracic joint. The second is located roughly above and cranially to the hip joint (VPPPL). The positions of VPPs and the patterns of the limbs' axial and tangential projections of the GRF were gaits but not always breeds-related. When they existed, breed-related changes were mainly exposed by the French Bulldog. During trot, positions of the VPPs tended to be closer to the hip joint or the scapulothoracic joint, and variability between and within breeds lessened compared to walk. In some dogs, VPPPL was located below the pelvis during trot. Further analyses revealed that leg length and not breed may better explain differences in the vertical position of VPPTL or the horizontal position of VPPPL. The vertical position of VPPPL was only influenced by gait, while the horizontal position of VPPTL was not breed or gait-related. Accordingly, torque profiles in the scapulothoracic joint were likely between breeds while hip torque profiles were size-related. In dogs, gait and leg length are likely the main VPPs positions' predictors. Thus, variations of VPP positions may follow a reduction of limb work. Stability issues need to be addressed in further studies.

Limb, joint and pelvic kinematic control in the quail coping with steps upwards and downwards.

Small cursorial birds display remarkable walking skills and can negotiate complex and unstructured terrains with ease. The neuromechanical control strategies necessary to adapt to these challenging terrains are still not well understood. Here, we analyzed the 2D- and 3D pelvic and leg kinematic strategies employed by the common quail to negotiate visible steps (upwards and downwards) of about 10%, and 50% of their leg length. We used biplanar fluoroscopy to accurately describe joint positions in three dimensions and performed semi-automatic landmark localization using deep learning. Quails negotiated the vertical obstacles without major problems and rapidly regained steady-state locomotion. When coping with step upwards, the quail mostly adapted the trailing limb to permit the leading leg to step on the elevated substrate similarly as it did during level locomotion. When negotiated steps downwards, both legs showed significant adaptations. For those small and moderate step heights that did not induce aerial running, the quail kept the kinematic pattern of the distal joints largely unchanged during uneven locomotion, and most changes occurred in proximal joints. The hip regulated leg length, while the distal joints maintained the spring-damped limb patterns. However, to negotiate the largest visible steps, more dramatic kinematic alterations were observed. There all joints contributed to leg lengthening/shortening in the trailing leg, and both the trailing and leading legs stepped more vertically and less abducted. In addition, locomotion speed was decreased. We hypothesize a shift from a dynamic walking program to more goal-directed motions that might be focused on maximizing safety.

Single limb dynamics of jumping turns in dogs.

Maneuverability is of paramount importance for many animals, e.g., in predator-prey interactions. Despite this fact, quadrupedal limb behavior in complicated maneuvers like simultaneous jumping and turning are not well studied. Twenty adult sport Border Collies were recorded while jumping over an obstacle and simultaneously turning. Kinetic and kinematic data were captured in synchrony using eight force plates and sixteen infrared cameras. These dogs were familiar with the task through regular participation in the dog sport agility. The experiments revealed that during landing, higher lateral forces acting in the forelimbs compared to hindlimbs. During landing, the outer limbs produced about twice the inner limbs' force in both vertical and lateral directions, showing their dominant contribution to turning. Advanced dogs showed significantly higher lateral impulse and stronger inner-outer limb asymmetry regarding lateral impulses than beginner dogs, leading to significantly stronger turning for advanced dogs. Somewhat unexpected, skill effects rarely explained global limb dynamics, indicating that landing a turn jump is a constrained motion. Constrained motions leave little space for individual techniques suggesting that the results can be generalized to quadrupedal turn jumps in other animals.

A three-dimensional musculoskeletal model of the dog.

