Mixed gaits in small avian terrestrial locomotion

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 (VPP_TL) and is roughly located above and caudally to the scapulothoracic joint. The second is located roughly above and cranially to the hip joint (VPP_PL). 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, VPP_PL 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 VPP_TL or the horizontal position of VPP_PL. The vertical position of VPP_PL was only influenced by gait, while the horizontal position of VPP_TL 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.

Effects of the speed on the webbed foot kinematics of mallard (Anas platyrhynchos)

In this study, the effect of the speed on the webbed foot locomotion of the mallard was analyzed based on a considerable number of reliable indoor test data. Four adult male mallards were selected for analysis, and the locomotion speed of the mallard was controlled using the treadmill at an accurate and adjustable speed. The locomotion pattern of the webbed foot of the mallard at different speeds was recorded using a high-speed camera. The changes in the position and conformation of the webbed foot during locomotion on a treadmill were tracked and analyzed using Simi-Motion kinematics software. The results indicated that the stride length of the mallard increased, and the stance phase duration was shortened with the increase of the speed, whereas the swing phase duration did not vary significantly. The duty factor decreased with the increase of the mallard speed but not drop below to 0.5, because the mallards flew with their wings, or moved backward relative to the treadmill with the further increase of the speed. Using the energy method to further distinguish gait, and through the percentage of congruity analysis, it was found that between 0.73 and 0.93 m/s, the gait experienced a transition from walking to grounded running, with no significant changes in spatiotemporal parameters. At speeds between 0.93 and 1.6 m/s, mallards adopt a grounded running gait. The instantaneous changes of the tarsometatarso-phalangeal joint (TMTPJ) angle and the intertarsal joint (ITJ) angle at touch-down, mid-stance and lift-off concomitant with the change of the speed were examined with the TMTPJ and ITJ angle as the research objects. Moreover, the continuous changes of the joint angles were examined in a complete stride cycle. The result indicated that the increase of the speed will also make the TMTPJ and ITJ angle change ahead of time in a stride cycle, proving the shortened stance phase duration. The ITJ angle changed much more than the TMTPJ. Thus, the above result reveals that the mallard primarily responds with the increase of the speed by adjusting the ITJ, instead of the TMTPJ. The vertical displacement of the toe joint points and the toe joint angle was studied (α joint angle is between the second toe and the third toe; β joint angle is between the third toe and the fourth toe) with a complete stride cycle as the research object. The distal phalanxes of the second, third and fourth toes first contacted the ground, and the proximal phalanx touched the ground in turn during the early stance phase duration of the mallard, as indicated by the result of this study. However, the toes got off the ground in turn from the proximal phalanxes when the mallard foot got off the ground. With the decrease of the interphalangeal α and β joint angles, the foot web tended to be close and rapidly recovered before the next touch-down. The above result reveals that the webbed foot of the mallard is a coupling system that plays a role in the adjustment of speed.

Tail feather strength in tail-assisted climbing birds is achieved through geometric, not material change

Birds encompass vast ecomorphological diversity and practise numerous distinct locomotor modes. One oft-cited feature seen in climbing birds is an increase in tail 'stiffness', yet it remains unclear to what extent these feathers are altered, and the specific mechanism by which differences in functional performance are attained. We collected a broad taxonomic sample of tail feathers (6525 total, from 774 species representing 21 avian orders and ranging in size from approximately 3 g to greater than 11 kg) and present data on their material properties, cross-sectional geometry and morphometrics. Ordinary and phylogenetic least-squares regressions of each variable versus body mass were conducted to assess scaling relationships and demonstrate that tail-supported climbers exhibit longer tail feathers with a wider rachis base and tip, and a greater second moment of area and maximum bending moment. However, no differences were observed in the material properties of the keratin itself. This suggests that tail-supported arboreal climbing birds of multiple orders have independently adopted similar morphologies. Moreover, these geometric relationships follow the same allometric scaling relationships as seen in the long bones of mammalian limbs, suggesting that the morphology of these developmentally and evolutionarily distinct structures are governed by similar functional constraints of weight support.

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.

Wading through water: effects of water depth and speed on the drag and kinematics of walking Chilean flamingos, Phoenicopterus chilensis

Wading behaviours, in which an animal walks while partially submerged in water, are present in a variety of taxa including amphibians, reptiles, mammals and birds. Despite the ubiquity of wading behaviours, few data are available to evaluate how animals adjust their locomotion to accommodate changes in water depth. Because drag from water might impose additional locomotor costs, wading animals might be expected to raise their feet above the water up to a certain point until such behaviours lead to awkward steps and are abandoned. To test for such mechanisms, we measured drag on models of the limbs of Chilean flamingos (Phoenicopterus chilensis) and measured their limb and body kinematics as they walked and waded through increasing depths of water in a zoo enclosure. Substantial drag was incurred by models of both open- and closed-toed feet, suggesting that flamingos could avoid some locomotor costs by stepping over water, rather than through it, during wading. Step height was highest while wading through intermediate water depths and while wading at a faster speed. Stride length increased with increasing water depth and velocity, and the limb joints generally flexed more while moving through intermediate water depths. However, movements of the head and neck were not strongly correlated with water depth or velocity. Our results show a wide range of kinematic changes that occur to allow wading birds to walk through different water depths, and have implications for better understanding the locomotor strategies employed by semi-aquatic species.

