Pendular mechanics and the kinematics and energetics of brachiating locomotion

Because brachiating locomotion is characterized by a pattern of swinging movements, brachiation has often been analogized to pendular motion, and aspects of the mechanics of pendular systems have been used to provide insight into both energetic and structural design aspects of this locomotor mode. However, there are several limitations to this approach. First, the motions of brachiating animals only approximate pendular motion, and therefore the energetics of these two systems are only roughly comparable. Second, the kinematic similarity between brachiation and pendular motion will be maximal at only one velocity, and the correspondence will be even less at greater or lesser speeds. Third, all forms of terrestrial locomotion that involve the use of limbs incorporate elements of pendular systems, and therefore brachiation is not unusual in this respect. Finally, it has been suggested that the mechanics of pendular motion will constrain the maximum attainable body size of brachiating animals and that this mechanical situation explains the lack of brachiating primates of greater than 30-kg body size; the present analysis provides evidence that the constraints on body size are far less strict than previously indicated and that extrinsic factors such as the geometry of the forest environment are more likely to dictate maximum body size for brachiators.     

Substrate alters forelimb to hindlimb peak force ratios in primates

It is often claimed that the walking gaits of primates are unusual because, unlike most other mammals, primates appear to have higher vertical peak ground reaction forces on their hindlimbs than on their forelimbs. Many researchers have argued that this pattern of ground reaction force distribution is part of a general adaptation to arboreal locomotion. This argument is frequently used to support models of primate locomotor evolution. Unfortunately, little is known about the force distribution patterns of primates walking on arboreal supports, nor do we completely understand the mechanisms that regulate weight distribution in primates. We collected vertical peak force data for seven species of primates walking quadrupedally on instrumented terrestrial and arboreal supports. Our results show that, when walking on arboreal vs. terrestrial substrates, primates generally have lower vertical peak forces on both limbs but the difference is most extreme for the forelimb. We found that force reduction occurs primarily by decreasing forelimb and, to a lesser extent, hindlimb stiffness. As a result, on arboreal supports, primates experience significantly greater functional differentiation of the forelimb and hindlimb than on the ground. These data support long-standing theories that arboreal locomotion was a critical factor in the differentiation of the forelimbs and hindlimbs in primates. This change in functional role of the forelimb may have played a critical role in the origin of primates and facilitated the evolution of more specialized locomotor behaviors.     

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.     

Editorial

Quantitative and qualitative analyses of filming studies reveal that fundamental differences exist between the gaits of the New Zealand fur seal (Arctocephalus forsteri) and the Hooker's sea lion (Phocarctos hookeri). Terrestrial locomotion of the latter species is similar to that of terrestrial vertebrates in which the limbs are moved in sequence, alternately and independently. In contrast, the gait of the New Zealand fur seal does not conform to this sequence, the hind limbs being moved in unison. The gaits of both species are defined and illustrated. The limbs of otariids are structurally adapted for a semi-aquatic lifestyle and consequently large oscillations of the centre of gravity are necessary to enable the limbs to be lifted and protracted during terrestrial locomotion. Phocarctos hookeri achieves this by transferring weight in the transverse plane while in A.forsteri it is in the sagittal plane. Hind limb movements are distinctly different; P. hookeri moves each hind limb individually by the combined action of limb protraction and rotation of the pelvis while A. forsteri moves its hind limbs together, predominantly by flexion of the posterior axial skeleton. While terrestrial locomotion in these species is achieved by fundamentally different gaits, post cranial elements of A. forsteri and P. hookeri are barely distinguishable; selection for the behavioural control of terrestrial locomotion has apparently preceded structural modifications. The gaits are considered to be ecological specializations which are adaptations to the mechanical problems imposed by different habitats. Gaits of these species appear typical or representative of members of their inferred subfamilies (Arctocephalinae and Otariinae). The gaits of A. forsteri and P. hookeri are however paradoxical in light of their inferred evolutionary history since the gait of the Hooker's sea lion resembles more closely that of the putative ancestors of otariids (arctoid fissiped carnivores) than does the gait of the supposedly more primitive New Zealand fur seal.     