The domestic dog is interesting to investigate because of the wide range of body size, body mass, and physique in the many breeds. In the last several years, the number of clinical and biomechanical studies on dog locomotion has increased. However, the relationship between body structure and joint load during locomotion, as well as between joint load and degenerative diseases of the locomotor system (e.g. dysplasia), are not sufficiently understood. Collecting this data through in vivo measurements/records of joint forces and loads on deep/small muscles is complex, invasive, and sometimes unethical. The use of detailed musculoskeletal models may help fill the knowledge gap. We describe here the methods we used to create a detailed musculoskeletal model with 84 degrees of freedom and 134 muscles. Our model has three key-features: three-dimensionality, scalability, and modularity. We tested the validity of the model by identifying forelimb muscle synergies of a walking Beagle. We used inverse dynamics and static optimization to estimate muscle activations based on experimental data. We identified three muscle synergy groups by using hierarchical clustering. The activation patterns predicted from the model exhibit good agreement with experimental data for most of the forelimb muscles. We expect that our model will speed up the analysis of how body size, physique, agility, and disease influence neuronal control and joint loading in dog locomotion.

Three-dimensional motion of the patella in French bulldogs with and without medial patellar luxation.

BACKGROUND: French bulldogs exhibit significantly larger femoral external rotation and abduction than other breeds. We were curious as to whether this peculiar leg kinematic affects patellar motion and/or might induce medial patellar subluxation (MPSL) or medial patellar permanent luxation (MPPL). We hypothesized that the more abducted leg posture during stance causes an unusual medial pull direction of the rectus femoris muscle during stance, and that this may facilitate the occurrence of MPSL or even MPPL during locomotion. To test our hypothesis, we analyzed existing stifle-joint X-ray-sequences collected during the treadmill walk and trot of seven adult female French bulldogs. We estimated 3D-patellar kinematics using Scientific Rotoscoping. RESULTS: The three-dimensional motion of the patella comprises rotations and translations. From the seven dogs analyzed, three exhibited MPSL and one MPPL during the gait cycle. Medial patellar luxation (MPL) occurred mostly around toe-off in both gaits studied. Patellar position was generally not gait-related at the analyzed timepoints. In dogs with MPL, the patella was placed significantly more distally (p = 0.037) at touch-down (TD) and at midswing (p = 0.024), and significantly more medial at midswing (p = 0.045) compared to dogs without MPL. CONCLUSIONS: Medial patellar luxation seems to be the consequence of the far from parasagittal position of the stifle joint during stance due to a broad trunk, and a wide pelvis. This peculiar leg orientation leads to a medial sideway pull caused by the rectus femoris muscle and the quadriceps femoris and may initiate plastic deformation of the growing femur and tibia. Thus, a way to avoid MPL could be to control breeding by selecting dogs with lean bodies and narrow pelvis. Actual breeding control programs based on the orthopedic examination are susceptible to errors. Systematic errors arise from the fact that the grading system is highly dependent on the dog's condition and the veterinarians' ability to perform the palpation on the stifle. Based on our results, the position of the patella at TD, or even perhaps during stand might offer a possibility of an objective radioscopic diagnostic of the MPL.

Trunk and leg kinematics of grounded and aerial running in bipedal macaques.

Across a wide range of Froude speeds, non-human primates such as macaques prefer to use grounded and aerial running when locomoting bipedally. Both gaits are characterized by bouncing kinetics of the center of mass. In contrast, a discontinuous change from pendular to bouncing kinetics occurs in human locomotion. To clarify the mechanism underlying these differences in bipedal gait mechanics between humans and non-human primates, we investigated the influence of gait on joint kinematics in the legs and trunk of three macaques crossing an experimental track. The coordination of movement was compared with observations available for primates. Compared with human running, macaque leg retraction cannot merely be produced by hip extension, but needs to be supported by substantial knee flexion. As a result, despite quasi-elastic whole-leg operation, the macaque's knee showed only minor rebound behavior. Ankle extension resembled that observed during human running. Unlike human running and independent of gait, torsion of the trunk represents a rather conservative feature in primates, and pelvic axial rotation added to step length. Pelvic lateral lean during grounded running by macaques (compliant leg) and human walking (stiff leg) depends on gait dynamics at the same Froude speed. The different coordination between the thorax and pelvis in the sagittal plane as compared with human runners indicates different bending modes of the spine. Morphological adaptations in non-human primates to quadrupedal locomotion may prevent human-like operation of the leg and limit exploitation of quasi-elastic leg operation despite running dynamics.

