Symmetrical gaits of dogs in relation to body build

Amphibious robotic dog: design, paddling gait planning, and experimental characterization

Mammal-inspired quadruped robots excel in traversing diverse terrestrial terrains but often lack aquatic mobility, limiting their effectiveness in amphibious environments. To address this challenge, an amphibious robotic dog (ARD) was developed, integrating efficient paddling gait in water with trotting capabilities on land. A canine-inspired paddling trajectory was first developed for a two-segment leg, and validated through theoretical modeling and experimental measurements of hydrodynamic forces. A waterproof ARD was then fabricated, with careful consideration of center-of-gravity and center-of-buoyancy relationships to ensure stable aquatic movement. Three distinct paddling gaits were developed and tested to evaluate the ARD's swimming speed and stability: two lateral sequence paddling gaits (LSPG) featuring 25% and 33% power phases (PP), and one trot-like paddling gait (TLPG) featuring a 50% PP. Theoretical modeling and numerical calculations were conducted to analyze the stability of different paddling gaits. Static water experiments measured gait-specific hydrodynamic forces, followed by dynamic swimming tests demonstrating that LSPG delivers superior propulsion and speed, while TLPG offers enhanced stability. The ARD achieved a maximum water speed of 0.16 m s-1(0.54 BL s-1) and a land speed of 0.35 m s-1(1.2 BL s-1). These findings provide theoretical and practical guidance for the development of mammal-inspired amphibious quadruped robots, particularly in structural design and paddling gait planning.

Assessing the Determinants of Platyrrhine Quadrupedal Gait Kinematics in an Ecological and Phylogenetic Framework

Laboratory studies have broadened our understanding of primate arboreal locomotor biomechanics and adaptation but are necessarily limited in species availability and substrate complexity. In this field study, we filmed the locomotion of 11 species of platyrrhines (Ecuador and Costa Rica; n = 1234 strides) and remotely measured substrate diameter and orientation. We then explored ecological and phylogenetic influences on quadrupedal kinematics in multivariate space using redundancy analysis combined with variation partitioning. Among all species, phylogenetic relatedness more strongly influenced quadrupedal kinematics than variation in substrate. Callitrichines were maximally divergent from other taxa, driven by their preferred use of higher speed asymmetrical gaits. Pitheciids were also distinctive in their use of lower limb phases, including lateral sequence gaits. The biomechanical implications of interspecific differences in body mass and limb proportions account for a substantial portion of the phylogenetic-based variation. Body mass and kinematic variation were inversely related-whereas the larger taxa (atelids) were relatively restricted in kinematic space, and preferred more stable, symmetrical gaits, the smallest species (callitrichines) used faster, more asymmetrical and less cautious gaits along with symmetrical gaits. Intermembral index had a positive relationship with limb phase, consistent with higher limb phases in atelines compared to pitheciids. Substrate alone accounted for only 2% of kinematic variation among all taxa, with substrate orientation influencing kinematics more than diameter. Substrate effects, though weak, were generally consistent with predictions and with previous laboratory and field-based research. Excluding callitrichines and asymmetrical gaits, the influence of substrate alone remained low (2%), and the phylogenetic signal dropped from 31% to 8%. The substantial residual kinematic variation may be attributable to substrate or morphological variables not measured here, but could also reflect basic biomechanical patterns shared by all taxa that serve them well when moving arboreally, regardless of the challenges provided by any particular substrate.

Spatiotemporal walking gait kinematics of semi-arboreal red pandas (Ailurus fulgens)

Semi-arboreal mammals must routinely cope with the differing biomechanical challenges of terrestrial versus arboreal locomotion; however, it is not clear to what extent semi-arboreal mammals adjust footfall patterns when moving on different substrates. We opportunistically filmed quadrupedal locomotion (n = 132 walking strides) of semi-arboreal red pandas (Ailurus fulgens; n = 3) housed at Cleveland Metroparks Zoo and examined the effects of substrate type on spatiotemporal gait kinematic variables using linear mixed models. We further investigated the effects of substrate diameter and orientation on arboreal gait kinematics. Red pandas exclusively used lateral sequence (LS) gaits and most frequently utilized LS lateral couplet gaits across terrestrial and arboreal substrates. Red pandas moved significantly slower (p < 0.001), and controlling for speed, had significantly greater relative stride length (p < 0.001), mean stride duration (p = 0.002), mean duty factor (p < 0.001), and mean number of supporting limbs (p < 0.001) during arboreal locomotion. Arboreal strides on inclined substrates were characterized by significantly faster relative speeds and increased limb phase values compared with those horizontal and declined substrates. These kinematics adjustments help to reduce substrate oscillations thereby promoting stability on potentially precarious arboreal substrates. Red panda limb phase values are similar to those of (primarily terrestrial) Carnivora examined to date. Despite the similarity in footfall patterns during arboreal and terrestrial locomotion, flexibility in other kinematic variables is important for semi-arboreal red pandas that must navigate disparate biomechanical challenges inherent to arboreal versus terrestrial locomotion.

