Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control

Like human walking, passive dynamic walking—i.e. walking down a slope with no actuation except gravity—is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG—i.e. the CPG’s eigenfrequency—is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.     

Walking is not like reaching: evidence from periodic mechanical perturbations

The control architecture underlying human reaching has been established, at least in broad outline. However, despite extensive research, the control architecture underlying human locomotion remains unclear. Some studies show evidence of high-level control focused on lower-limb trajectories; others suggest that nonlinear oscillators such as lower-level rhythmic central pattern generators (CPGs) play a significant role. To resolve this ambiguity, we reasoned that if a nonlinear oscillator contributes to locomotor control, human walking should exhibit dynamic entrainment to periodic mechanical perturbation; entrainment is a distinctive behavior of nonlinear oscillators. Here we present the first behavioral evidence that nonlinear neuro-mechanical oscillators contribute to the production of human walking, albeit weakly. As unimpaired human subjects walked at constant speed, we applied periodic torque pulses to the ankle at periods different from their preferred cadence. The gait period of 18 out of 19 subjects entrained to this mechanical perturbation, converging to match that of the perturbation. Significantly, entrainment occurred only if the perturbation period was close to subjects' preferred walking cadence: it exhibited a narrow basin of entrainment. Further, regardless of the phase within the walking cycle at which perturbation was initiated, subjects' gait synchronized or phase-locked with the mechanical perturbation at a phase of gait where it assisted propulsion. These results were affected neither by auditory feedback nor by a distractor task. However, the convergence to phase-locking was slow. These characteristics indicate that nonlinear neuro-mechanical oscillators make at most a modest contribution to human walking. Our results suggest that human locomotor control is not organized as in reaching to meet a predominantly kinematic specification, but is hierarchically organized with a semi-autonomous peripheral oscillator operating under episodic supervisory control.     

The role of phase shifts of sensory inputs in walking revealed by means of phase reduction

Detailed neural network models of animal locomotion are important means to understand the underlying mechanisms that control the coordinated movement of individual limbs. Daun-Gruhn and Tóth, Journal of Computational Neuroscience 31(2), 43–60 (2011) constructed an inter-segmental network model of stick insect locomotion consisting of three interconnected central pattern generators (CPGs) that are associated with the protraction-retraction movements of the front, middle and hind leg. This model could reproduce the basic locomotion coordination patterns, such as tri- and tetrapod, and the transitions between them. However, the analysis of such a system is a formidable task because of its large number of variables and parameters. In this study, we employed phase reduction and averaging theory to this large network model in order to reduce it to a system of coupled phase oscillators. This enabled us to analyze the complex behavior of the system in a reduced parameter space. In this paper, we show that the reduced model reproduces the results of the original model. By analyzing the interaction of just two coupled phase oscillators, we found that the neighboring CPGs could operate within distinct regimes, depending on the phase shift between the sensory inputs from the extremities and the phases of the individual CPGs. We demonstrate that this dependence is essential to produce different coordination patterns and the transition between them. Additionally, applying averaging theory to the system of all three phase oscillators, we calculate the stable fixed points - they correspond to stable tripod or tetrapod coordination patterns and identify two ways of transition between them.     

An inter-segmental network model and its use in elucidating gait-switches in the stick insect

Animal locomotion requires highly coordinated working of the segmental neuronal networks that control the limb movements. Experiments have shown that sensory signals originating from the extremities play a pivotal role in controlling locomotion patterns by acting on central networks. Based on the results from stick insect locomotion, we constructed an inter-segmental model comprising local networks for all three legs, i.e. for the pro-, meso- and meta-thorax, their inter-connections and the main sensory inputs modifying their activities. In the model, the local networks are uniform, and each of them consists of a central pattern generator (CPG) providing the rhythmic oscillation for the protractor-retractor motor systems, the corresponding motoneurons (MNs), and local inhibitory interneurons (IINs) between the CPGs and the MNs. Between segments, the CPGs are connected cyclically by both excitatory and inhibitory pathways that are modulated by the aforementioned sensory inputs. Simulations done with our network model showed that it was capable of reproducing basic patterns of locomotion such as those occurring during tri- and tetrapod gaits. The model further revealed a number of elementary neuronal processes (e.g. synaptic inhibition, or changing the synaptic drive at specific neurons) that in the simulations were necessary, and in their entirety sufficient, to bring about a transition from one type of gait to another. The main result of this simulation study is that exactly the same mechanism underlies the transition between the two types of gait irrespective of the direction of the change. Moreover, the model suggests that the majority of these processes can be attributed to direct sensory influences, and changes are required only in centrally controlled synaptic drives to the CPGs.     