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.

Limb dynamics in agility jumps of beginner and advanced dogs.

A considerable body of work has examined the dynamics of different dog gaits, but there are no studies that have focused on limb dynamics in jumping. Jumping is an essential part of dog agility, a dog sport in which handlers direct their dogs through an obstacle course in a limited time. We hypothesized that limb parameters like limb length and stiffness indicate the skill level of dogs. We analyzed global limb parameters in jumping for 10 advanced and 10 beginner dogs. In experiments, we collected 3D kinematics and ground reaction forces during dog jumping at high forward speeds. Our results revealed general strategies of limb control in jumping and highlighted differences between advanced and beginner dogs. In take-off, the spatially leading forelimb was 75% (P<0.001) stiffer than the trailing forelimb. In landing, the trailing forelimb was 14% stiffer (P<0.001) than the leading forelimb. This indicates a strut-like action of the forelimbs to achieve jumping height in take-off and to transfer vertical velocity into horizontal velocity in landing (with switching roles of the forelimbs). During landing, the more (24%) compliant forelimbs of beginner dogs (P=0.005) resulted in 17% (P=0.017) higher limb compression during the stance phase. This was associated with a larger amount of eccentric muscle contraction, which might in turn explain the soft tissue injuries that frequently occur in the shoulder region of beginner dogs. For all limbs, limb length at toe-off was greater for advanced dogs. Hence, limb length and stiffness might be used as objective measures of skill.

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.

Neuromechanical Model of Rat Hindlimb Walking with Two-Layer CPGs.

This work demonstrates a neuromechanical model of rat hindlimb locomotion undergoing nominal walking with perturbations. In the animal, two types of responses to perturbations are observed: resetting and non-resetting deletions. This suggests that the animal locomotor system contains a memory-like organization. To model this phenomenon, we built a synthetic nervous system that uses separate rhythm generator and pattern formation layers to activate antagonistic muscle pairs about each joint in the sagittal plane. Our model replicates the resetting and non-resetting deletions observed in the animal. In addition, in the intact (i.e., fully afferented) rat walking simulation, we observe slower recovery after perturbation, which is different from the deafferented animal experiment. These results demonstrate that our model is a biologically feasible description of some of the neural circuits in the mammalian spinal cord that control locomotion, and the difference between our simulation and fictive motion shows the importance of sensory feedback on motor output. This model also demonstrates how the pattern formation network can activate muscle synergies in a coordinated way to produce stable walking, which motivates the use of more complex synergies activating more muscles in the legs for three-dimensional limb motion.

Reverse-engineering the locomotion of a stem amniote.

Reconstructing the locomotion of extinct vertebrates offers insights into their palaeobiology and helps to conceptualize major transitions in vertebrate evolution1-4. However, estimating the locomotor behaviour of a fossil species remains a challenge because of the limited information preserved and the lack of a direct correspondence between form and function5,6. The evolution of advanced locomotion on land-that is, locomotion that is more erect, balanced and mechanically power-saving than is assumed of anamniote early tetrapods-has previously been linked to the terrestrialization and diversification of amniote lineages7. To our knowledge, no reconstructions of the locomotor characteristics of stem amniotes based on multiple quantitative methods have previously been attempted: previous methods have relied on anatomical features alone, ambiguous locomotor information preserved in ichnofossils or unspecific modelling of locomotor dynamics. Here we quantitatively examine plausible gaits of the stem amniote Orobates pabsti, a species that is known from a complete body fossil preserved in association with trackways8. We reconstruct likely gaits that match the footprints, and investigate whether Orobates exhibited locomotor characteristics that have previously been linked to the diversification of crown amniotes. Our integrative methodology uses constraints derived from biomechanically relevant metrics, which also apply to extant tetrapods. The framework uses in vivo assessment of locomotor mechanics in four extant species to guide an anatomically informed kinematic simulation of Orobates, as well as dynamic simulations and robotics to filter the parameter space for plausible gaits. The approach was validated using two extant species that have different morphologies, gaits and footprints. Our metrics indicate that Orobates exhibited more advanced locomotion than has previously been assumed for earlier tetrapods7,9, which suggests that advanced terrestrial locomotion preceded the diversification of crown amniotes. We provide an accompanying website for the exploration of the filters that constrain our simulations, which will allow revision of our approach using new data, assumptions or methods.