Locomotor characteristics of the ground-walking chameleon Brookesia superciliaris

Understanding the locomotor characteristics of early diverging ground-walking chameleons (members of the genera Brookesia, Rhampholeon, Palleon, and Rieppeleon) can help to explain how their unique morphology is adapted to fit their environment and mode of life. However, nearly all quantitative studies of chameleon locomotion thus far have focused on the larger "true arboreal" chameleons. We investigated kinematics and spatiotemporal gait characteristics of the Brown Leaf Chameleon (Brookesia superciliaris) on different substrates and compared them with true arboreal chameleons, nonchameleon lizards, and other small arboreal animals. Brookesia exhibits a combination of locomotor traits, some of which are traditionally arboreal, others more terrestrial, and a few that are very unusual. Like other chameleons, Brookesia moved more slowly on narrow dowels than on broad planks (simulating arboreal and terrestrial substrates, respectively), and its speed was primarily regulated by stride frequency rather than stride length. While Brookesia exhibits the traditionally arboreal trait of a high degree of humeral protraction at the beginning of stance, unlike most arboreal tetrapods, it uses smaller shoulder and hip excursions on narrower substrates, possibly reflecting its more terrestrial habits. When moving at very slow speeds, Brookesia often adopts an unusual footfall pattern, lateral-sequence lateral-couplets. Because Brookesia is a member of one of the earliest-diverging groups of chameleons, its locomotion may provide a good model for an intermediate stage in the evolution of arboreal chameleons. Thus, the transition to a fully arboreal way of life in "true arboreal" chameleons may have involved changes in spatiotemporal and kinematic characteristics as well as morphology.

Diagonal-couplet gaits on discontinuous supports in Japanese macaques and implications for the adaptive significance of the diagonal-sequence, diagonal-couplet gait of primates

OBJECTIVES

Diagonal-sequence, diagonal-couplet (DSDC) gaits have been proposed as an adaptation to travel on discontinuously arranged arboreal branches. Only a few studies have examined primate gait adjustment to support discontinuity. We analyzed the gaits of Japanese macaques walking on the "ground" and two discontinuous conditions, "circle" and "point," to better understand the advantages of DSDC gaits on discontinuous supports.

MATERIALS AND METHODS

Seventy-eight vertical posts, each with a circular upper surface, were arranged in four rows at a spacing of 200 mm. The diameter of the circular upper surface was 150 mm ("circle condition") or 50 mm ("point condition"). We calculated the limb phase, duty factor, and time interval from hindlimb touchdown to ipsilateral forelimb liftoff. The supports the fore- and hindlimbs landed on during walking were identified in the circle and point condition.

RESULTS

The macaques predominantly used DSDC gaits in the ground and circle conditions and lateral-sequence, diagonal-couplet (LSDC) gaits in the point condition. The macaques usually placed their hindlimbs on the same supports as their ipsilateral forelimbs during the gait cycle.

DISCUSSION

Japanese macaques overlapped the ipsilateral fore- and hindlimb stance phase in all DSDC and some LSDC gaits to proximate the ipsilateral limbs on the discontinuous support, allowing the forelimb to guide the hindlimb placement to the support. The overlap duration of the ipsilateral limb stance phases may be extended by DSDC gaits longer than by LSDC gaits, allowing for a direct pass of the support being held by the prehensile hand to the prehensile foot.

Eigenproperties of perception (dynamic touch) and action (phase dynamic) out of diversities

This study explores perception-action heuristics from a fundamental theoretical perspective to describe the comprehensive frameworks of movement as a process within a system dynamic. We address issues related to the identification of dynamics by using a nonrepresentational perspective, namely, functional nonlinearity. Experimental-based tools and calculation procedures for perception (dynamic touch) and action (inter-limb synchrony) revealed a basic pattern of response. The applied models and analyses strongly reflect the invariant principles of a collective structure, which could be the key to understanding complex behavioral processes with simple underlying properties. Our results provide an empirical perspective on dynamic systems and may potentially lead to a set of interconnected elements whose interactions lead to various syntheses.

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.

Fore-Aft Asymmetry Improves the Stability of Trotting in the Transverse Plane: A Modeling Study

Quadrupedal mammals have fore-aft asymmetry in their body structure, which affects their walking and running dynamics. However, the effects of asymmetry, particularly in the transverse plane, remain largely unclear. In this study, we examined the effects of fore-aft asymmetry on quadrupedal trotting in the transverse plane from a dynamic viewpoint using a simple model, which consists of two rigid bodies connected by a torsional joint with a torsional spring and four spring legs. Specifically, we introduced fore-aft asymmetry into the model by changing the physical parameters between the fore and hind parts of the model based on dogs, which have a short neck, and horses, which have a long neck. We numerically searched the periodic solutions for trotting and investigated the obtained solutions and their stability. We found that three types of periodic solutions with different foot patterns appeared that depended on the asymmetry. Additionally, the asymmetry improved gait stability. Our findings improve our understanding of gait dynamics in quadrupeds with fore-aft asymmetry.

Control of Mammalian Locomotion by Somatosensory Feedback

When animals walk overground, mechanical stimuli activate various receptors located in muscles, joints, and skin. Afferents from these mechanoreceptors project to neuronal networks controlling locomotion in the spinal cord and brain. The dynamic interactions between the control systems at different levels of the neuraxis ensure that locomotion adjusts to its environment and meets task demands. In this article, we describe and discuss the essential contribution of somatosensory feedback to locomotion. We start with a discussion of how biomechanical properties of the body affect somatosensory feedback. We follow with the different types of mechanoreceptors and somatosensory afferents and their activity during locomotion. We then describe central projections to locomotor networks and the modulation of somatosensory feedback during locomotion and its mechanisms. We then discuss experimental approaches and animal models used to investigate the control of locomotion by somatosensory feedback before providing an overview of the different functional roles of somatosensory feedback for locomotion. Lastly, we briefly describe the role of somatosensory feedback in the recovery of locomotion after neurological injury. We highlight the fact that somatosensory feedback is an essential component of a highly integrated system for locomotor control. © 2021 American Physiological Society. Compr Physiol 11:1-71, 2021.