Limb kinematics during locomotion in the two-toed sloth (Choloepus didactylus,Xenarthra) and its implications for the evolution of the sloth locomotor apparatus

In order to gain insight into the function of the extant sloth locomotion and its evolution, we conducted a detailed videoradiographic analysis of two-toed sloth locomotion (Xenarthra: Choloepus didactylus). Both unrestrained as well as steady-state locomotion was analyzed. Spatio-temporal gait parameters, data on interlimb coordination, and limb kinematics are reported. Two-toed sloths displayed great variability in spatio-temporal gait parameters over the observed range of speeds. They increase speed by decreasing the durations of contact and swing phases, as well as by increasing step length. Gait utilization also varies with no strict gait sequence or interlimb timing evident in slow movements, but a tendency to employ diagonal sequence, diagonal couplet gaits in fast movements. In contrast, limb kinematics were highly conserved with respect to ‘normal’ pronograde locomotion. Limb element and joint angles at touch down and lift off, element and joint excursions, and contribution to body progression of individual elements are similar to those reported for non-cursorial mammals of small to medium size. Hands and feet are specialized to maintain firm connection to supports, and do not contribute to step length or progression. In so doing, the tarsometatarsus lost its role as an individual propulsive element during the evolution of suspensory locomotion. Conservative kinematic behavior of the remaining limb elements does not preclude that muscle recruitment and neuromuscular control for limb pro- and retraction are also conserved. The observed kinematic patterns of two-toed sloths improve our understanding of the convergent evolution of quadrupedal suspensory posture and locomotion in the two extant sloth lineages.     

Artificial neural network model for the generation of muscle activation patterns for human locomotion.

Skilled locomotor behaviour requires information from various levels within the central nervous system (CNS). Mathematical models have permitted researchers to simulate various mechanisms in order to understand the organization of the locomotor control system. While it is difficult to adequately characterize the numerous inputs to the locomotor control system, an alternative strategy may be to use a kinematic movement plan to represent the complex inputs to the locomotor control system based on the possibility that the CNS may plan movements at a kinematic level. We propose the use of artificial neural network (ANN) models to represent the transformation of a kinematic plan into the necessary motor patterns. Essentially, kinematic representation of the actual limb movement was used as the input to an ANN model which generated the EMG activity of 8 muscles of the lower limb and trunk. Data from a wide variety of gait conditions was necessary to develop a robust model that could accommodate various environmental conditions encountered during everyday activity. A total of 120 walking strides representing normal walking and ten conditions where the normal gait was modified in terms of cadence, stride length, stance width or required foot clearance. The final network was assessed on its ability to predict the EMG activity on individual walking trials as well as its ability to represent the general activation pattern of a particular gait condition. The predicted EMG patterns closely matched those recorded experimentally, exhibiting the appropriate magnitude and temporal phasing required for each modification. Only 2 of the 96 muscle/gait conditions had RMS errors above 0.10, only 5 muscle/gait conditions exhibited correlations below 0.80 (most were above 0.90) and only 25 muscle/gait conditions deviated outside the normal range of muscle activity for more than 25% of the gait cycle. These results indicate the ability of single network ANNs to represent the transformation between a kinematic movement plan and the necessary muscle activations for normal steady state locomotion but they were also able to generate muscle activation patterns for conditions requiring changes in walking speed, foot placement and foot clearance. The abilities of this type of network have implications towards both the fundamental understanding of the control of locomotion and practical realizations of artificial control systems for use in rehabilitation medicine.     