Global dynamics of bipedal macaques during grounded and aerial running.

Macaques trained to perform bipedally use grounded running, skipping and aerial running, but avoid walking. The preference for grounded running across a wide range of speeds is substantially different from the locomotion habits observed in humans, which may be the result of differences in leg compliance. In the present study, based on kinematic and dynamic observations of three individuals crossing an experimental track, we investigated global leg properties such as leg stiffness and viscous damping during grounded and aerial running. We found that, in macaques, similar to human and bird bipedal locomotion, the vector of the ground reaction force is directed from the center of pressure (COP) to a virtual pivot point above the center of mass (COM). The visco-elastic leg properties differ for the virtual leg (COM-COP) and the effective leg (hip-COP) because of the position of the anatomical hip with respect to the COM. The effective leg shows damping in the axial direction and positive work in the tangential component. Damping does not prevent the exploration of oscillatory modes. Grounded running is preferred to walking because of leg compliance. The transition from grounded to aerial running is not accompanied by a discontinuous change. With respect to dynamic properties, macaques seem to be well placed between bipedal specialists (humans and birds). We speculate that the losses induced in the effective leg by hip placement and slightly pronograde posture may not pay off by facilitating stabilization, making bipedal locomotion expensive and insecure for macaques.

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.

Three-dimensional kinematics of canine hind limbs: in vivo, biplanar, high-frequency fluoroscopic analysis of four breeds during walking and trotting.

The first high-precision 3D in vivo hindlimb kinematic data to be recorded in normal dogs of four different breeds (Beagle, French bulldog, Malinois, Whippet) using biplanar, high-frequency fluoroscopy combined with a 3D optoelectric system followed by a markerless XROMM analysis (Scientific Rotoscoping, SR or 3D-2D registration process) reveal a) 3D hindlimb kinematics to an unprecedented degree of precision and b) substantial limitations to the use of skin marker-based data. We expected hindlimb kinematics to differ in relation to body shape. But, a comparison of the four breeds sets the French bulldog aside from the others in terms of trajectories in the frontal plane (abduction/adduction) and long axis rotation of the femur. French bulldogs translate extensive femoral long axis rotation (>30°) into a strong lateral displacement and rotations about the craniocaudal (roll) and the distal-proximal (yaw) axes of the pelvis in order to compensate for a highly abducted hindlimb position from the beginning of stance. We assume that breeds which exhibit unusual kinematics, especially high femoral abduction, might be susceptible to a higher long-term loading of the cruciate ligaments.

Skipping on uneven ground: trailing leg adjustments simplify control and enhance robustness.

It is known that humans intentionally choose skipping in special situations, e.g. when descending stairs or when moving in environments with lower gravity than on Earth. Although those situations involve uneven locomotion, the dynamics of human skipping on uneven ground have not yet been addressed. To find the reasons that may motivate this gait, we combined experimental data on humans with numerical simulations on a bipedal spring-loaded inverted pendulum model (BSLIP). To drive the model, the following parameters were estimated from nine subjects skipping across a single drop in ground level: leg lengths at touchdown, leg stiffness of both legs, aperture angle between legs, trailing leg angle at touchdown (leg landing first after flight phase), and trailing leg retraction speed. We found that leg adjustments in humans occur mostly in the trailing leg (low to moderate leg retraction during swing phase, reduced trailing leg stiffness, and flatter trailing leg angle at lowered touchdown). When transferring these leg adjustments to the BSLIP model, the capacity of the model to cope with sudden-drop perturbations increased.

Three-dimensional inverse dynamics of the forelimb of Beagles at a walk and trot.