Three-Dimensional Kinematics of the Pelvis and Caudal Lumbar Spine in German Shepherd Dogs

Lumbosacral vertebral motion is thought to be a factor in the development of degenerative lumbosacral stenosis in German shepherd dogs. So far, few studies exist describing natural canine lumbosacral movement in vivo. Therefore, this investigation aims to achieve a detailed in vivo analysis of bone movement of the lumbosacral region to gain a better understanding of the origin of degenerative lumbosacral stenosis using three-dimensional non-invasive in vivo analysis of canine pelvic and caudal lumbar motion (at L6 and L7). Biplanar cineradiography of the pelvis and caudal lumbar spine of four clinically sound German shepherd dogs at a walk and at a trot on a treadmill was recorded. Pelvic and intervertebral motion was virtually reconstructed and analyzed with scientific rotoscoping. The use of this technique made possible non-invasive measurement of physiological vertebral motion in dogs with high accuracy. Furthermore, the gait patterns of the dogs revealed a wide variation both between individual steps and between dogs. Pelvic motion showed a common basic pattern throughout the stride cycle. Motion at L6 and L7, except for sagittal rotation at a trot, was largely asynchronous with the stride cycle. Intervertebral motion in all dogs was small with approximately 2–3° rotation and translations of approximately 1–2 mm. The predominant motion of the pelvis was axial rotation at a walk, whereas lateral rotation was predominant at a trot. L7 showed a predominance of sagittal rotation (with up to 5.1° at a trot), whereas lateral rotation was the main component of the movement at L6 (about 2.3° in both gaits). During trotting, a coupling of various motions was detected: axial rotation of L7 and the pelvis was inverse and was coupled with craniocaudal translation of L7. In addition, a certain degree of compensation of abnormal pelvic movements during walking and trotting by the caudal lumbar spine was evident.

Three-Dimensional Kinematic Motion of the Craniocervical Junction of Chihuahuas and Labrador Retrievers

All vertebrate species have a distinct morphology and movement pattern, which reflect the adaption of the animal to its habitat. Yet, our knowledge of motion patterns of the craniocervical junction of dogs is very limited. The aim of this prospective study is to perform a detailed analysis and description of three-dimensional craniocervical motion during locomotion in clinically sound Chihuahuas and Labrador retrievers. This study presents the first in vivo recorded motions of the craniocervical junction of clinically sound Chihuahuas (n = 8) and clinically sound Labrador retrievers (n = 3) using biplanar fluoroscopy. Scientific rotoscoping was used to reconstruct three-dimensional kinematics during locomotion. The same basic motion patterns were found in Chihuahuas and Labrador retrievers during walking. Sagittal, lateral, and axial rotation could be observed in both the atlantoaxial and the atlantooccipital joints during head motion and locomotion. Lateral and axial rotation occurred as a coupled motion pattern. The amplitudes of axial and lateral rotation of the total upper cervical motion and the atlantoaxial joint were higher in Labrador retrievers than in Chihuahuas. The range of motion (ROM) maxima were 20°, 26°, and 24° in the sagittal, lateral, and axial planes, respectively, of the atlantoaxial joint. ROM maxima of 30°, 16°, and 18° in the sagittal, lateral, and axial planes, respectively, were found at the atlantooccipital joint. The average absolute sagittal rotation of the atlas was slightly higher in Chihuahuas (between 9.1 ± 6.8° and 18.7 ± 9.9°) as compared with that of Labrador retrievers (between 5.7 ± 4.6° and 14.5 ± 2.6°), which corresponds to the more acute angle of the atlas in Chihuahuas. Individual differences for example, varying in amplitude or time of occurrence are reported.

Evolutionary history of quadrupedal walking gaits shows mammalian release from locomotor constraint

Vertebrates employ an impressive range of strategies for coordinating their limb movements while walking. Although this gait variation has been quantified and hypotheses for its origins tested in select tetrapod lineages, a comprehensive understanding of gait evolution in a macroevolutionary context is currently lacking. We used freely available internet videos to nearly double the number of species with quantitative gait data, and used phylogenetic comparative methods to test key hypotheses about symmetrical gait origin and evolution. We find strong support for an ancestral lateral-sequence diagonal-couplet gait in quadrupedal gnathostomes, and this mode is remarkably conserved throughout tetrapod phylogeny. Evolutionary rate analyses show that mammals overcame this ancestral constraint, resulting in a greater range of phase values than any other tetrapod lineage. Diagonal-sequence diagonal-couplet gaits are significantly associated with arboreality in mammals, though this relationship is not recovered for other tetrapod lineages. Notably, the lateral-sequence lateral-couplet gait, unique to mammals among extant tetrapods, is not associated with any traditional explanations. The complex drivers of gait diversification in mammals remain unclear, but our analyses suggest that their success was due, in part, to release from a locomotor constraint that has probably persisted in other extant tetrapod lineages for over 375 Myr.

The effect of a traditional and a stick gang-line on the body position of working sled dogs

This study aimed to investigate the effect of two different gang-lines on the pulling angle of sled dogs. It was hypothesised that dogs would run with a straighter angle of pull (in relation to the main-line) in stick gang-lines (STICK) than they would do in traditional gang-lines (TRAD). Eight sled dogs, divided into two teams, ran a 3.1 km trail twice in both types of gang-lines, pulling a quadbike on dry ground. Each dog remained in its team in the same position (side of gang line, and forward or back in the line) for both runs, using both types of lines in randomised order between the runs. Markers were placed on the dogs and on the main lines, and the runs were recorded by a video camera. The dogs’ angle of pull measured from the video recordings was compared between the two conditions. Thirteen positional measurements for each dog during each run were taken. The dogs were used to running in TRAD and were not acclimatised to STICK. Data was analysed using Wilcoxon and Spearmans rho tests. Data regarding individual dogs (n=13), teams (n=52), dogs’ placements in teams (n=4), and gang-line related pulling angles (n=104) was analysed. Overall, the position of the dogs was straighter when pulling in STICK, than when pulling in TRAD, with a median of 19° (inter quartile range (IQR) 24.75°) and 32° (IQR 25.75°), respectively (P<0.001). Between the two teams, there was no significant difference in pulling positions when running in STICK (P=0.543), but there was in TRAD (P<0.001). In individual assessment, six of the eight dogs ran in a straighter position (P=0.003 to 0.046) in STICK. Dogs running in the front of both teams pulled significantly straighter when in STICK (21°; IQR 23.75) than in TRAD (median 39°; IQR 18; P<0.001).

