A model of bipedal locomotion on compliant legs.

Simple mathematical models capable of walking or running are used to compare the merits of bipedal gaits. Stride length, duty factor (the fraction of the stride, for which the foot is on the ground) and the pattern of force on the ground are varied, and the optimum gait is deemed to be the one that minimizes the positive work that the muscles must perform, per unit distance travelled. Even the simplest model, whose legs have neither mass nor elastic compliance, predicts the changes of duty factor and force pattern that people make as they increase their speed of walking. It predicts a sudden change to running at a critical speed, but this is much faster than the speed at which people make the change. When elastic compliance is incorporated in the model, unnaturally fast walking becomes uncompetitive. However, a slow run with very brief foot contact becomes the optimum gait at low speeds, at which people would walk, unless severe energy dissipation occurs in the compliance. A model whose legs have mass as well as elastic compliance predicts well the relationship between speed and stride length in human walking.     

Biomechanical analysis of primate bipedal walking by computer simulation

A computer simulation technique was applied to make clear the mechanical characteristics of primate bipedal walking. A primate body and the walking mechanism were modeled mathematically with a set of dynamic equations. Using a digital computer, the following were calculated from these equations by substituting measured displacements and morphological data of each segment of the primate: the acceleration, joint angle, center of gravity, foot force, joint moment, muscular force, transmitted force at the joint, electric activity of the muscle, generated power by the leg and energy expenditure in walking.The model was evaluated by comparing some of the calculated results with the experimental results such as foot force and electromyographic data, and improved in order to obtain the agreement between them.The level bipedal walking of man, chimpanzee and Japanese monkey and several types of synthesized walking were analyzed from the viewpoint of biomechanics.It is concluded that the bipedal walking of chimpanzee is nearer to that of man than to that of the Japanese monkey because of its propulsive mechanism, but it requires large muscular force for supporting the body weight.     

Synthesis of natural arm swing motion in human bipedal walking

It has historically been believed that the role of arm motion during walking is related to balancing. Arm motion during natural walking is distinguished in that each arm swing is with the motion of the opposing leg. Although this arm swing motion is generated naturally during bipedal walking, it is interesting to note that the arm swing motion is not necessary for stable walking. This paper attempts to explain the contribution of out-of-phase arm swing in human bipedal walking. Consequently, a human motion control methodology that generates this arm swing motion during walking is proposed. The relationship between arm swing and reaction moment about the vertical axis of the foot is explained in the context of the dynamics of a multi-body articulated system. From this understanding, it is reasoned that arm swing is the result of an effort to reduce the reaction moment about the vertical axis of the foot while the torso and legs are being controlled. This idea is applied to the generation of walking motion. The arm swing motion can be generated, not by designing and tracking joint trajectories of the arms, but by limiting the allowable reaction moment at the foot and minimizing whole-body motion while controlling the lower limbs and torso to follow the designed trajectory. Simulation results, first with the constraint on the foot vertical axis moment and then without, verify the relationship between arm swing and foot reaction moment. These results also demonstrate the use of the dynamic control method in generating arm swing motion.     

Infant stepping: a window to the behaviour of the human pattern generator for walking

The aim of this paper is to provide evidence, both published and new, to support the notion that human infants are particularly good subjects for the study of the pattern generator for walking. We and others have shown that stepping can be initiated by sensory input from the legs or by general heightened excitability of the infant. New results are presented here to suggest that weight support through the feet and rapid extension of the legs are important proprioceptive inputs to initiate stepping. Our previous work has shown that infants can step at many different speeds when supported on a treadmill. The step cycle duration shortens as the speed increases, with the changes coming largely from the stance phase, just as in most other terrestrial animals. Moreover, we have shown that infants will step in all directions. Regardless of the direction of stepping, the step cycle changes in the same way with walking speed, suggesting the circuitry that controls different directions of walking share common elements. We have also shown that infant stepping is highly organized. Sensory inputs, whether proprioceptive or touch, are gated in a functional way so that only important sensory inputs generate a response. For example, touch to the lateral surface of the foot elicits a response only in sideways walking, and only in the leading limb. New data is presented here to show that the pattern generators from each limb can operate somewhat independently. On a split-belt treadmill with the 2 belts running at different speeds or in different directions, the legs showed considerable independence in behaviour. Yet, the pattern generators on each side interact to ensure that swing phase does not occur at the same time. These studies have provided insight into the organization of the pattern generator for walking in humans. It will be interesting in the future to study how maturation of the descending tracts changes walking behaviour to allow independent bipedal walking.     

