Support polygons and symmetricalgaits in mammals

The symmetrical gaits of quadrupedal mammals are oftendescribed in terms of two variables: duty factor (S = the stanceperiod of one foot, as a percentage of the gait cycle) and diagonality(D = the percentage of the cycle period by whichthe left hind footfall precedes the left fore footfall). We showthat support polygons are optimized during walking (i.e.the percentage of the locomotor cycle spent standing on only twofeet is minimized) for: (1) the diagonal-sequence, diagonal-coupletswalks characteristic of primates (50 < D < 75)when D = [hindlimb S]; (2) lateral-sequence,lateral-couplets walks (0 < D < 25)when D = [hindlimb S]− 50;(3) lateral-sequence, diagonal-couplets walks (25 < D < 50)when D = 100 −[forelimb S].To determine whether animal behaviour is optimal in this sense,we examined 346 symmetrical gait cycles in 45 mammal species. Ourempirical data show that mammalian locomotor behaviour approximatesthe theoretical optima. We suggest that diagonal-sequence walkingmay be adopted by ­primates as a means of ensuring thata grasping hindfoot is placed in a protracted position on a testedsupport at the moment when the contralateral forefoot strikes downon an untested support.  © 2002 The Linnean Societyof London, Zoological Journal of the Linnean Society , 2002, 136 ,401−420     

Footfall patterns and interlimb co-ordination in opossums (Family Didelphidae): evidence for the evolution of diagonal-sequence walking gaits in primates

Most primates typically use a diagonal-sequence footfall pattern during walking. This footfall pattern, which is unusual for mammals, is believed to have originated in ancestral primates in association with the use of grasping extremities for movement and foraging on thin, flexible branches. This theory was tested by comparing gait parameters between the grey short-tailed opossum Monodelphis domestica and the woolly opossum Caluromys philander , two didelphid marsupials that are strongly differentiated in grasping morphology of the extremities and in their reliance on foraging strategies involving thin branches. One hundred and thirty gait cycles were analysed quantitatively from videotapes of subjects moving quadrupedally on a runway and on poles of different diameters (7 and 28 mm). Duty factor (i.e. duration of the stance phase as a percentage of the stride period) for the forelimb and hindlimb, as well as diagonality (i.e. phase relationship between the forelimb and hindlimb cycles), were calculated for each of these symmetrical gait cycles. We found that the highly terrestrial Monodelphis , like most other non-primate mammals, relies primarily on lateral-sequence walking gaits on both runway and poles, and has relatively higher forelimb duty factors. Like primates, the highly arboreal Caluromys uses primarily diagonal-sequence walking gaits on the runway and pole, with relatively higher hindlimb duty factors and diagonality. The fact that the woolly opossum, a marsupial with primate-like feet that moves and forages mainly on thin branches, uses primarily diagonal-sequence gaits when walking supports the view that primate gaits evolved to meet the demands of locomotion on narrow supports. This also demonstrates the functional role of a grasping foot, in association with relatively higher hindlimb duty factors, protraction, and substrate reaction forces, in the production of such walking gaits.     

Locomotor mechanics of the slender loris (Loris tardigradus)

The quadrupedal walking gaits of most primates can be distinguished from those of most other mammals by the presence of diagonal-sequence (DS) footfall patterns and higher peak vertical forces on the hindlimbs compared to the forelimbs. The walking gait of the woolly opossum (Caluromys philander), a highly arboreal marsupial, is also characterized by diagonal-sequence footfalls and relatively low peak forelimb forces. Among primates, three species--Callithrix, Nycticebus, and Loris--have been reported to frequently use lateral-sequence (LS) gaits and experience relatively higher peak vertical forces on the forelimbs. These patterns among primates and other mammals suggest a strong association between footfall patterns and force distribution on the limbs. However, current data for lorises are limited and the frequency of DS vs. LS walking gaits in Loris is still ambiguous. To test the hypothesis that patterns of footfalls and force distribution on the limbs are functionally linked, kinematic and kinetic data were collected simultaneously for three adult slender lorises (Loris tardigradus) walking on a 1.25 cm horizontal pole. All subjects in this study consistently used diagonal-sequence walking gaits and always had higher peak vertical forces on their forelimbs relative to their hindlimbs. These results call into question the hypothesis that a functional link exists between the presence of diagonal-sequence walking gaits and relatively higher peak vertical forces on the hindlimbs. In addition, this study tested models that explain patterns of force distribution based on limb protraction angle or limb compliance. None of the Loris subjects examined showed kinematic patterns that would support current models proposing that weight distribution can be adjusted by actively shifting weight posteriorly or by changing limb stiffness. These data reveal the complexity of adaptations to arboreal locomotion in primates and indicate that diagonal-sequence walking gaits and relatively low forelimb forces could have evolved independently.     