The dog-human connection

This special issue of The Anatomical Record is the end result of a rare convergence of researchers scattered around the globe who came together to explore the mystery of the dog-human connection. Many of the discussions at the 12th International Congress of Vertebrate Morphology in Prague (July 23, 2019) are echoed within this issue. The enigmatic origins of dog domestication (as well as feralized descendants such as the dingo) are discussed, including phases of domestication that we might infer, and our historical knowledge of dog breeding. Emphasized by the morphological and genetic data are the forces of selection, both unintentional and intentional. In our modern life with dogs, we enjoy their companionship and benefit from the utility of many breeds, but we encounter unintended health care issues that are often breed-specific. Dogs are so different in their sensory specializations (especially olfaction), but have uniquely (among other domestic mammals) developed highly sophisticated means of interspecific communication with humans. In sum, the manuscripts within this issue discuss anatomical, paleontological, genetic, and behavioral evidence bearing on the antiquity of the domestic dog, the process of domestication, and the many ways in which dogs continue to affect human life.

Frontal plane dynamics of the centre of mass during quadrupedal locomotion on a split-belt treadmill

Our previous study of cat locomotion demonstrated that lateral displacements of the centre of mass (COM) were strikingly similar to those of human walking and resembled the behaviour of an inverted pendulum (Park et al. 2019 J. Exp. Biol.222, 14. (doi:10.1242/jeb.198648)). Here, we tested the hypothesis that frontal plane dynamics of quadrupedal locomotion are consistent with an inverted pendulum model. We developed a simple mathematical model of balance control in the frontal plane based on an inverted pendulum and compared model behaviour with that of four cats locomoting on a split-belt treadmill. The model accurately reproduced the lateral oscillations of cats' COM vertical projection. We inferred the effects of experimental perturbations on the limits of dynamic stability using data from different split-belt speed ratios with and without ipsilateral paw anaesthesia. We found that the effect of paw anaesthesia could be explained by the induced bias in the perceived position of the COM, and the magnitude of this bias depends on the belt speed difference. Altogether, our findings suggest that the balance control system is actively involved in cat locomotion to provide dynamic stability in the frontal plane, and that paw cutaneous receptors contribute to the representation of the COM position in the nervous system.

Body torsional flexibility effects on stability during trotting and pacing based on a simple analytical model

Quadruped animals use not only their legs but also their trunks during walking and running. Although many previous studies have investigated the flexion, extension, and lateral bending of the trunk, few studies have investigated the body torsion, and its dynamic effects on locomotion thus remain unclear. In this study, we investigated the effects of body torsion on gait stability during trotting and pacing. Specifically, we constructed a simple model consisting of two rigid bodies connected via a torsional joint that has a torsional spring and four leg springs. We then derived periodic solutions for trotting and pacing and evaluated the stabilities of these motion types using a Poincaré map. We found that the moments of inertia of the bodies and the spring constant ratio of the torsional spring and the leg springs determine the stability of these periodic solutions. We then determined the stability conditions for these parameters and elucidated the relevant mechanisms. In addition, we clarified the importance of the body torsion to the gait stability by comparison with a rigid model. Finally, we analyzed the biological relevance of our findings and provided a design principle for development of quadruped robots.

A 60:40 split: Differential mass support in dogs

Dogs have been bred for different sizes and functions, which can affect their locomotor biomechanics. As quadrupeds, dogs must distribute their mass between fore and hind legs when standing. The mass distribution in dogs was studied to determine if the proportion of supported mass on each limb couplet is dependent on body size. A total of 552 dogs from 123 breeds ranging in size from Chihuahua to Mastiff were examined. Each dog was weighed on a digital scale while standing, alternating foreleg, and hind leg support. The overall "grand" mean proportion of mass on the forelegs to the total mass was 60.4% (range: 47.6-74.4%). The data set indicated no significant change in the ratio with total mass but there was a significant difference by sex. When separated into American Kennel Club categories, no group was notably different from the grand mean or from each other, but when sex was also considered, there was a significant difference that was not specifically discerned by post hoc analysis. The mean for female Hounds was notably below the grand mean. For clades based on genetics, the mean for European origin mastiffs was notably greater than the grand mean and significantly different from UK origin herders and coursers. The mass of the head, chest, and musculature for propulsion could explain the mass support differential. Mass distribution and terrestrial locomotion in dogs shows substantial variation among breeds.

The "dog paddle": Stereotypic swimming gait pattern in different dog breeds

The term "dog paddle" has been applied to the swimming behavior of various terrestrial and aquatic species. Dog paddling refers to a form of drag-based, paddle propulsion in which the limbs are oriented underneath the body and moved through an arc. Despite the ubiquity of the term, there has been no analysis of the swimming kinematics of dogs. Underwater video was recorded of surface swimming dogs (velocity: 0.4-1.1 m/s) for eight individuals from six breeds, ranging in size from Yorkshire Terrier (3.6 kg) to Newfoundland dog (63.5 kg). The quadrupedal paddling stroke was analyzed to determine kinematics and coordination of the limbs. The paddling stroke represented a modified terrestrial gait, which was outside typical gaits for terrestrial locomotion by dogs. Stroke frequency decreased with increasing body size. The stroke cycle consisted of power and recovery phases. During the power phase, digits of the paw were abducted and the forelimb was swept posteriorly until perpendicular to the body. In the recovery phase, digits were adducted while the brachium was retracted anteriorly and the manus supinated. The power phase was about 34% of stroke cycle and shorter than the recovery phase for both fore and hindlimbs. Maximum velocity during the power phase was greater than the recovery phase. The modified terrestrial gait used for swimming by dogs appears to be stereotypic among breeds, whereas terrestrial locomotion in dogs shows substantial variation in gait. Without constraints imposed by gravity and substrate contact, swimming dogs can utilize a gait profile different from terrestrial gaits. SUMMARY STATEMENT: Despite the ubiquity of the term "dog paddle" to describe the swimming motions of animals, this is the first time that the swimming motions of dogs have been analyzed.