Distal Humeral Morphology Indicates Locomotory Divergence in Extinct Giant Kangaroos

Previous studies of the morphology of the humerus in kangaroos showed that the shape of the proximal humerus could distinguish between arboreal and terrestrial taxa among living mammals, and that the extinct “giant” kangaroos (members of the extinct subfamily Sthenurinae and the extinct macropodine genus Protemnodon) had divergent humeral anatomies from extant kangaroos. Here, we use 2D geometric morphometrics to capture the shape of the distal humerus in a range of extant and extinct marsupials and obtain similar results: sthenurines have humeral morphologies more similar to arboreal mammals, while large Protemnodon species (P. brehus and P. anak) have humeral morphologies more similar to terrestrial quadrupedal mammals. Our results provide further evidence for prior hypotheses: that sthenurines did not employ a locomotor mode that involved loading the forelimbs (likely employing bipedal striding as an alternative to quadrupedal or pentapedal locomotion at slow gaits), and that large Protemnodon species were more reliant on quadrupedal locomotion than their extant relatives. This greater diversity of locomotor modes among large Pleistocene kangaroos echoes studies that show a greater diversity in other aspects of ecology, such as diet and habitat occupancy.

     

Functional differentiation of trailing and leading forelimbs during locomotion on the ground and on a horizontal branch in the European red squirrel (Sciurus vulgaris, Rodentia)

Mammalian locomotion is characterized by the frequent use of in-phase gaits in which the footfalls of the left and right fore- or hindlimbs are unevenly spaced in time. Although previous studies have identified a functional differentiation between the first limb (trailing limb) and the second limb (leading limb) to touch the ground during terrestrial locomotion, the influence of a horizontal branch on limb function has never been explored. To determine the functional differences between trailing and leading forelimbs during locomotion on the ground and on a horizontal branch, X-ray motion analysis and force measurements were carried out in two European red squirrels (Sciurus vulgaris, Rodentia). The differences observed between trailing and leading forelimbs were minimal during terrestrial locomotion, where both limbs fulfill two functions and go through a shock-absorbing phase followed by a generating phase. During locomotion on a horizontal branch, European red squirrels reduce speed and all substrate reaction forces transmitted may be due to the reduction of vertical oscillation of the center of mass. Further adjustments during locomotion on a horizontal branch differ significantly between trailing and leading forelimbs and include limb flexion, lead intervals, limb protraction and vertical displacement of the scapular pivot. Consequently, trailing and leading forelimbs perform different functions. Trailing forelimbs function primarily as shock-absorbing elements, whereas leading forelimbs are characterized by a high level of stiffness. This functional differentiation indicates that European red squirrels ‘test’ the substrate for stability with the trailing forelimb, while the leading forelimb responds to or counteracts swinging or snapping branches.     

Scale Effects between Body Size and Limb Design in Quadrupedal Mammals

Recently the metabolic cost of swinging the limbs has been found to be much greater than previously thought, raising the possibility that limb rotational inertia influences the energetics of locomotion. Larger mammals have a lower mass-specific cost of transport than smaller mammals. The scaling of the mass-specific cost of transport is partly explained by decreasing stride frequency with increasing body size; however, it is unknown if limb rotational inertia also influences the mass-specific cost of transport. Limb length and inertial properties – limb mass, center of mass (COM) position, moment of inertia, radius of gyration, and natural frequency – were measured in 44 species of terrestrial mammals, spanning eight taxonomic orders. Limb length increases disproportionately with body mass via positive allometry (length ∝ body mass^0.40); the positive allometry of limb length may help explain the scaling of the metabolic cost of transport. When scaled against body mass, forelimb inertial properties, apart from mass, scale with positive allometry. Fore- and hindlimb mass scale according to geometric similarity (limb mass ∝ body mass^1.0), as do the remaining hindlimb inertial properties. The positive allometry of limb length is largely the result of absolute differences in limb inertial properties between mammalian subgroups. Though likely detrimental to locomotor costs in large mammals, scale effects in limb inertial properties appear to be concomitant with scale effects in sensorimotor control and locomotor ability in terrestrial mammals. Across mammals, the forelimb''s potential for angular acceleration scales according to geometric similarity, whereas the hindlimb''s potential for angular acceleration scales with positive allometry.     