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.

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.

Duty Factor Is a Viable Measure to Classify Spontaneous Running Forms

Runners were classified using two different methods based on their spontaneous running form: (1) subjectively using the V®score from the Volodalen® scale, leading to terrestrial and aerial groups; and (2) objectively using the duty factor (DF), leading to high (DFhigh) and low (DFlow) DF groups. This study aimed to compare these two classification schemes. Eighty-nine runners were divided in two groups using the V®score (VOL groups) and were also ranked according to their DF. They ran on a treadmill at 12 km·h-1 with simultaneous recording of running kinematics, using a three-dimensional motion capture system. DF was computed from data as the ratio of ground contact time to stride time. The agreement (95% confidence interval) between VOL and DF groups was 79.8% (69.9%, 87.6%), with relatively high sensitivity (81.6% (68.0%, 91.2%)) and specificity (77.5% (61.6%, 89.2%)). Our results suggest that the DF and V®score reflect similar constructs and lead to similar subgroupings of spontaneous running form (aerial runners if DF < 27.6% and terrestrial runners if DF > 28.8% at 12 km·h-1). These results suggest that DF could be a useful objective measure to monitor real-time changes in spontaneous running form using wearable technology. As a forward-looking statement, spontaneous changes in running form during racing or training could assist in identifying fatigue or changes in environmental conditions, allowing for a better understanding of runners.

A dynamics and stability framework for avian jumping take-off

Jumping take-off in birds is an explosive behaviour with the goal of providing a rapid transition from ground to airborne locomotion. An effective jump is predicated on the need to maintain dynamic stability through the acceleration phase. The present study concerns understanding how birds retain control of body attitude and trajectory during take-off. Cursory observation suggests that stability is achieved with relatively little cost. However, analysis of the problem shows that the stability margins during jumping are actually very small and that stability considerations play a significant role in the selection of appropriate jumping kinematics. We use theoretical models to understand stability in prehensile take-off (from a perch) and also in non-prehensile take-off (from the ground). The primary instability is tipping, defined as rotation of the centre of gravity about the ground contact point. Tipping occurs when the centre of pressure falls outside the functional foot. A contribution of the paper is the development of graphical tipping stability margins for both centre of gravity location and acceleration angle. We show that the nose-up angular acceleration extends stability bounds forward and is hence helpful in achieving shallow take-offs. The stability margins are used to interrogate simulated take-offs of real birds using published experimental kinematic data from a guinea fowl (ground take-off) and a diamond dove (perch take-off). For the guinea fowl, the initial part of the jump is stable; however, simulations exhibit a stuttering instability not observed experimentally that is probably due to the absence of compliance in the idealized joints. The diamond dove model confirms that the foot provides an active torque reaction during take-off, extending the range of stable jump angles by around 45°.

Motion analysis of non-model organisms using a hierarchical model: Influence of setup enclosure dimensions on gait parameters of Swinhoe's striped squirrels as a test case

In in-vivo motion analyses, data from a limited number of subjects and trials is used as proxy for locomotion properties of entire populations, yet the inherent hierarchy of the individual and population level is usually not accounted for. Despite the increasing availability of hierarchical model frameworks for statistical analyses, they have not been applied extensively to comparative motion analysis. As a case study for the use of hierarchical models, we analyzed locomotor parameters of four Swinhoe's striped squirrels. The small-bodied arboreal mammals exhibit brief bouts of rapid asymmetric gaits. Spatio-temporal parameters on runways with experimentally varied dimensions of the setup enclosure were compared to test for their potentially confounding effects. We applied principal component analysis to evaluate changes to the overall locomotor pattern. A common, non-hierarchical, pooled statistical analysis of the data revealed significant differences in some of the parameters depending on enclosure dimensions. In contrast, we used a hierarchical Bayesian generalized linear model (GLM) that considers subject specific differences and population effects to compare the effect of enclosure dimensions on the measured parameters and the principal components. None of the population effects were confirmed by the hierarchical GLM. The confounding effect of a single subject that deviates in its locomotor behavior is potentially bigger than the influence of the experimental variation in enclosure dimensions. Our findings justify the common practice of researchers to intuitively select an enclosure with dimensions assumed as "non-constraining". Hierarchical models can easily be designed to cope with limited sample size and bias introduced by deviating behavior of individuals. When limited data is available-a typical restriction of in-vivo motion analyses of non-model organisms-density distributions of the Bayesian GLM used here remain reliable and the hierarchical structure of the model optimally exploits all available information. We provide code to be adjusted to other research questions.