An inelastic quadrupedal model discovers four-beat walking, two-beat running, and pseudo-elastic actuation as energetically optimal

It is widely held that quadrupeds choose steady gaits that minimize their energetic cost of transport, but it is difficult to explore the entire range of possible footfall sequences empirically. We present a simple model of a quadruped that can spontaneously produce any of the thousands of planar footfall sequences available to quadrupeds. The inelastic, planar model consists of two point masses connected with a rigid trunk on massless legs. It requires only center of mass position, hind and forelimb proportions and a stride-length to speed relationship as input. Through trajectory optimization of a work and force-rate cost, and a large sample of random initial guesses, we provide evidence for the global optimality of symmetrical four-beat walking at low speeds and two beat running (trotting) at intermediate speeds. Using input parameters based on measurements in dogs (Canis lupus familiaris), the model predicts the correct phase offset in walking and a realistic walk-trot transition speed. It also spontaneously reproduces the double-hump ground reaction force profile observed in walking, and the smooth single-hump profile observed in trotting. Actuation appears elastic, despite the model's lack of springs, suggesting that spring-like locomotory behaviour emerges as an optimal tradeoff between work minimization and force-rate penalties.

Relationship Between Gait Mechanics and the Speed of the Trot in the Weimaraner Dog Breed

While the size of the Weimaraner may assist in the breed performing the tasks of a sporting dog, the large size coupled with these tasks may also make the breed more susceptible to orthopedic issues. The understanding of the normal gait mechanics of the Weimaraner can be a useful tool in examining for gait abnormalities associated with these orthopedic issues, and yet, research concerning breed-specific gaits in the canine is limited. Therefore, study objectives were to define the normal Weimaraner trotting kinematics and determine the influence of speed on these parameters. Markers were attached to palpation points on the limbs and head of American Kennel Club registered Weimaraners. Dogs were tracked while performing a slow (1.2-1.7 m/s) and fast (1.9-2.3 m/s) trotting speed. Frame-by-frame analysis was performed. Paw ground contact and lift-off was documented and marker displacement was tracked. At both speeds, the trot had a diagonal footfall sequence with diagonal limb pairing alternating between diagonal bipedal support and suspension. The faster speed was achieved with significant increases in stride length and displacements of the head, withers, and fore and hind paws (P < .05). Range of motion of the elbow and hip significantly increased as the dog transitioned from a slow to fast speed (P < .05). Through gait analysis, the Weimaraner trot was defined as a 2-beat diagonal rhythm gait with suspension. Speed did not change these characteristics, but did influence stride length and linear and angular displacements, and thus, should be a consideration in clinical examination.

Use it or lose it? Effects of age, experience, and disuse on crawling

What happens to early acquired but later abandoned motor skills? To investigate effects of disuse on early-developing motor skills, we examined crawling in two groups of habitual crawlers (34 6-12-month-old infants and five adults with Uner Tan Syndrome) and two groups of rusty crawlers (27 11-12-year-old children and 13 college-aged adults). Habitual crawlers showed striking similarities in gait patterns, limbs supporting the body, and crawling speed, despite dramatic differences in crawling practice, posture, and body size. Habitual crawlers trotted predominantly, whereas rusty crawlers showed a variety of gait patterns. Within sequences, habitual crawlers and children showed more switches in gait patterns than young adults. Children crawled faster and kept fewer limbs on the grounds than the other groups. Old crawling patterns were retained despite disuse, but new ones were also added. Surprisingly, results indicate that nothing was lost with disuse, but some features of crawling were gained or altered.

Linking Gait Dynamics to Mechanical Cost of Legged Locomotion

For millenia, legged locomotion has been of central importance to humans for hunting, agriculture, transportation, sport, and warfare. Today, the same principal considerations of locomotor performance and economy apply to legged systems designed to serve, assist, or be worn by humans in urban and natural environments. Energy comes at a premium not only for animals, wherein suitably fast and economical gaits are selected through organic evolution, but also for legged robots that must carry sufficient energy in their batteries. Although a robot's energy is spent at many levels, from control systems to actuators, we suggest that the mechanical cost of transport is an integral energy expenditure for any legged system—and measuring this cost permits the most direct comparison between gaits of legged animals and robots. Although legged robots have matched or even improved upon total cost of transport of animals, this is typically achieved by choosing extremely slow speeds or by using regenerative mechanisms. Legged robots have not yet reached the low mechanical cost of transport achieved at speeds used by bipedal and quadrupedal animals. Here we consider approaches used to analyze gaits and discuss a framework, termed mechanical cost analysis, that can be used to evaluate the economy of legged systems. This method uses a point mass perspective to evaluate the entire stride as well as to identify individual events that accrue mechanical cost. The analysis of gait began at the turn of the last century with spatiotemporal analysis facilitated by the advent of cine film. These advances gave rise to the “gait diagram,” which plots duty factors and phase separations between footfalls. This approach was supplanted in the following decades by methods using force platforms to determine forces and motions of the center of mass (CoM)—and analytical models that characterize gait according to fluctuations in potential and kinetic energy. Mechanical cost analysis draws from these approaches and provides a unified framework that interprets the spatiotemporal sequencing of leg contacts within the context of CoM dynamics to determine mechanical cost in every instance of the stride. Diverse gaits can be evaluated and compared in biological and engineered systems using mechanical cost analysis.