Evolutionary implications of the unusual walking mechanics of the common marmoset (C. jacchus)

Several features that appear to differentiate the walking gaits of most primates from those of most other mammals (the prevalence of diagonal-sequence footfalls, high degrees of humeral protraction, and low forelimb vs. hindlimb peak vertical forces) are believed to have evolved in response to requirements of locomotion on thin arboreal supports by early primates that had developed clawless grasping hands and feet. This putative relationship between anatomy, behavior, and ecology is tested here by examining gait mechanics in the common marmoset (Callithrix jacchus), a primate that has sharp claws and reduced pedal grasping, and that spends much of its time clinging on large trunks. Kinematic and kinetic data were collected on three male Callithrix jacchus as they walked across a force platform attached to the ground or to raised horizontal poles. The vast majority of all walking gaits were lateral-sequence. For all steps, the humerus was retracted (<90 degrees relative to a horizontal axis) or held in a neutral (90 degrees ) position at forelimb touchdown. Peak vertical forces on the forelimb were always higher than those on the hindlimb. These three features of the walking gaits of C. jacchus separate it from any other primate studied (including other callitrichids). The walking gaits of C. jacchus are mechanically more similar to those of small, nonprimate mammals. The results of this study support previous models that suggest that the unusual suite of features that typify the walking gaits of most primates are adaptations to the requirements of locomotion on thin arboreal supports. These data, along with data from other primates and marsupials, suggest that primate postcranial and locomotor characteristics are part of a basal adaptation for walking on thin branches.     

Lateral sequence walking in infant Papio cynocephalus: implications for the evolution of diagonal sequence walking in primates

One of the most distinctive aspects of primate quadrupedal walking is the use of diagonal sequence footfalls in combination with diagonal-couplets interlimb timing. Numerous hypotheses have been offered to explain why primates might have evolved this type of gait, yet this important question remains unresolved. Because infant primates use a wider variety of quadrupedal gaits than do adults, they provide a natural experiment with which to test hypotheses about the evolution of unique aspects of primate quadrupedalism. In this study, we present kinematic data on two infant baboons (Papio cynocephalus) in order to test the recent hypothesis that diagonal sequence, diagonal couplets walking might have evolved in primates because their limb positioning provides stability in a small branch environment (Cartmill et al. [2002] Zool J Linn Soc 136:401-420). To assess hindlimb position at the moment of forelimb touchdown, we measured hindlimb angular excursion and ankle position for 84 walking strides, across three different types of gaits (diagonal sequence, diagonal couplets (DSDC); lateral sequence lateral couplets (LSLC); and lateral sequence diagonal couplets (LSDC)). Results indicate that if a forelimb were to contact an unstable substrate, LSLC walking provides as much, and perhaps more, stability when compared to DSDC walking. Therefore, it appears that this moment in a stride was unlikely to be a particularly important selective factor in the evolution of DSDC walking. Further insight into this issue will likely be gained by observations of primate quadrupedalism in natural environments, where the use of lateral sequence gaits might be more common than currently known.     