Modulation of limb dynamics in the swing phase of locomotion

A method was presented for quantifying cat (Felis catus) hind limb dynamics during swing phase of locomotion using a two-link rigid body model of leg and paw, which highlighted the dynamic interactions between segments. Comprehensive determination was made of cat segment parameters necessary for dynamic analysis, and regression equations were formulated to predict the inertial parameters of any comparable cat. Modulations in muscle and non-muscle components of knee and ankle joint moments were examined at two treadmill speeds using three gaits: (a) pace-like walk and trot-like walk, at 1.0 ms-1, and (b) gallop, at 2.1 ms-1. Results showed that muscle and segment interactive moments significantly effected limb trajectories during swing. Some moment components were greater in galloping than in walking, but net joint maxima were not significantly different between speeds. Moment magnitudes typically were greater for pace-like walking than for trot-like walking at the same speed. Generally, across gaits, the net and muscle moments were in phase with the direction of distal joint motion, and these same moments were out of phase with proximal joint motion. Intersegmental dynamics were not modulated exclusively by speed of locomotion, but interactive moments were also influenced significantly by gait mode.     

Evaluating functional roles of phase resetting in generation of adaptive human bipedal walking with a physiologically based model of the spinal pattern generator

The central pattern generators (CPGs) in the spinal cord strongly contribute to locomotor behavior. To achieve adaptive locomotion, locomotor rhythm generated by the CPGs is suggested to be functionally modulated by phase resetting based on sensory afferent or perturbations. Although phase resetting has been investigated during fictive locomotion in cats, its functional roles in actual locomotion have not been clarified. Recently, simulation studies have been conducted to examine the roles of phase resetting during human bipedal walking, assuming that locomotion is generated based on prescribed kinematics and feedback control. However, such kinematically based modeling cannot be used to fully elucidate the mechanisms of adaptation. In this article we proposed a more physiologically based mathematical model of the neural system for locomotion and investigated the functional roles of phase resetting. We constructed a locomotor CPG model based on a two-layered hierarchical network model of the rhythm generator (RG) and pattern formation (PF) networks. The RG model produces rhythm information using phase oscillators and regulates it by phase resetting based on foot-contact information. The PF model creates feedforward command signals based on rhythm information, which consists of the combination of five rectangular pulses based on previous analyses of muscle synergy. Simulation results showed that our model establishes adaptive walking against perturbing forces and variations in the environment, with phase resetting playing important roles in increasing the robustness of responses, suggesting that this mechanism of regulation may contribute to the generation of adaptive human bipedal locomotion.     

The relationship between joint kinetic factors and the walk-run gait transition speed during human locomotion

The primary purpose of this project was to examine whether lower extremity joint kinetic factors are related to the walk-run gait transition during human locomotion. Following determination of the preferred transition speed (PTS), each of the 16 subjects walked down a 25-m runway, and over a floor-mounted force platform at five speeds (70, 80, 90, 100, and 110% of the PTS), and ran over the force platform at three speeds (80, 100, and 120% of the PTS) while being videotaped (240 Hz) from the right sagittal plane. Two-dimensional kinematic data were synchronized with ground reaction force data (960 Hz). After smoothing, ankle and knee joint moments and powers were calculated using standard inverse dynamics calculations. The maximum dorsiflexor moment was the only variable tested that increased as walking speed increased and then decreased when gait changed to a run at the PTS, meeting the criteria set to indicate that this variable influences the walk-run gait transition during human locomotion. This supports previous research suggesting that an important factor in changing gaits at the PTS is the prevention of undue stress in the dorsiflexor muscles.     

Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation

This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.     

Footfall patterns, stride length and speed of vertical climbing in spider monkeys (Ateles fusciceps robustus) and woolly monkeys (Lagothrix lagotricha)

Vertical climbing is central to theories surrounding the locomotor specialisations of large primates. In this paper, we present spatiotemporal gait parameters obtained from video recordings of captive spider monkeys (Ateles fusciceps robustus) and woolly monkeys (Lagothrix lagotricha) in semi-natural enclosures, with the aim of discovering the influence of body weight and differences in general locomotor behaviour on vertical climbing kinematics on various substrates. Results show that there are only few differences between gait parameters of climbing on thin trees, vertical and oblique ropes, while climbing on large-diameter trees differs considerably, reflecting the higher costs of locomotion on the latter. At the same speed, Ateles takes longer strides and the support phase takes a smaller percentage of cycle duration than in Lagothrix. Footfall patterns are more diverse in Ateles and include a higher proportion of ipsilateral limb coupling. Compared to other primates, the gait characteristics of vertical climbing of atelines most closely resemble those of African apes.     

