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.     

Gait transitions in simulated reduced gravity

Gravity has a strong effect on gait and the speed of gait transitions. A gait has been defined as a pattern of locomotion that changes discontinuously at the transition to another gait. On Earth, during gradual speed changes, humans exhibit a sudden discontinuous switch from walking to running at a specific speed. To study the effects of altered gravity on both the stance and swing legs, we developed a novel unloading exoskeleton that allows a person to step in simulated reduced gravity by tilting the body relative to the vertical. Using different simulation techniques, we confirmed that at lower gravity levels the transition speed is slower (in accordance with the previously reported Froude number ～0.5). Surprisingly, however, we found that at lower levels of simulated gravity the transition between walking and running was generally gradual, without any noticeable abrupt change in gait parameters. This was associated with a significant prolongation of the swing phase, whose duration became virtually equal to that of stance in the vicinity of the walk-run transition speed, and with a gradual shift from inverted-pendulum gait (walking) to bouncing gait (running).     

Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking?

It is widely accepted that humans and animals minimize energetic cost while walking. While such principles predict average behavior, they do not explain the variability observed in walking. For robust performance, walking movements must adapt at each step, not just on average. Here, we propose an analytical framework that reconciles issues of optimality, redundancy, and stochasticity. For human treadmill walking, we defined a goal function to formulate a precise mathematical definition of one possible control strategy: maintain constant speed at each stride. We recorded stride times and stride lengths from healthy subjects walking at five speeds. The specified goal function yielded a decomposition of stride-to-stride variations into new gait variables explicitly related to achieving the hypothesized strategy. Subjects exhibited greatly decreased variability for goal-relevant gait fluctuations directly related to achieving this strategy, but far greater variability for goal-irrelevant fluctuations. More importantly, humans immediately corrected goal-relevant deviations at each successive stride, while allowing goal-irrelevant deviations to persist across multiple strides. To demonstrate that this was not the only strategy people could have used to successfully accomplish the task, we created three surrogate data sets. Each tested a specific alternative hypothesis that subjects used a different strategy that made no reference to the hypothesized goal function. Humans did not adopt any of these viable alternative strategies. Finally, we developed a sequence of stochastic control models of stride-to-stride variability for walking, based on the Minimum Intervention Principle. We demonstrate that healthy humans are not precisely “optimal,” but instead consistently slightly over-correct small deviations in walking speed at each stride. Our results reveal a new governing principle for regulating stride-to-stride fluctuations in human walking that acts independently of, but in parallel with, minimizing energetic cost. Thus, humans exploit task redundancies to achieve robust control while minimizing effort and allowing potentially beneficial motor variability.     

Criteria for dynamic similarity in bouncing gaits

Animals of different sizes tend to move in a dynamically similar manner when travelling at speeds corresponding to equal values of a dimensionless parameter (DP) called the Froude number. Consequently, the Froude number has been widely used for defining equivalent speeds and predicting speeds of locomotion by extinct species and on other planets. However, experiments using simulated reduced gravity have demonstrated that equality of the Froude number does not guarantee dynamic similarity. This has cast doubt upon the usefulness of the Froude number in locomotion research. Here we use dimensional analysis of the planar spring-mass model, combined with Buckingham's Pi-Theorem, to demonstrate that four DPs must be equal for dynamic similarity in bouncing gaits such as trotting, hopping and bipedal running. This can be reduced to three DPs by applying the constraint of maintaining a constant average speed of locomotion. Sensitivity analysis indicates that all of these DPs are important for predicting dynamic similarity. We show that the reason humans do not run in a dynamically similar manner at equal Froude number in different levels of simulated reduced gravity is that dimensionless leg stiffness decreases as gravity increases. The reason that the Froude number can predict dynamic similarity in Earth gravity is that dimensionless leg stiffness and dimensionless vertical landing speed are both independent of size. In conclusion, although equal Froude number is not sufficient for dynamic similarity, it is a necessary condition. Therefore, to detect fundamental differences in locomotion, animals of different sizes should be compared at equal Froude number, so that they can be as close to dynamic similarity as possible. More generally, the concept of dynamic similarity provides a powerful framework within which similarities and differences in locomotion can be interpreted.     