Gait selection and the ontogeny of quadrupedal walking in squirrel monkeys (Saimiri boliviensis)

Locomotor researchers have long known that adult primates employ a unique footfall sequence during walking. Most mammals use lateral sequence (LS) gaits, in which hind foot touchdowns are followed by ipsilateral forefoot touchdowns. In contrast, most quadrupedal primates use diagonal sequence (DS) gaits, in which hind foot touchdowns are followed by contralateral forefoot touchdowns. However, gait selection in immature primates is more variable, with infants and juveniles frequently using LS gaits either exclusively or in addition to DS gaits. I explored the developmental bases for this phenomenon by examining the ontogeny of gait selection in juvenile squirrel monkeys walking on flat and simulated arboreal substrates (i.e., a raised pole). Although DS gaits predominated throughout development, the juvenile squirrel monkeys nonetheless utilized LS gaits in one-third of the ground strides and in one-sixth of pole strides. Multiple logistic regression analyses showed that gait selection within the juvenile squirrel monkey sample was not significantly associated with either age or body mass per se, arguing against the oft-cited argument that general neuromuscular maturation is responsible for ontogenetic changes in preferred footfall sequence. Rather, lower level biomechanical variables, specifically the position of the whole-body center of mass and the potential for interference between ipsilateral fore and hindlimbs, best explained variation in footfall patterns. Overall, results demonstrate the promise of developmental studies of growth and locomotor development to serve as "natural laboratories" in which to explore how variability in morphology is, or is not, associated with variability in locomotor behavior.     

The effects of natural substrate discontinuities on the quadrupedal gait kinematics of free‐ranging Saimiri sciureus

Wild primates encounter complex matrices of substrates that differ in size, orientation, height, and compliance, and often move on multiple, discontinuous substrates within a single bout of locomotion. Our current understanding of primate gait is limited by artificial laboratory settings in which primate quadrupedal gait has primarily been studied. This study analyzes wild Saimiri sciureus (common squirrel monkey) gait on discontinuous substrates to capture the realistic effects of the complex arboreal habitat on walking kinematics. We collected high‐speed video footage at Tiputini Biodiversity Station, Ecuador between August and October 2017. Overall, the squirrel monkeys used more asymmetrical walking gaits than symmetrical gaits, and specifically asymmetrical lateral sequence walking gaits when moving across discontinuous substrates. When individuals used symmetrical gaits, they used diagonal sequence gaits more than lateral sequence gaits. In addition, individuals were more likely to change their footfall sequence during strides on discontinuous substrates. Squirrel monkeys increased the time lag between touchdowns both of ipsilaterally paired limbs (pair lag) and of the paired forelimbs (forelimb lag) when walking across discontinuous substrates compared to continuous substrates. Results indicate that gait flexibility and the ability to alter footfall patterns during quadrupedal walking may be critical for primates to safely move in their complex arboreal habitats. Notably, wild squirrel monkey quadrupedalism is diverse and flexible with high proportions of asymmetrical walking. Studying kinematics in the wild is critical for understanding the complexity of primate quadrupedalism.     

Symmetrical gaits of dogs in relation to body build

Symmetrical gaits of 37 breeds of dogs were analyzed. Usual walking and trotting gaits resemble those of other carnivores of similar size and conformation. Only certain long-legged dogs pace – usually at the fast walk or slow run. At the moderate walk, long-legged dogs tend to use lateral-couplets gaits, whereas short-legged breeds tend to use single-foot gaits. Many dogs must turn the axis of the body slightly from the line of travel at the trot to prevent interference between fore and hind feet. The relative duration with the ground made by fore and hind feet is discussed, usual support-sequences of the varicus gaits are presented, and the amount of variation is shown.     

Trot Gait Design and CPG Method for a Quadruped Robot

Developing efficient walking gaits for quadruped robots has intrigued investigators for years. Trot gait, as a fast locomotion gait, has been widely used in robot control. This paper follows the idea of the six determinants of gait and designs a trot gait for a parallel-leg quadruped robot, Baby Elephant. The walking period and step length are set as constants to maintain a relatively fast speed while changing different foot trajectories to test walking quality. Experiments show that kicking leg back improves body stability. Then, a steady and smooth trot gait is designed. Furthermore, inspired by Central Pattern Generators （CPG）, a series CPG model is proposed to achieve robust and dynamic trot gait. It is generally believed that CPG is capable of producing rhythmic movements, such as swimming, walking, and flying, even when isolated from brain and sensory inputs. The proposed CPG model, inspired by the series concept, can automatically learn the previous well-designed trot gait and reproduce it, and has the ability to change its walking frequency online as well. Experiments are done in real world to verify this method.     