Optimum walking techniques for idealized animals

The vertical component of the force exerted by a foot on the ground, in the course of a step, may rise to a single maximum and decline again (as in human running) or may show two distinct maxima (as in human walking). A foot may remain on the ground for a large or small fraction of the duration of a stride. Mathematical models are used to investigate the effects of these differences of technique on the energy cost of locomotion. The optimum technique for a biped at a given speed is different from the optimum for a hypothetical many-legged animal. The optima for quadrupedal walking are likely to lie between these extremes.
The walking techniques adopted by men at different speeds are close to the optima indicated by the bipedal model. The two maxima of the force exerted by a foot are higher, and have a lower minimum between them, at higher speeds of walking. The techniques adopted by a sheep are close to the optima indicated by the many-legged model but dogs use techniques rather closer to the optima for bipeds.
The limitations of the models are discussed.     

Segment and joint angles of hind limb during bipedal and quadrupedal walking of the bonobo (Pan paniscus)

We describe segment angles (trunk, thigh, shank, and foot) and joint angles (hip, knee, and ankle) for the hind limbs of bonobos walking bipedally ("bent-hip bent-knee walking," 17 sequences) and quadrupedally (33 sequences). Data were based on video recordings (50 Hz) of nine subjects in a lateral view, walking at voluntary speed. The major differences between bipedal and quadrupedal walking are found in the trunk, thigh, and hip angles. During bipedal walking, the trunk is approximately 33-41 degrees more erect than during quadrupedal locomotion, although it is considerably more bent forward than in normal human locomotion. Moreover, during bipedal walking, the hip has a smaller range of motion (by 12 degrees ) and is more extended (by 20-35 degrees ) than during quadrupedal walking. In general, angle profiles in bonobos are much more variable than in humans. Intralimb phase relationships of subsequent joint angles show that hip-knee coordination is similar for bipedal and quadrupedal walking, and resembles the human pattern. The coordination between knee and ankle differs much more from the human pattern. Based on joint angles observed throughout stance phase and on the estimation of functional leg length, an efficient inverted pendulum mechanism is not expected in bonobos.     

Voluntary bipedal walking of infant chimpanzees

The voluntary bipedal walking of infant chimpanzees was studied by the analysis of foot force and by motion analysis. The infants were trained to locomote on a level platform without any restrictions on the locomotor pattern. The voluntary bipedal walking was compared with the other types of locomotion at the same age and with the trained bipedal walking performed by other chimpanzees, including adult chimpanzees. The characteristics of voluntary bipedal walking in the infant until one year of age were: (1) high-speed walking with short cycle duration; (2) short stance phase duration; (3) small braking component of the preceding leg and large acceleration of the following leg; (4) one downward peak in the vertical component; and (5) a relatively small transverse component. Bipedal walking usually continued for less than one second and ended in quadrupedal locomotion. During walking, the preceding foot touched the floor, heel first, as in the case of older chimpanzees and humans. At this age, bipedal walking was similar to high-speed locomotion. The voluntary bipedal walking of the two-year-old and frour-yearold chimpanzees was characterized as follows: (1) slower speed than during quadrupedal locomotion, (2) relatively long periods and distances; (3) well balanced accelerating and braking components; and (4) a vertical component showing two downward peaks and a trough in between during numerous trials. The last characteristic means that the body center of gravity is higher in the single stance phase, just as in the bipedal walkinbg of the adult chimpanzees and humans. The bipedal walking of infant chimpanzees was discussed in comparison with the walking of humans, including infants.     