Effect of Trunk Sagittal Attitude on Shoulder,Thorax and Pelvis Three-Dimensional Kinematics in Able-Bodied Subjects during Gait

It has been shown that an original attitude in forward or backward inclination of the trunk is maintained at gait initiation and during locomotion, and that this affects lower limb loading patterns. However, no studies have shown the extent to which shoulder, thorax and pelvis three-dimensional kinematics are modified during gait due to this sagittal inclination attitude. Thirty young healthy volunteers were analyzed during level walking with video-based motion analysis. Reflecting markers were mounted on anatomical landmarks to form a two-marker shoulder line segment, and a four-marker thorax and pelvis segments. Absolute and relative spatial rotations were calculated, for a total of 11 degrees of freedom. The subjects were divided into two groups of 15 according to the median of mean thorax inclination angle over the gait cycle. Preliminary MANOVA analysis assessed whether gender was an independent variable. Then two-factor nested ANOVA was used to test the possible effect of thorax inclination on body segments, planes of motion and gait periods, separately. There was no significant difference in all anthropometric and spatio-temporal parameters between the two groups, except for subject mass. The three-dimensional kinematics of the thorax and pelvis were not affected by gender. Nested ANOVA revealed group effect in all segment rotations apart those at the pelvis, in the sagittal and frontal planes, and at the push-off. Attitudes in sagittal thorax inclination altered trunk segments kinematics during gait. Subjects with a backward thorax showed less thorax-to-pelvis motion, but more shoulder-to-thorax and thorax-to-laboratory motion, less motion in flexion/extension and in lateral bending, and also less motion during push-off. This contributes to the understanding of forward propulsion and sideways load transfer mechanisms, fundamental for the maintenance of balance and the risk of falling.     

Dominance of local sensory signals over inter-segmental effects in a motor system: experiments

Legged locomotion requires that information local to one leg, and inter-segmental signals coming from the other legs are processed appropriately to establish a coordinated walking pattern. However, very little is known about the relative importance of local and inter-segmental signals when they converge upon the central pattern generators (CPGs) of different leg joints. We investigated this question on the CPG of the middle leg coxa?Ctrochanter (CTr)-joint of the stick insect which is responsible for lifting and lowering the leg. We used a semi-intact preparation with an intact front leg stepping on a treadmill, and simultaneously stimulated load sensors of the middle leg. We found that middle leg load signals induce bursts in the middle leg depressor motoneurons (MNs). The same local load signals could also elicit rhythmic activity in the CPG of the middle leg CTr-joint when the stimulation of middle leg load sensors coincided with front leg stepping. However, the influence of front leg stepping was generally weak such that front leg stepping alone was only rarely accompanied by switching between middle leg levator and depressor MN activity. We therefore conclude that the impact of the local sensory signals on the levator?Cdepressor motor system is stronger than the inter-segmental influence through front leg stepping.     

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.     

Human odometer is gait-symmetry specific

In 1709, Berkeley hypothesized of the human that distance is measurable by ‘the motion of his body, which is perceivable by touch’. To be sufficiently general and reliable, Berkeley''s hypothesis must imply that distance measured by legged locomotion approximates actual distance, with the measure invariant to gait, speed and number of steps. We studied blindfolded human participants in a task in which they travelled by legged locomotion from a fixed starting point A to a variable terminus B, and then reproduced, by legged locomotion from B, the A–B distance. The outbound (‘measure’) and return (‘report’) gait could be the same or different, with similar or dissimilar step sizes and step frequencies. In five experiments we manipulated bipedal gait according to the primary versus secondary distinction revealed in symmetry group analyses of locomotion patterns. Berkeley''s hypothesis held only when the measure and report gaits were of the same symmetry class, indicating that idiothetic distance measurement is gait-symmetry specific. Results suggest that human odometry (and perhaps animal odometry more generally) entails variables that encompass the limbs in coordination, such as global phase, and not variables at the level of the single limb, such as step length and step number, as traditionally assumed.     