High prevalence of gait abnormalities in pugs

The objective of this prospective study was to determine the prevalence of gait abnormalities in a cohort of Swedish pugs by using an owner-based questionnaire targeting signs of gait abnormality and video footage showing the dog’s gait. This study also evaluated associated conditions of abnormal gait, including other health disorders prevalent in the breed. Five hundred and fifty (550) pugs registered in the Swedish Kennel Club, of one, five and eight years of age, in 2015 and 2016, were included in the study. Gait abnormalities were reported in 30.7 per cent of the responses. In the majority of cases, the character of the described gait indicated a neurological cause for the gait abnormality. An association was observed between abnormal gait and age, with gait abnormalities being significantly more common in older pugs (P=0.004). An association was also found between abnormal gait and dyspnoea, with dyspnoea being significantly more common in pugs with gait abnormalities (P<0.0001). This study demonstrated that the prevalence of gait abnormalities was high in the Swedish pug breed and increased with age. Future studies on the mechanisms behind these gait abnormalities are warranted.

Work minimization accounts for footfall phasing in slow quadrupedal gaits

Quadrupeds, like most bipeds, tend to walk with an even left/right footfall timing. However, the phasing between hind and forelimbs shows considerable variation. Here, we account for this variation by modeling and explaining the influence of hind-fore limb phasing on mechanical work requirements. These mechanics account for the different strategies used by: (1) slow animals (a group including crocodile, tortoise, hippopotamus and some babies); (2) normal medium to large mammals; and (3) (with an appropriate minus sign) sloths undertaking suspended locomotion across a range of speeds. While the unusual hind-fore phasing of primates does not match global work minimizing predictions, it does approach an only slightly more costly local minimum. Phases predicted to be particularly costly have not been reported in nature.

Longitudinal quasi-static stability predicts changes in dog gait on rough terrain

Legged animals utilize gait selection to move effectively and must recover from environmental perturbations. We show that on rough terrain, domestic dogs, Canis lupus familiaris, spend more time in longitudinal quasi-statically stable patterns of movement. Here, longitudinal refers to the rostro-caudal axis. We used an existing model in the literature to quantify the longitudinal quasi-static stability of gaits neighbouring the walk, and found that trot-like gaits are more stable. We thus hypothesized that when perturbed, the rate of return to a stable gait would depend on the direction of perturbation, such that perturbations towards less quasi-statically stable patterns of movement would be more rapid than those towards more stable patterns of movement. The net result of this would be greater time spent in longitudinally quasi-statically stable patterns of movement. Limb movement patterns in which diagonal limbs were more synchronized (those more like a trot) have higher longitudinal quasi-static stability. We therefore predicted that as dogs explored possible limb configurations on rough terrain at walking speeds, the walk would shift towards trot. We gathered experimental data quantifying dog gait when perturbed by rough terrain and confirmed this prediction using GPS and inertial sensors (n=6, P<0.05). By formulating gaits as trajectories on the n-torus we are able to make tractable the analysis of gait similarity. These methods can be applied in a comparative study of gait control which will inform the ultimate role of the constraints and costs impacting locomotion, and have applications in diagnostic procedures for gait abnormalities, and in the development of agile legged robots.

Summary: Dogs co-ordinate their limbs on rough terrain in a manner consistent with optimization for quasi-static longitudinal stability.

The private life of echidnas: using accelerometry and GPS to examine field biomechanics and assess the ecological impact of a widespread, semi-fossorial monotreme

The short-beaked echidna (Tachyglossus aculeatus) is a monotreme and therefore provides a unique combination of phylogenetic history, morphological differentiation and ecological specialisation for a mammal. The echidna has a unique appendicular skeleton, a highly specialised myrmecophagous lifestyle and a mode of locomotion that is neither typically mammalian nor reptilian, but has aspects of both lineages. We therefore were interested in the interactions of locomotor biomechanics, ecology and movements for wild, free-living short-beaked echidnas. To assess locomotion in its complex natural environment, we attached both GPS and accelerometer loggers to the back of echidnas in both spring and summer. We found that the locomotor biomechanics of echidnas is unique, with lower stride length and stride frequency than reported for similar-sized mammals. Speed modulation is primarily accomplished through changes in stride frequency, with a mean of 1.39 Hz and a maximum of 2.31 Hz. Daily activity period was linked to ambient air temperature, which restricted daytime activity during the hotter summer months. Echidnas had longer activity periods and longer digging bouts in spring compared with summer. In summer, echidnas had higher walking speeds than in spring, perhaps because of the shorter time suitable for activity. Echidnas spent, on average, 12% of their time digging, which indicates their potential to excavate up to 204 m3 of soil a year. This information highlights the important contribution towards ecosystem health, via bioturbation, of this widespread Australian monotreme.

Running With Symmetry

Symmetry can simplify the control of dynamic legged sys tems. In this paper, the symmetries studied describe motion of the body and legs in terms of even and odd functions of time. A single set of equations describes symmetric running for systems with any number of legs and for a wide range of gaits. Techniques based on symmetry have been used in laboratory experiments to control machines that run on one, two, and four legs. In addition to simplifying the control of legged machines, symmetry may help us to understand legged locomotion in animals. Data from a cat trotting and galloping on a treadmill and from a human running on a track conform reasonably well to the predicted symmetries.