Mechanical energy oscillations of two brachiation gaits: measurement and simulation

How do arm‐swinging apes locomote effectively over a variety of speeds? One way to reduce the metabolic energy cost of locomotion is to transfer energy between reversible mechanical modes. In terrestrial animals, at least two transfer mechanisms have been identified: 1) a pendulum‐like mechanism for walking, with exchange between gravitational potential energy and translational kinetic energy, and 2) a spring‐like mechanism for running, where the elastic strain energy of stretched muscle and tendon is largely returned to reaccelerate the animal. At slower speeds, a brachiator will always have at least one limb in contact with the support, similar to the overlap of foot contact in bipedal walking. At faster speeds, brachiators exhibit an aerial phase, similar to that seen in bipedal running. Are there two distinct brachiation gaits even though the animal appears to simply swing beneath its overhead support? If so, are different exchange mechanisms employed? Our kinetic analysis of brachiation in a white‐handed gibbon (Hylobates lar) indicates that brachiation is indeed comprised of two mechanically distinct gaits. At slower speeds in “continuous contact” brachiation, the gibbon utilizes a simple pendulum‐like transfer of mechanical energy within each stride. At faster speeds in “ricochetal” brachiation, translational and rotational kinetic energy are exchanged in a novel “whip‐like” transfer. We propose that brachiators utilize the transfer between translational and rotational kinetic energy to control the dynamics of their swing. This maneuver may allow muscle action at the shoulder to control the transfer and adjust the ballistic portion of the step to meet the requirements for the next hand contact. Am J Phys Anthropol 115:319–326, 2001. © 2001 Wiley‐Liss, Inc.     

Center of mass mechanics of chimpanzee bipedal walking

Center of mass (CoM) oscillations were documented for 81 bipedal walking strides of three chimpanzees. Full‐stride ground reaction forces were recorded as well as kinematic data to synchronize force to gait events and to determine speed. Despite being a bent‐hip, bent‐knee (BHBK) gait, chimpanzee walking uses pendulum‐like motion with vertical oscillations of the CoM that are similar in pattern and relative magnitude to those of humans. Maximum height is achieved during single support and minimum height during double support. The mediolateral oscillations of the CoM are more pronounced relative to stature than in human walking when compared at the same Froude speed. Despite the pendular nature of chimpanzee bipedalism, energy recoveries from exchanges of kinetic and potential energies are low on average and highly variable. This variability is probably related to the poor phasic coordination of energy fluctuations in these facultatively bipedal animals. The work on the CoM per unit mass and distance (mechanical cost of transport) is higher than that in humans, but lower than that in bipedally walking monkeys and gibbons. The pronounced side sway is not passive, but constitutes 10% of the total work of lifting and accelerating the CoM. CoM oscillations of bipedally walking chimpanzees are distinctly different from those of BHBK gait of humans with a flat trajectory, but this is often described as “chimpanzee‐like” walking. Human BHBK gait is a poor model for chimpanzee bipedal walking and offers limited insights for reconstructing early hominin gait evolution. Am J Phys Anthropol 156:422–433, 2015. © 2014 Wiley Periodicals, Inc.     

New method of three-dimensional analysis of bipedal locomotion for the study of displacements of the body and body-parts centers of mass in man and non-human primates: Evolutionary framework

The current biomechanical interpretation of the chimpanzee's bipedal walking argues that larger lateral and vertical displacements of the body center of mass occur in the chimpanzee's “side-to-side” gait than in the human striding gait. The evolutionary hypothesis underlying this study is the following: during the evolution of human bipedalism one of the necessary changes could have been the progressive reduction of these displacements of the body center of mass. In order to quantitatively test this hypothesis, it is necessary to obtain simultaneously the trajectories of the centers of mass of the whole body and of the different body parts. To solve this problem, a new method of three-dimensional analysis of walking, associated with a volumetric modelling of the body, has been developed based on finite-element modelling. An orthogonal synchrophotographic device yielding four synchronous pictures of the walking subject allows a qualitative analysis of the photographic sequences together with the results of their quantitative analysis. This method was applied to an adult man, a 3-year-old girl and a 9-year-old male chimpanzee. Our results suggest that the trajectory of the body center of mass of the human is distinguished from that of the chimpanzee not by a lower movement amplitude but by the synchronization of the transverse and vertical displacements into two periodic curves in phase with one another. The non-human primate uses its repertoire of arboreal movements in its bipedal terrestrial gait, provisionally referred to as a “rope-walker” gait. We show that the interpretation of a “side-to-side” gait is not applicable to the chimpanzee. We argue that similarly this interpretation and the initial hypothesis presuppose a basic symmetric structure of the gait, in relation to the sagittal plane of progression, similar to the human one. This lateral symmetry of the right and left displacements of the center of gravity, in phase with the right and left single supports of walking, is probably a very derived feature of the human gait. We suggest that low lateral and vertical displacements of the body center of mass are not indicative of a progressive bipedal gait and we discuss the new evolutionary implications of our results. © 1993 Wiley-Liss, Inc.     