Posture, gait and the ecological relevance of locomotor costs and energy-saving mechanisms in tetrapods

A reanalysis of locomotor data from functional, energetic, mechanical and ecological perspectives reveals that limb posture has major effects on limb biomechanics, energy-saving mechanisms and the costs of locomotion. Regressions of data coded by posture (crouched vs. erect) reveal nonlinear patterns in metabolic cost, limb muscle mass, effective mechanical advantage, and stride characteristics. In small crouched animals energy savings from spring and pendular mechanisms are inconsequential and thus the metabolic cost of locomotion is driven by muscle activation costs. Stride frequency appears to be the principal functional parameter related to the decreasing cost of locomotion in crouched animals. By contrast, the shift to erect limb postures invoked a series of correlated effects on the metabolic cost of locomotion: effective mechanical advantage increases, relative muscle masses decrease, metapodial limb segments elongate dramatically (as limbs shift from digitigrade to unguligrade designs) and biological springs increase in size and effectiveness. Each of these factors leads to decreases in the metabolic cost of locomotion in erect forms resulting from real and increasing contributions of pendular savings and spring savings. Comparisons of the relative costs and ecological relevance of different gaits reveal that running is cheaper than walking in smaller animals up to the size of dogs but running is more expensive than walking in horses. Animals do not necessarily use their cheapest gaits for their predominant locomotor activity. Therefore, locomotor costs are driven more by ecological relevance than by the need to optimize locomotor economy.     

Bridging “Romer’s Gap”: Limb Mechanics of an Extant Belly-Dragging Lizard Inform Debate on Tetrapod Locomotion During the Early Carboniferous

Devonian stem tetrapods are thought to have used ‘crutching’ on land, a belly-dragging form of synchronous forelimb action-powered locomotion. During the Early Carboniferous, early tetrapods underwent rapid radiation, and the terrestrial locomotion of crown-group node tetrapods is believed to have been hindlimb-powered and ‘raised’, involving symmetrical gaits similar to those used by modern salamanders. The fossil record over this period of evolutionary transition is remarkably poor (Romer’s Gap), but we hypothesize a phase of belly-dragging sprawling locomotion combined with symmetrical gaits. Since belly-dragging sprawling locomotion has differing functional demands from ‘raised’ sprawling locomotion, we studied the limb mechanics of the extant belly-dragging blue-tongued skink. We used X-ray reconstruction of moving morphology to quantify the three-dimensional kinematic components, and simultaneously recorded single limb substrate reaction forces (SRF) in order to calculate SRF moment arms and the external moments acting on the proximal limb joints. In the hindlimbs, stylopodal long-axis rotation is more emphasized than in the forelimbs, and much greater vertical and propulsive forces are exerted. The SRF moment arm acting on the shoulder is at a local minimum at the instant of peak force. The hindlimbs display patterns that more closely resemble ‘raised’ sprawling species. External moment at the shoulder of the skink is smaller than in ‘raised’ sprawlers. We propose an evolutionary scenario in which the locomotor mechanics of belly-dragging early tetrapods were gradually modified towards hindlimb-powered, raised terrestrial locomotion with symmetrical gait. In accordance with the view that limb evolution was an exaptation for terrestrial locomotion, the kinematic pattern of the limbs for the generation of propulsion preceded, in our scenario, the evolution of permanent body weight support.     

Patterns of mechanical energy change in tetrapod gait: pendula, springs and work

Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.     