Neuron-specific inactivation of Wt1 alters locomotion in mice and changes interneuron composition in the spinal cord

Locomotion is coordinated by neuronal circuits of the spinal cord. Recently, dI6 neurons were shown to participate in the control of locomotion. A subpopulation of dI6 neurons expresses the Wilms tumor suppressor gene Wt1. However, the function of Wt1 in these cells is not understood. Here, we aimed to identify behavioral changes and cellular alterations in the spinal cord associated with Wt1 deletion. Locomotion analyses of mice with neuron-specific Wt1 deletion revealed a slower walk with a decreased stride frequency and an increased stride length. These mice showed changes in their fore-/hindlimb coordination, which were accompanied by a loss of contralateral projections in the spinal cord. Neonates with Wt1 deletion displayed an increase in uncoordinated hindlimb movements and their motor neuron output was arrhythmic with a decreased frequency. The population size of dI6, V0, and V2a neurons in the developing spinal cord of conditional Wt1 mutants was significantly altered. These results show that the development of particular dI6 neurons depends on Wt1 expression and that loss of Wt1 is associated with alterations in locomotion.

The gibbon's Achilles tendon revisited: consequences for the evolution of the great apes?

The well-developed Achilles tendon in humans is generally interpreted as an adaptation for mechanical energy storage and reuse during cyclic locomotion. All other extant great apes have a short tendon and long-fibred triceps surae, which is thought to be beneficial for locomotion in a complex arboreal habitat as this morphology enables a large range of motion. Surprisingly, highly arboreal gibbons show a more human-like triceps surae with a long Achilles tendon. Evidence for a spring-like function similar to humans is not conclusive. We revisit and integrate our anatomical and biomechanical data to calculate the energy that can be recovered from the recoiling Achilles tendon during ankle plantar flexion in bipedal gibbons. Only 7.5% of the required external positive work in a stride can come from tendon recoil, yet it is delivered at an instant when the whole-body energy level drops. Consequently, an additional similar amount of mechanical energy must simultaneously dissipate elsewhere in the system. Altogether, this challenges the concept of an energy-saving function in the gibbon's Achilles tendon. Cercopithecids, sister group of the apes, also have a human-like triceps surae. Therefore, a well-developed Achilles tendon, present in the last common 'Cercopithecoidea-Hominoidea' ancestor, seems plausible. If so, the gibbon's anatomy represents an evolutionary relict (no harm-no benefit), and the large Achilles tendon is not the premised key adaptation in humans (although the spring-like function may have further improved during evolution). Moreover, the triceps surae anatomy of extant non-human great apes must be a convergence, related to muscle control and range of motion. This perspective accords with the suggestions put forward in the literature that the last common hominoid ancestor was not necessarily great ape-like, but might have been more similar to the small-bodied catarrhines.

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

How extinct, non-avian theropod dinosaurs moved is a subject of considerable interest and controversy. A better understanding of non-avian theropod locomotion can be achieved by better understanding terrestrial locomotor biomechanics in their modern descendants, birds. Despite much research on the subject, avian terrestrial locomotion remains little explored in regards to how kinematic and kinetic factors vary together with speed and body size. Here, terrestrial locomotion was investigated in twelve species of ground-dwelling bird, spanning a 1,780-fold range in body mass, across almost their entire speed range. Particular attention was devoted to the ground reaction force (GRF), the force that the feet exert upon the ground. Comparable data for the only other extant obligate, striding biped, humans, were also collected and studied. In birds, all kinematic and kinetic parameters examined changed continuously with increasing speed, while in humans all but one of those same parameters changed abruptly at the walk-run transition. This result supports previous studies that show birds to have a highly continuous locomotor repertoire compared to humans, where discrete 'walking' and 'running' gaits are not easily distinguished based on kinematic patterns alone. The influences of speed and body size on kinematic and kinetic factors in birds are developed into a set of predictive relationships that may be applied to extinct, non-avian theropods. The resulting predictive model is able to explain 79-93% of the observed variation in kinematics and 69-83% of the observed variation in GRFs, and also performs well in extrapolation tests. However, this study also found that the location of the whole-body centre of mass may exert an important influence on the nature of the GRF, and hence some caution is warranted, in lieu of further investigation.

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.

Investigating the running abilities of Tyrannosaurus rex using stress-constrained multibody dynamic analysis

The running ability of Tyrannosaurus rex has been intensively studied due to its relevance to interpretations of feeding behaviour and the biomechanics of scaling in giant predatory dinosaurs. Different studies using differing methodologies have produced a very wide range of top speed estimates and there is therefore a need to develop techniques that can improve these predictions. Here we present a new approach that combines two separate biomechanical techniques (multibody dynamic analysis and skeletal stress analysis) to demonstrate that true running gaits would probably lead to unacceptably high skeletal loads in T. rex. Combining these two approaches reduces the high-level of uncertainty in previous predictions associated with unknown soft tissue parameters in dinosaurs, and demonstrates that the relatively long limb segments of T. rex—long argued to indicate competent running ability—would actually have mechanically limited this species to walking gaits. Being limited to walking speeds contradicts arguments of high-speed pursuit predation for the largest bipedal dinosaurs like T. rex, and demonstrates the power of multiphysics approaches for locomotor reconstructions of extinct animals.

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.