Dynamics of primate bipedal walking as viewed from the force of foot

Bipedal walking of the six species of anthropoid primates including man were examined by means of the force plate technique. Though each species has a particular pattern of bipedal walking, we can classify two types of patterns in these primates as far as the foot force is concerned. The first type includes the man, chimpanzee, and spider monkey and the second type contains the Japanese monkey, hamadryas baboon, and gibbon. It was emphasized that the similarity of man to the chimpanzee and spider monkey in bipedal walking has some evolutionary significance.     

Compliant leg behaviour explains basic dynamics of walking and running

The basic mechanics of human locomotion are associated with vaulting over stiff legs in walking and rebounding on compliant legs in running. However, while rebounding legs well explain the stance dynamics of running, stiff legs cannot reproduce that of walking. With a simple bipedal spring-mass model, we show that not stiff but compliant legs are essential to obtain the basic walking mechanics; incorporating the double support as an essential part of the walking motion, the model reproduces the characteristic stance dynamics that result in the observed small vertical oscillation of the body and the observed out-of-phase changes in forward kinetic and gravitational potential energies. Exploring the parameter space of this model, we further show that it not only combines the basic dynamics of walking and running in one mechanical system, but also reveals these gaits to be just two out of the many solutions to legged locomotion offered by compliant leg behaviour and accessed by energy or speed.     

The relationship between speed, contact time and peak plantar pressure in terrestrial walking of bonobos

The aim of this paper is twofold. Firstly, we investigate whether contact times, as recorded by pedobarographic systems during quadrupedal and bipedal walking of bonobos, can be used to reliably calculate actual velocities, by applying formulae based on lateral-view video recordings. Secondly, we investigate the effect of speed on peak plantar pressures during bipedal and quadrupedal walking of the bonobo. Data were obtained from 4 individuals from a group of bonobos at the Animal Park Planckendael. From our study, we can conclude that both walking speeds calculated from contact times and lower leg length or simply from recorded contact times are good estimators for walking speed, when direct observation of the latter is impossible. Further, it was found that effects of speed on peak plantar pressures and vertical forces are absent or at least subtle in comparison to a large variation in pressure patterns. In bonobos, the same pressure patterns are used at all walking speeds, and, in consequence, we do not expect major changes in foot function.     

Analysis of the human and ape foot during bipedal standing with implications for the evolution of the foot

The ratio of the power arm (the distance from the heel to the talocrural joint) to the load arm (that from the talocrural joint to the distal head of the metatarsals), or RPL, differs markedly between the human and ape foot. The arches are relatively higher in the human foot in comparison with those in apes. This study evaluates the effect of these two differences on biomechanical effectiveness during bipedal standing, estimating the forces acting across the talocrural and tarsometatarsal joints, and attempts to identify which type of foot is optimal for bipedal standing. A simple model of the foot musculoskeletal system was built to represent the geometric and force relationships in the foot during bipedal standing, and measurements for a variety of human and ape feet applied. The results show that: (1) an RPL of around 40% (as is the case in the human foot) minimizes required muscle force at the talocrural joint; (2) the presence of an high arch in the human foot reduces forces in the plantar musculature and aponeurosis; and (3) the human foot has a lower total of force in joints and muscles than do the ape feet. These results indicate that the proportions of the human foot, and the height of the medial arch are indeed better optimized for bipedal standing than those of apes, further suggesting that their current state is to some extent the product of positive selection for enhanced bipedal standing during the evolution of the foot.     