Locomotion in degus on terrestrial substrates varying in orientation – implications for biomechanical constraints and gait selection

To gain new insights into running gaits on sloped terrestrial substrates, metric and selected kinematic parameters of the common degu (Octodon degus) were examined. Individuals were filmed at their maximum voluntary running speed using a high-speed camera placed laterally to the terrestrial substrate varying in orientations from −30° to +30°, at 10° increments. Degus used trotting, lateral-sequence (LS) and diagonal-sequence (DS) running gaits at all substrate orientations. Trotting was observed across the whole speed range whereas DS running gaits occurred at significantly higher speeds than LS running gaits. Metric and kinematic changes on sloped substrates in degus paralleled those noted for most other mammals. However, the timing of metric and kinematic locomotor adjustments differed significantly between individual degus. In addition, most of these adjustments took place at 10° rather than 30° inclines and declines, indicating significant biomechanical demands even on slightly sloped terrestrial substrates. The results of this study suggest that DS and LS running gaits may represent an advantage in small to medium-sized mammals for counteracting some level of locomotor instability. Finally, changes in locomotor parameters of the forelimbs rather than the hindlimbs seem to play an important role in gait selection in small to medium-sized mammals.     

Three-dimensional kinematics of capuchin monkey bipedalism

Capuchin monkeys are known to use bipedalism when transporting food items and tools. The bipedal gait of two capuchin monkeys in the laboratory was studied with three-dimensional kinematics. Capuchins progress bipedally with a bent-hip, bent-knee gait. The knee collapses into flexion during stance and the hip drops in height. The knee is also highly flexed during swing to allow the foot which is plantarflexed to clear the ground. The forefoot makes first contact at touchdown. Stride frequency is high, and stride length and limb excursion low. Hind limb retraction is limited, presumably to reduce the pitch moment of the forward-leaning trunk. Unlike human bipedalism, the bipedal gait of capuchins is not a vaulting gait, and energy recovery from pendulum-like exchanges is unlikely. It extends into speeds at which humans and other animals run, but without a human-like gait transition. In this respect it resembles avian bipedal gaits. It remains to be tested whether energy is recovered through cyclic elastic storage and release as in bipedal birds at higher speeds. Capuchin bipedalism has many features in common with the facultative bipedalism of other primates which is further evidence for restrictions on a fully upright striding gait in primates that transition to bipedalism. It differs from the facultative bipedalism of other primates in the lack of an extended double-support phase and short aerial phases at higher speeds that make it a run by kinematic definition. This demonstrates that facultative bipedalism of quadrupedal primates need not necessarily be a walking gait.     

Origins of primate locomotion: gait mechanics of the woolly opossum

The locomotion of primates differs from that of other mammals in three fundamental ways. During quadrupedal walking, primates use diagonal sequence gaits, protract their arms more at forelimb touchdown, and experience lower vertical substrate reaction forces on their forelimbs relative to their hindlimbs. It is widely held that the unusual walking gaits of primates represent a basal adaptation for movement on thin, flexible branches and reflect a major change in the functional role of the forelimb. However, little data on nonprimate arboreal mammals exist to test this notion. To that end, we examined the gait mechanics of the woolly opossum (Caluromys philander), a marsupial convergent with small-bodied prosimians in ecology, behavior, and morphology. Data on the footfall sequence, relative arm protraction, and peak vertical substrate reaction forces were obtained from videotapes and force records for three adult woolly opossums walking quadrupedally on a wooden runway and a thin pole. For all steps recorded on both substrates, woolly opossums always used diagonal sequence walking gaits, protracted their arms beyond 90 degrees relative to horizontal body axis, and experienced peak vertical substrate reaction forces on forelimbs that were significantly lower than on hindlimbs. The woolly opossum is the first nonprimate mammal to show locomotor mechanics that are identical to those of primates. This case of convergence between primates and a committed fine-branch, arboreal marsupial strongly implies that the earliest primates evolved gait specializations for fine-branch locomotion, which reflect important changes in forelimb function.     