Speed-Dependent Modulation of the Locomotor Behavior in Adult Mice Reveals Attractor and Transitional Gaits

Locomotion results from an interplay between biomechanical constraints of the muscles attached to the skeleton and the neuronal circuits controlling and coordinating muscle activities. Quadrupeds exhibit a wide range of locomotor gaits. Given our advances in the genetic identification of spinal and supraspinal circuits important to locomotion in the mouse, it is now important to get a better understanding of the full repertoire of gaits in the freely walking mouse. To assess this range, young adult C57BL/6J mice were trained to walk and run on a treadmill at different locomotor speeds. Instead of using the classical paradigm defining gaits according to their footfall pattern, we combined the inter-limb coupling and the duty cycle of the stance phase, thus identifying several types of gaits: lateral walk, trot, out-of-phase walk, rotary gallop, transverse gallop, hop, half-bound, and full-bound. Out-of-phase walk, trot, and full-bound were robust and appeared to function as attractor gaits (i.e., a state to which the network flows and stabilizes) at low, intermediate, and high speeds respectively. In contrast, lateral walk, hop, transverse gallop, rotary gallop, and half-bound were more transient and therefore considered transitional gaits (i.e., a labile state of the network from which it flows to the attractor state). Surprisingly, lateral walk was less frequently observed. Using graph analysis, we demonstrated that transitions between gaits were predictable, not random. In summary, the wild-type mouse exhibits a wider repertoire of locomotor gaits than expected. Future locomotor studies should benefit from this paradigm in assessing transgenic mice or wild-type mice with neurotraumatic injury or neurodegenerative disease affecting gait.

Siblings in Kars, Turkey, with Uner Tan syndrome (quadrupedal locomotion, severe mental retardation, and no speech): a novel theory for the evolution of human bipedalism

OBJECTIVE

To investigate siblings from Kars (n  =  2), Turkey, with diagonal-sequence quadrupedal locomotion (QL), severe mental retardation, and no speech (Uner Tan syndrome, UTS), in relation to the evolutionary emergence of human bipedal locomotion (BL).

METHODS

Video recordings were made to assess gaits. Brain MRI scanning was performed to visualize the cerebro-cerebellar malformations. Genome-wide association analyses were performed in venous blood samples.

RESULTS

One of the two men with UTS showed early-onset QL and late-onset BL without infantile hypotonia, the other consistent QL with infantile hypotonia. No homozygosity was found in the genetic analysis. The family lived under extremely poor socioeconomic conditions.

CONCLUSIONS

Low socioeconomic status may be a triggering factor for the epigenetic emergence of UTS. The neural networks responsible for the ancestral diagonal-sequence QL, evolutionarily preserved since about 400 MYA, may be selected during locomotor development, under the influence of self-organizing processes during pre- and postnatal periods. The diagonal-sequence QL induced ipsilateral limb interference in UTS cases as in nonhuman primates. To overcome this condition, our ancestors would prefer the attractor BL. This novel theory for the evolution of human bipedalism was evaluated in light of dynamical systems theory.

Human quadrupeds, primate quadrupedalism, and Uner Tan Syndrome

Since 2005, an extensive literature documents individuals from several families afflicted with "Uner Tan Syndrome (UTS)," a condition that in its most extreme form is characterized by cerebellar hypoplasia, loss of balance and coordination, impaired cognitive abilities, and habitual quadrupedal gait on hands and feet. Some researchers have interpreted habitual use of quadrupedalism by these individuals from an evolutionary perspective, suggesting that it represents an atavistic expression of our quadrupedal primate ancestry or "devolution." In support of this idea, individuals with "UTS" are said to use diagonal sequence quadrupedalism, a type of quadrupedal gait that distinguishes primates from most other mammals. Although the use of primate-like quadrupedal gait in humans would not be sufficient to support the conclusion of evolutionary "reversal," no quantitative gait analyses were presented to support this claim. Using standard gait analysis of 518 quadrupedal strides from video sequences of individuals with "UTS", we found that these humans almost exclusively used lateral sequence-not diagonal sequence-quadrupedal gaits. The quadrupedal gait of these individuals has therefore been erroneously described as primate-like, further weakening the "devolution" hypothesis. In fact, the quadrupedalism exhibited by individuals with UTS resembles that of healthy adult humans asked to walk quadrupedally in an experimental setting. We conclude that quadrupedalism in healthy adults or those with a physical disability can be explained using biomechanical principles rather than evolutionary assumptions.

Stride to stride variability in joint angle profiles during transitions from trot to canter in horses

Spontaneous transitions from anti-phase to in-phase manual coordination are explained in the Haken model that describes the two preferred states as stable regions that work as attractors in a stability landscape. Switching between states coincides with a temporary loss of stability. Coordination variability is believed to be indicative of such a loss of stability. In this study, the hypothesis was tested that an increase in variability in the angle profiles of the joints responsible for the transition will precede the transition. A full gait analysis of four miniature horses transitioning from trot to canter was performed. Joint angle profiles were determined for the joints of all four limbs and were time-normalised to stride duration. Per horse and per stride, the coefficient of variance was calculated as the mean standard deviation of the joint profile over all trials divided by the mean joint angle × 100. As hypothesised, the most proximal limb joints (hip, scapulothoracic, shoulder) followed the predictions to a large extent. The variability of the hip joint angle of the trailing hind limb showed a peak of variability at stride 0; this was quickly reduced after the transition was completed. The detection of this brief perturbation in the hip joint indicates the importance of this joint in the transition process. The hip joint is related to the movements of the limb, pelvis and back, which is one of the main differences between symmetrical and asymmetrical gaits.