Angular momentum and arboreal stability in common marmosets (Callithrix jacchus)

Despite the importance that concepts of arboreal stability have in theories of primate locomotor evolution, we currently lack measures of balance performance during primate locomotion. We provide the first quantitative data on locomotor stability in an arboreal primate, the common marmoset (Callithrix jacchus), predicting that primates should maximize arboreal stability by minimizing side-to-side angular momentum about the support (i.e., L_sup). If net L_sup becomes excessive, the animal will be unable to arrest its angular movement and will fall. Using a novel, highly integrative experimental procedure we directly measured whole-body L_sup in two adult marmosets moving along narrow (2.5 cm diameter) and broad (5 cm diameter) poles. Marmosets showed a strong preference for asymmetrical gaits (e.g., gallops and bounds) over symmetrical gaits (e.g., walks and runs), with asymmetrical gaits representing >90% of all strides. Movement on the narrow support was associated with an increase in more “grounded” gaits (i.e., lacking an aerial phase) and a more even distribution of torque production between the fore- and hind limbs. These adjustments in gait dynamics significantly reduced net L_sup on the narrow support relative to the broad support. Despite their lack of a well-developed grasping apparatus, marmosets proved adept at producing muscular “grasping” torques about the support, particularly with the hind limbs. We contend that asymmetrical gaits permit small-bodied arboreal mammals, including primates, to expand “effective grasp” by gripping the substrate between left and right limbs of a girdle. This model of arboreal stability may hold important implications for understanding primate locomotor evolution. Am J Phys Anthropol 156:565–576, 2015. © 2014 Wiley Periodicals, Inc.     

Locomotion in some small to medium-sized mammals: a geometric morphometric analysis of the penultimate lumbar vertebra,pelvis and hindlimbs

We assessed the influence of a variety of aspects of locomotion and ecology including gait and locomotor types, maximal running speed, home range, and body size on postcranial shape variation in small to medium-sized mammals, employing geometric morphometric analysis and phylogenetic comparative methods. The four views analyzed, i.e., dorsal view of the penultimate lumbar vertebra, lateral view of the pelvis, posterior view of the proximal femur and proximal view of the tibia, showed clear phylogenetic signal and interesting patterns of association with movement. Variation in home range size was related to some tibia shape changes, while speed was associated with lumbar vertebra, pelvis and tibia shape changes. Femur shape was not related to any locomotor variables. In both locomotor type and high-speed gait analyses, locomotor groups were distinguished in both pelvis and tibia shape analyses. These results suggest that adaptations to both typical and high-speed gaits could explain a considerable portion of the shape of those elements. In addition, lumbar vertebra and tibia showed non-significant relationships with body mass, which suggests that they might be used in morpho-functional analyses and locomotor inferences on fossil taxa, with little or no bias for body size. Lastly, we observed morpho-functional convergences among several mammalian taxa and detected some taxa that achieve similar locomotor features following different morphological paths.     

The impact of locomotor energetics on mammalian foraging

The ecological impact of energy expended on an activity stems from its effect on foraging requirements. For locomotion, the effect of moving each additional unit distance probably depends on the proportional increase in energy expenditure. Other common measures of the cost of locomotion do not reflect the impact of energy expenditure on foraging requirements. In terrestrial mammals, both the effect of body mass and the unit cost itself are very small: moving one kilometre requires less than 2% of all other energy expenditures combined. Total locomotor energy expenditure ranges from 1/2% of daily metabolism for a 10 g mammal to 6% for an elephant. Potential sources of bias in the estimation of these costs include systematic bias in estimates of distance traversed and extra energy required for non-linear locomotion. Because larger mammals can readily locomote at greater speeds, the primary locomotor advantage of large size may not be conservation of energy but of time, which can mean greater safety and more or better food.     

Evolution of chameleon locomotion,or how to become arboreal as a reptile

High-speed, biplanar X-ray motion analysis, X-ray reconstruction of moving morphology (XROMM) and morphological studies have led to the identification of those traits which are considered to be crucial for the evolution of arboreal locomotion in chameleons. The loss of the extensive lateral undulation typical of reptiles needs to be compensated by high mobility in the shoulder girdle and a clear functional regionalization of the trunk. Large limb excursion angles provide a compliant gait and are made possible by a functional parasagittalization of fore- and hind limbs, at least temporarily. All these evolutionary novelties parallel very similar modifications in the evolution of the locomotor apparatus in therian mammals. We propose that the convergent “invention” of dynamic stability and a compliant gait seem to be responsible for the locomotor similarities between chameleons and mammals.     