The biomechanics of skipping gaits: a third locomotion paradigm?

Skipping, a gait children display when they are about four- to five-years-old, is revealed to be more than a behavioural peculiarity. By means of metabolic and biomechanical measurements at several speeds, the relevance of skipping is shown to extend from links between bipedal and quadrupedal locomotion (namely galloping) to understanding why it could be a gait of choice in low-gravity conditions, and to some aspects of locomotion evolution (ground reaction forces of skipping seem to originate from pushing the walking gait to unnaturally high speeds). When the time-courses of mechanical energy and the horizontal ground reaction force are considered, a different locomotion paradigm emerges, enabling us to separate, among the bouncing gaits, the trot from the gallop (quadrupeds) and running from skipping (bipeds). The simultaneous use of pendulum-like and elastic mechanisms in skipping gaits, as shown by the energy curve analysis, helps us to understand the low cost of transport of galloping quadrupeds.     

Body mass distribution and gait mechanics in fat-tailed dwarf lemurs (Cheirogaleus medius) and patas monkeys (Erythrocebus patas)

Most quadrupeds walk with lateral sequence (LS) gaits, where hind limb touchdowns are followed by ipsilateral forelimb touchdowns. Primates, however, typically walk with diagonal sequence (DS) gaits, where hind limb touchdowns are followed by contralateral forelimb touchdowns. Because the use of DS gaits is nearly ubiquitous among primates, understanding gait selection in primates is critical to understanding primate locomotor evolution. The Support Polygon Model [Tomita, M., 1967. A study on the movement pattern of four limbs in walking. J. Anthropol. Soc. Nippon 75, 120-146; Rollinson, J., Martin, R.D., 1981. Comparative aspects of primate locomotion, with special reference to arboreal cercopithecines. Symp. Zool. Soc. Lond. 48, 377-427] argues that primates' use of DS gaits stems from a more caudal position of the whole-body center of mass (COM) relative to other mammals. We tested the predictions of the Support Polygon Model by examining the effects of natural and experimental variations in COM position on gait mechanics in two distantly related primates: fat-tailed dwarf lemurs (Cheirogaleus medius) and patas monkeys (Erythrocebus patas). Dwarf lemur experiments compared individuals with and without a greatly enlarged tail (a feature associated with torpor that can be expected to shift the COM caudally). During patas monkey experiments, we experimentally shifted the COM cranially with the use of a weighted belt (7-12% of body mass) positioned above the scapulae. Examination of limb kinematics revealed changes consistent with systematic deviations in COM position. Nevertheless, footfall patterns changed in a direction contrary to the predictions of the Support Polygon Model in the dwarf lemurs and did not change at all in the patas monkey. These results suggest that body mass distribution is unlikely to be the sole determinant of footfall pattern in primates and other mammals.     

Substrate determines asymmetrical gait dynamics in marmosets (Callithrix jacchus) and squirrel monkeys (Saimiri boliviensis)

Studies of skeletal pathology indicate that injury from falling accounts for most long bone trauma in free‐ranging primates, suggesting that primates should be under strong selection to manifest morphological and behavioral mechanisms that increase stability on arboreal substrates. Although previous studies have identified several kinematic and kinetic features of primate symmetrical gaits that serve to increase arboreal stability, very little work has focused on the dynamics of primate asymmetrical gaits. Nevertheless, asymmetrical gaits typify the rapid locomotion of most primates, particularly in smaller bodied taxa. This study investigated asymmetrical gait dynamics in growing marmosets and squirrel monkeys moving on terrestrial and simulated arboreal supports (i.e., an elevated pole). Results showed that monkeys used several kinematic and kinetic adjustments to increase stability on the pole, including reducing peak vertical forces, limiting center of mass movements, increasing substrate contact durations, and using shorter and more frequent strides (thus limiting disruptive whole‐body aerial phases). Marmosets generally showed greater adjustment to pole locomotion than did squirrel monkeys, perhaps as a result of their reduced grasping abilities and retreat from the fine‐branch niche. Ontogenetic increases in body size had relatively little independent influence on asymmetrical gait dynamics during pole locomotion, despite biomechanical theory suggesting that arboreal instability is exacerbated as body size increases relative to substrate diameter. Overall, this study shows that 1) symmetrical gaits are not the only stable way to travel arboreally and 2) small‐bodied primates utilize specific kinematic and kinetic adjustments to increase stability when using asymmetrical gaits on arboreal substrates. Am J Phys Anthropol, 2009. © 2008 Wiley‐Liss, Inc.     