A complete second metatarsal (StW 89) from Sterkfontein Member 4, South Africa

The functional anatomy of the hominin foot has played a crucial role in studies of locomotor evolution in human ancestors and extinct relatives. However, foot fossils are rare, often isolated, and fragmentary. Here, we describe a complete hominin second metatarsal (StW 89) from the 2.0-2.6 million year old deposits of Member 4, Sterkfontein Cave, South Africa. Like many other fossil foot bones, it displays a mosaic of derived human-like features and primitive ape-like features. StW 89 possesses a domed metatarsal head with a prominent sulcus, indicating dorsiflexion at the metatarsophalangeal joint during bipedal walking. However, while the range of motion at the metatarsophalangeal joint is human-like in dorsiflexion, it is ape-like in plantarflexion. Furthermore, StW 89 possesses internal torsion of the head, an anatomy decidedly unlike that found in humans today. Unlike other hominin second metatarsals, StW 89 has a dorsoplantarly gracile base, perhaps suggesting more midfoot laxity. In these latter two anatomies, the StW 89 second metatarsal is quite similar to the recently described second metatarsal of the partial foot from Burtele, Ethiopia. We interpret this combination of anatomies as evidence for a low medial longitudinal arch in a foot engaged in both bipedal locomotion, but also some degree of pedal, and perhaps even hallucal, grasping. Additional fossil evidence will be required to determine if differences between this bone and other second metatarsals from Sterkfontein reflect normal variation in an evolving lineage, or taxonomic diversity.     

A collisional model of the energetic cost of support work qualitatively explains leg sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition

Terrestrial legged locomotion requires repeated support forces to redirect the body's vertical velocity component from down to up. We assume that the redirection is accomplished by impulsive leg forces that cause small-angle glancing collisions of a point-mass model of the animal. We estimate the energetic costs of these collisions by assuming a metabolic cost proportional to positive muscle work involved in generating the impulses. The cost of bipedal running estimated from this collisional model becomes less than that of walking at a Froude number (v2/gl) of about 0.7. Two strategies to reduce locomotion costs associated with the motion redirection are: (1) having legs simulate purely elastic springs, as is observed in human running; and (2) sequencing the leg forces during the redirection phase; examples of this sequencing are the ba-da-dump pattern of a horse gallop and having push-off followed by heel-strike in human walking.     

Human Locomotion

The development of bipedal plantigrade progression is a purely human, and apparently learned, accomplishment. Experimental findings confirm the hypothesis that the human body will integrate the motion of various segments of the body and control the activity of muscles to minimize energy expenditure.Movements which are integrated for this purpose include vertical displacement of the body, horizontal rotation of the pelvis, mediolateral pelvic tilt, flexion of the knee, plantar flexion of the ankle and foot, lateral displacement of the torso and rotation of the shoulder girdle.Raising and lowering the body results in gains and losses of potential energy, and acceleration and deceleration result in gains and losses of kinetic energy. The motions are so co-ordinated that a transfer of energy back and forth from kinetic to potential occurs during walking, which tends to minimize total energy expenditure as well as muscle work.     

A mathematical model of hind-limb control in cats when walking backward

The “walking backward” mode was achieved within a single model of cat hind-limb locomotion with the balance maintenance only due to a change in the controlling actions (in addition to the “forward walking” mode). The skeletal part of the model contains the spine, pelvis, and two limbs consisting of the thigh, shin, and foot. The hip joint and spine mount in the thoracic region have three degrees of freedom; the knee and ankle joints have one degree of freedom. The pelvis is rigidly connected to the spine. Control is performed by model muscles (flexors and extensors of the thigh, shin, and foot). The muscle activation is performed by the effects that are typical for motoneurons that control the muscles. The feet in the support phase touch the treadmill, which moves at a constant speed. The model qualitatively reproduces multiple characteristics of feline movements during forward and backward walking (supporting its validity).