Biomechanics and kinematics of limb-based locomotion in lizards: review, synthesis and prospectus.

The sprawling pattern of locomotion in lizards is kinematically intriguing and is underpinned by a distinctive pattern of appendicular morphology. The statics of the sprawling posture dictate fundamental design principles, and these place constraints on the three-dimensional kinematics of the limbs and body axis as locomotion is effected. The fore and hind limbs accommodate these constraints and dictates in fundamentally similar, but positionally different ways, resulting in different kinematic profiles for these two appendages. Recent kinematic investigations have helped to clarify earlier generalizations about lizard locomotion and have revealed that kinematic patterns are more variable than was previously supposed. Such analyses, and attendant detailed studies of the anatomy of the locomotor system, promise a new synthesis and enhanced understanding of evolutionary patterns of locomotion of lizards and adjustment to various locomotor substrata and modes of progression.     

Scaling of the limb long bones to body mass in terrestrial mammals

Long‐bone scaling has been analyzed in a large number of terrestrial mammals for which body masses were known. Earlier proposals that geometric or elastic similarity are suitable as explanations for long‐bone scaling across a large size range are not supported. Differential scaling is present, and large mammals on average scale with lower regression slopes than small mammals. Large mammals tend to reduce bending stress during locomotion by having shorter limb bones than predicted rather than by having very thick diaphyses, as is usually assumed. The choice of regression model used to describe data samples in analyses of scaling becomes increasingly important as correlation coefficients decrease, and theoretical models supported by one analysis may not be supported when applying another statistical model to the same data. Differences in limb posture and locomotor performance have profound influence on the amount of stress set up in the appendicular bones during rigorous physical activity and make it unlikely that scaling of long bones across a large size range of terrestrial mammals can be satisfactorily explained by any one power function. J. Morphol. 239:167–190, 1999. © 1999 Wiley‐Liss, Inc.     

Size- and locomotion-related aspects of hominid and anthropoid pelves: An osteometrical multivariate analysis

Two multivariate methods — the logarithmic principal component analysis (LPCA), and the logarithmic factorial analysis (LFA) — have been used tocompare the hip bone proportions of hominoids biometrically. The results have shown that size effects among apes and hominids interact to a centain extent with locomotor specializations, which are related to the attainment of more or less terrestrial behaviors. The pelvic morphology of great apes (Pongo, Pan, Gorilla) has retained numerous morphological traits — such as a gracile and elongated hip bone —, which were inherited from common adaptations to arboreal locomotion. In spite of these common traits, the African pongids (Pan, Gorilla) present two very different pelvic morphologies corresponding to two adaptative modes of terrestrial quadrupedalism. The hip bone of humans is proportionnally short and robust, most particularly at the level of its axial part. These characteristics, as well as the whole pelvic proportions, clearly indicate that gravitational forces exert a strong pressure on the pelvic walls during bipedalism. Among hominids, the transition from an australopithecine-like pelvic pattern to a human-like one corresponds to an increase of loading constraints on the hip jiont. This seems to indicate an evident change in locomotor behavior. Progression apparently became exclusively terrestrial with the genusHomo.     

Comparative trends in shortening velocity and force production in skeletal muscles

Skeletal muscles are diverse in their properties, with specific contractile characteristics being matched to particular functions. In this study, published values of contractile properties for >130 diverse skeletal muscles were analyzed to detect common elements that account for variability in shortening velocity and force production. Body mass was found to be a significant predictor of shortening velocity in terrestrial and flying animals, with smaller animals possessing faster muscles. Although previous studies of terrestrial mammals revealed similar trends, the current study indicates that this pattern is more universal than previously appreciated. In contrast, shortening velocity in muscles used for swimming and nonlocomotory functions is not significantly affected by body size. Although force production is more uniform than shortening velocity, a significant correlation with shortening velocity was detected in muscles used for locomotion, with faster muscles tending to produce more force. Overall, the contractile properties of skeletal muscles are conserved among phylogenic groups, but have been significantly influenced by other factors such as body size and mode of locomotion.