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.     

Ground reaction forces and center of mass mechanics of bipedal capuchin monkeys: Implications for the evolution of human bipedalism

Tufted capuchin monkeys are known to use both quadrupedalism and bipedalism in their natural environments. Although previous studies have investigated limb kinematics and metabolic costs, their ground reaction forces (GRFs) and center of mass (CoM) mechanics during two and four‐legged locomotion are unknown. Here, we determine the hind limb GRFs and CoM energy, work, and power during bipedalism and quadrupedalism over a range of speeds and gaits to investigate the effect of differential limb number on locomotor performance. Our results indicate that capuchin monkeys use a “grounded run” during bipedalism (0.83–1.43 ms^?1) and primarily ambling and galloping gaits during quadrupedalism (0.91–6.0 ms^?1). CoM energy recoveries are quite low during bipedalism (2–17%), and in general higher during quadrupedalism (4–72%). Consistent with this, hind limb vertical GRFs as well as CoM work, power, and collisional losses are higher in bipedalism than quadrupedalism. The positive CoM work is 2.04 ± 0.40 Jkg^?1 m^?1 (bipedalism) and 0.70 ± 0.29 Jkg^?1 m^?1 (quadrupedalism), which is within the range of published values for two and four‐legged terrestrial animals. The results of this study confirm that facultative bipedalism in capuchins and other nonhuman primates need not be restricted to a pendulum‐like walking gait, but rather can include running, albeit without an aerial phase. Based on these results and similar studies of other facultative bipeds, we suggest that important transitions in the evolution of hominin locomotor performance were the emergences of an obligate, pendulum‐like walking gait and a bouncy running gait that included a whole‐body aerial phase. Am J Phys Anthropol, 2013. © 2012 Wiley Periodicals, Inc.     

Kinematics of bipedalism in Propithecus verreauxi

Bipedalism is rare in primates and has evolved in two distantly related groups: hominoids and indrids. Although copious data are available on the mechanics of bipedal locomotion in hominoids and vertical clinging and leaping (VCL) in indrids, no research has addressed the unique mode of bipedal locomotion exhibited by select indrid primates. Propithecus verreauxi is a highly specialized indrid vertical clinger and leaper that uses a peculiar form of bipedalism on the ground. The objectives of this study were to describe the bipedal gait of Propithecus , to assess the influence of VCL specializations on the kinematic patterns and propulsion mechanisms used by Propithecus during bipedalism, and to compare Propithecus bipedalism with the bipedal gaits of other primates capable of using bipedalism. Video was collected of five adult P. verreauxi moving bipedally in a seminatural setting at the Duke University Primate Center. Duty factor, footfall patterns, joint angles and center of mass movement were quantified in the sagittal plane for 73 steps. Propithecus uses a bipedal gallop, a gait unique to Propithecus . The kinematic similarities (e.g. large hip and knee angular excursions and preparatory countermovements) between bipedal galloping and VCL lead us to suggest that Propithecus takes advantage of specializations for VCL to conserve energy during bipedal galloping. Propithecus also walks bipedally at slower speeds. When Propithecus walks, it utilizes a relatively compliant gait similar to that of other primate facultative bipeds ( Pan , Hylobates ). During bipedal walking, energy conservation may be sacrificed for increased balance and reduced joint loads.