Exploring diagonal gait using a forward dynamic three-dimensional chimpanzee simulation

Primates are unusual among terrestrial quadrupedal mammals in that at walking speeds they prefer diagonal rather than lateral gaits. A number of reasons have been proposed for this preference in relation to the arboreal ancestry of modern primates: stability, energetic cost, neural control, skeletal loading, and limb interference avoiding. However, this is a difficult question to explore experimentally since most primates only occasionally use anything other than diagonal gaits. An alternative approach is to produce biologically realistic computer simulations of primate gait that enable the constraints of biomechanical loading and the energetics of different modes of locomotion to be explored. In this paper we describe such a model for the chimpanzee Pan troglodytes. The simulation is able to produce spontaneous quadrupedal locomotion, and the footfall sequences generated are split between lateral and diagonal footfall sequences with no obvious energetic benefit associated with either option. However, out of 10 successful simulation runs, 5 were lateral sequence/lateral couplet gaits indicating a preference for a specific lateral footfall sequence with a relatively tightly constrained phase difference between the fore- and hindlimbs. This suggests that the choice of diagonal walking gaits in chimpanzees is not a simple mechanical phenomenon and that diagonal walking gaits in primates are selected for by multiple factors.

The metabolic and mechanical costs of step time asymmetry in walking

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

Cavemen were better at depicting quadruped walking than modern artists: erroneous walking illustrations in the fine arts from prehistory to today

The experts of animal locomotion well know the characteristics of quadruped walking since the pioneering work of Eadweard Muybridge in the 1880s. Most of the quadrupeds advance their legs in the same lateral sequence when walking, and only the timing of their supporting feet differ more or less. How did this scientific knowledge influence the correctness of quadruped walking depictions in the fine arts? Did the proportion of erroneous quadruped walking illustrations relative to their total number (i.e. error rate) decrease after Muybridge? How correctly have cavemen (upper palaeolithic Homo sapiens) illustrated the walking of their quadruped prey in prehistoric times? The aim of this work is to answer these questions. We have analyzed 1000 prehistoric and modern artistic quadruped walking depictions and determined whether they are correct or not in respect of the limb attitudes presented, assuming that the other aspects of depictions used to determine the animals gait are illustrated correctly. The error rate of modern pre-Muybridgean quadruped walking illustrations was 83.5%, much more than the error rate of 73.3% of mere chance. It decreased to 57.9% after 1887, that is in the post-Muybridgean period. Most surprisingly, the prehistoric quadruped walking depictions had the lowest error rate of 46.2%. All these differences were statistically significant. Thus, cavemen were more keenly aware of the slower motion of their prey animals and illustrated quadruped walking more precisely than later artists.

Simple robot suggests physical interlimb communication is essential for quadruped walking

Quadrupeds have versatile gait patterns, depending on the locomotion speed, environmental conditions and animal species. These locomotor patterns are generated via the coordination between limbs and are partly controlled by an intraspinal neural network called the central pattern generator (CPG). Although this forms the basis for current control paradigms of interlimb coordination, the mechanism responsible for interlimb coordination remains elusive. By using a minimalistic approach, we have developed a simple-structured quadruped robot, with the help of which we propose an unconventional CPG model that consists of four decoupled oscillators with only local force feedback in each leg. Our robot exhibits good adaptability to changes in weight distribution and walking speed simply by responding to local feedback, and it can mimic the walking patterns of actual quadrupeds. Our proposed CPG-based control method suggests that physical interaction between legs during movements is essential for interlimb coordination in quadruped walking.

Kinematics of quadrupedal locomotion in sugar gliders (Petaurus breviceps): effects of age and substrate size

Arboreal mammals face unique challenges to locomotor stability. This is particularly true with respect to juveniles, who must navigate substrates similar to those traversed by adults, despite a reduced body size and neuromuscular immaturity. Kinematic differences exhibited by juveniles and adults on a given arboreal substrate could therefore be due to differences in body size relative to substrate size, to differences in neuromuscular development, or to both. We tested the effects of relative body size and age on quadrupedal kinematics in a small arboreal marsupial (the sugar glider, Petaurus breviceps; body mass range of our sample 33-97 g). Juvenile and adult P. breviceps were filmed moving across a flat board and three poles 2.5, 1.0 and 0.5 cm in diameter. Sugar gliders (regardless of age or relative speed) responded to relative decreases in substrate diameter with kinematic adjustments that promote stability; they increased duty factor, increased the average number of supporting limbs during a stride, increased relative stride length and decreased relative stride frequency. Limb phase increased when moving from the flat board to the poles, but not among poles. Compared with adults, juveniles (regardless of relative body size or speed) used lower limb phases, more pronounced limb flexion, and enhanced stability with higher duty factors and a higher average number of supporting limbs during a stride. We conclude that although substrate variation in an arboreal environment presents similar challenges to all individuals, regardless of age or absolute body size, neuromuscular immaturity confers unique problems to growing animals, requiring kinematic compensation.

Substrate diameter and compliance affect the gripping strategies and locomotor mode of climbing boa constrictors

Arboreal habitats pose unique challenges for locomotion as a result of their narrow cylindrical surfaces and discontinuities between branches. Decreased diameter of branches increases compliance, which can pose additional challenges, including effects on stability and energy damping. However, the combined effects of substrate diameter and compliance are poorly understood for any animal. We quantified performance, kinematics and substrate deformation while boa constrictors (Boa constrictor) climbed vertical ropes with three diameters (3, 6 and 9 mm) and four tensions (0.5, 1.0, 1.5 and 2.0 body weights). Mean forward velocity decreased significantly with both decreased diameter and increased compliance. Both diameter and compliance had numerous effects on locomotor kinematics, but diameter had larger and more pervasive effects than compliance. Locomotion on the largest diameter had a larger forward excursion per cycle, and the locomotor mode and gripping strategy differed from that on the smaller diameters. On larger diameters, snakes primarily applied opposing forces at the same location on the rope to grip. By contrast, on smaller diameters forces were applied in opposite directions at different locations along the rope, resulting in increased rope deformation. Although energy is likely to be lost during deformation, snakes might use increased surface deformation as a strategy to enhance their ability to grip.