Guineafowl hind limb function. I: Cineradiographic analysis and speed effects

Avian striding bipedalism was studied in the helmeted guineafowl, Numida meleagris. High‐speed cineradiographs, light films, and videos were used to record hind limb movements across a wide range of speeds. In particular, direct visualization of the skeleton in X‐ray images allowed changes in pelvic and femoral position to be quantified with great accuracy for the first time. With the exception of limb protraction angle, all stride parameters are speed‐dependent. During the stance phase, guineafowl primarily employ knee flexion at very low speeds. At higher speeds, the magnitudes of hip and knee extension in the second half of stance progressively increase. Pelvic rotations are relatively small, but birds gradually pitch further forward with speed. An aerial phase is not present at speeds less than 2.0 m/sec, but discontinuities in the relationship of some parameters to speed indicate a gait transition near 0.9 m/sec. Birds are considered to be flying theropod dinosaurs, making characterization of bipedalism in living birds essential to understanding the evolution of theropod locomotion. Data from guineafowl, including the kinematic effects of speed, are informative about several aspects of locomotion in extinct theropods. However, many details of avian bipedalism evolved only within a subset of Theropoda, and are therefore not directly applicable to all members of the clade. J. Morphol. 240:115–125, 1999. © 1999 Wiley‐Liss, Inc.     

Bipedal locomotion: effects of speed, size and limb posture in birds and humans

Seven species of ground-dwelling birds (body mass range: 0.045-90 kg) were filmed while walking and running on a treadmill. High-speed light films were also taken of humans to compare kinematic patterns of avian with human bipedalism. Consistent patterns of stride frequency, stride length, step length, duty factor and limb excursion were observed in all species, with most of the variation among species being due to differences in body size. In general, smaller bipeds have higher stride frequencies (α M ^−0.18), shorter stride lengths (α M ^0.38) and more limited ranges of speed within each gait than large bipeds. After normalizing for size (based on Froude number, after Alexander, 1977), remaining kinematic variation is largely due to interspecific differences in posture and relative limb segment lengths. For their size, smaller bipeds have greater step lengths, limb excursion angles and duty factors than large bipeds because of their more crouched posture and greater effective limb length. The most notable differences in limb kinematics between birds and humans occur at the walk-run transition and are maintained as running speed increases. Change of gait is smooth and difficult to discern in birds, but distinct in humans, involving abrupt decreases in step length and duty factor (time of contact) and a corresponding increase in limb swing time. These differences appear to reflect a spring-like run that is stiff in humans (favouring elastic energy recovery) but more compliant in birds (increasing time of ground contact). Differences between birds and humans in balance of the body's centre of mass not only affect femoral orientation and motion, but also affect pattern of limb excursion with speed.     

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.     

A mechanical link model of two-toed sloths: no pendular mechanics during suspensory locomotion

Sloths are morphologically specialized in suspensory quadrupedal locomotion and posture. During steady-state locomotion they utilize a trot-like footfall sequence. Contrasting the growing amount of published accounts of the functional morphology and kinematics of sloth locomotion, no study concerned with the dynamics of their quadrupedal suspensory locomotion has been conducted. Brachiating primates have been shown to travel at low mechanical costs using pendular mechanics, but this is associated with considerable dynamic forces exerted onto the support. To test whether sloth locomotion can be described by simple connected pendulum mechanics, we analyzed the dynamics of sloth locomotion with use of a mechanical segment link model. The model integrates the body segment parameters and is driven by kinematic data with both segment parameters and kinematic data obtained from the same sloth individual. No simple pendular mechanics were present. We then used the model to carry out an inverse dynamic analysis. The analysis allowed us to estimate net limb joint torques and substrate reaction forces during the contact phases. Predominant flexing limb joint torque profiles in the shoulder, elbow, hip, and knee are in stark contrast to published dominant extensor torques in the limb joints of pronograde quadrupedal mammals. This dissimilarity likely reflects the inverse orientation of the sloth towards the gravity vector. Nevertheless, scapular pivot and shoulder seem to provide the strongest torque for progression as expected based on unchanged basic kinematic pattern previously described. Our model predicts that sloths actively reduce the dynamical forces and moments that are transmitted onto the support. We conclude that these findings reflect the need to reduce the risk of breaking supports because in this case sloths would likely be unable to react quickly enough to prevent potentially lethal falls. To achieve this, sloths seem to avoid the dynamical consequences of effective pendular mechanics.