OBJECTIVE To perform 3-D inverse dynamics analysis of the entire forelimb of healthy dogs during a walk and trot. ANIMALS 5 healthy adult Beagles. PROCEDURES The left forelimb of each dog was instrumented with 19 anatomic markers. X-ray fluoroscopy was used to optimize marker positions and perform scientific rotoscoping for 1 dog. Inverse dynamics were computed for each dog during a walk and trot on the basis of data obtained from an infrared motion-capture system and instrumented quad-band treadmill. Morphometric data were obtained from a virtual reconstruction of the left forelimb generated from a CT scan of the same dog that underwent scientific rotoscoping. RESULTS Segmental angles, torque, and power patterns were described for the scapula, humerus, ulna, and carpus segments in body frame. For the scapula and humerus, the kinematics and dynamics determined from fluoroscopy-based data varied substantially from those determined from the marker-based data. The dominant action of scapular rotation for forelimb kinematics was confirmed. Directional changes in the torque and power patterns for each segment were fairly consistent between the 2 gaits, but the amplitude of those changes was often greater at a trot than at a walk. CONCLUSIONS AND CLINICAL RELEVANCE Results indicated that control of the forelimb joints of dogs is similar for both a walk and trot. Rotation of the forelimb around its longitudinal axis and motion of the scapula should be reconsidered in the evaluation of musculoskeletal diseases, especially before and after treatment or rehabilitation.

Stability in skipping gaits.

As an alternative to walking and running, humans are able to skip. However, adult humans avoid it. This fact seems to be related to the higher energetic costs associated with skipping. Still, children, some birds, lemurs and lizards use skipping gaits during daily locomotion. We combined experimental data on humans with numerical simulations to test whether stability and robustness motivate this choice. Parameters for modelling were obtained from 10 male subjects. They locomoted using unilateral skipping along a 12 m runway. We used a bipedal spring loaded inverted pendulum to model and to describe the dynamics of skipping. The subjects displayed higher peak ground reaction forces and leg stiffness in the first landing leg (trailing leg) compared to the second landing leg (leading leg). In numerical simulations, we found that skipping is stable across an amazing speed range from skipping on the spot to fast running speeds. Higher leg stiffness in the trailing leg permits longer strides at same system energy. However, this strategy is at the same time less robust to sudden drop perturbations than skipping with a stiffer leading leg. A slightly higher stiffness in the leading leg is most robust, but might be costlier.

Morphology and motion: hindlimb proportions and swing phase kinematics in terrestrially locomoting charadriiform birds.

Differing limb proportions in terms of length and mass, as well as differences in mass being concentrated proximally or distally, influence the limb's moment of inertia (MOI), which represents its resistance to being swung. Limb morphology - including limb segment proportions - thus probably has direct relevance for the metabolic cost of swinging the limb during locomotion. However, it remains largely unexplored how differences in limb proportions influence limb kinematics during swing phase. To test whether differences in limb proportions are associated with differences in swing phase kinematics, we collected hindlimb kinematic data from three species of charadriiform birds differing widely in their hindlimb proportions: lapwings, oystercatchers and avocets. Using these three species, we tested for differences in maximum joint flexion, maximum joint extension and range of motion (RoM), in addition to differences in maximum segment angular velocity and excursion. We found that the taxa with greater limb MOI - oystercatchers and avocets - flex their limbs more than lapwings. However, we found no consistent differences in joint extension and RoM among species. Likewise, we found no consistent differences in limb segment angular velocity and excursion, indicating that differences in limb inertia in these three avian species do not necessarily underlie the rate or extent of limb segment movements. The observed increased limb flexion among these taxa with distally heavy limbs resulted in reduced MOI of the limb when compared with a neutral pose. A trade-off between exerting force to actively flex the limb and potential savings by a reduction of MOI is skewed towards reducing the limb's MOI as a result of MOI being in part a function of the radius of gyration squared. Increased limb flexion is a likely means to lower the cost of swinging the limbs.