Forward dynamic simulation of bipedal walking in the Japanese macaque: investigation of causal relationships among limb kinematics, speed, and energetics of bipedal locomotion in a nonhuman primate

Japanese macaques that have been trained for monkey performances exhibit a remarkable ability to walk bipedally. In this study, we dynamically reconstructed bipedal walking of the Japanese macaque to investigate causal relationships among limb kinematics, speed, and energetics, with a view to understanding the mechanisms underlying the evolution of human bipedalism. We constructed a two-dimensional macaque musculoskeletal model consisting of nine rigid links and eight principal muscles. To generate locomotion, we used a trajectory-tracking control law, the reference trajectories of which were obtained experimentally. Using this framework, we evaluated the effects of changes in cycle duration and gait kinematics on locomotor efficiency. The energetic cost of locomotion was estimated based on the calculation of mechanical energy generated by muscles. Our results demonstrated that the mass-specific metabolic cost of transport decreased as speed increased in bipedal walking of the Japanese macaque. Furthermore, the cost of transport in bipedal walking was reduced when vertical displacement of the hip joint was virtually modified in the simulation to be more humanlike. Human vertical fluctuations in the body's center of mass actually contributed to energy savings via an inverted pendulum mechanism.     

Why not walk faster?

Bipedal walking following inverted pendulum mechanics is constrained by two requirements: sufficient kinetic energy for the vault over midstance and sufficient gravity to provide the centripetal acceleration required for the arc of the body about the stance foot. While the acceleration condition identifies a maximum walking speed at a Froude number of 1, empirical observation indicates favoured walk-run transition speeds at a Froude number around 0.5 for birds, humans and humans under manipulated gravity conditions. In this study, I demonstrate that the risk of 'take-off' is greatest at the extremes of stance. This is because before and after kinetic energy is converted to potential, velocities (and so required centripetal accelerations) are highest, while concurrently the component of gravity acting in line with the leg is least. Limitations to the range of walking velocity and stride angle are explored. At walking speeds approaching a Froude number of 1, take-off is only avoidable with very small steps. With realistic limitations on swing-leg frequency, a novel explanation for the walk-run transition at a Froude number of 0.5 is shown.     

Spatio-temporal gait characteristics of the hind-limb cycles during voluntary bipedal and quadrupedal walking in bonobos (Pan paniscus)

Spatio-temporal gait characteristics (step and stride length, stride frequency, duty factor) were determined for the hind-limb cycles of nine bonobos (Pan paniscus) walking quadrupedally and bipedally at a range of speeds. The data were recalculated to dimensionless quantities according to the principle of dynamic similarity. Lower leg length was used as the reference length. Interindividual variability in speed modulation strategy of bonobos appears to be low. Compared to quadrupedal walking, bipedal bonobos use smaller steps to attain a given speed (differences increase with speed), resulting in shorter strides at a higher frequency. In the context of the ("hybrid") dynamic pattern approach to locomotion (Latach, 1998) we argue that, despite these absolute differences, intended walking speed is the basic control variable which elicits both quadrupedal and bipedal walking kinematics in a similar way. Differences in the initial status of the dynamic system may be responsible for the differences in step length between both gaits. Comparison with data deduced from the literature shows that the effects of walking speed on stride length and frequency are similar in bonobos, common chimpanzees, and humans. This suggests that (at least) within extant homininae, spatio-temporal gait characteristics are highly comparable, and this in spite of obvious differences in mass distribution and bipedal posture.     

The kangaroo's tail propels and powers pentapedal locomotion

When moving slowly, kangaroos plant their tail on the ground in sequence with their front and hind legs. To determine the tail''s role in this ‘pentapedal’ gait, we measured the forces the tail exerts on the ground and calculated the mechanical power it generates. We found that the tail is responsible for as much propulsive force as the front and hind legs combined. It also generates almost exclusively positive mechanical power, performing as much mass-specific mechanical work as does a human leg during walking at the same speed. Kangaroos use their muscular tail to support, propel and power their pentapedal gait just like a leg.     

A dynamic similarity hypothesis for the gaits of quadrupedal mammals

The dynamic similarity hypothesis postulates that different mammals move in a dynamically similar fashion whenever they travel at speeds that give them equal values of a dimensionless parameter, the Froude number. Thus, given information about one species, it could be possible to predict for others relationships between size, speed and features of gait such as stride length, duty factor, the phase relationships of the feet and the patterns of force exerted on the ground.
Data for a diverse sample of mammals have been used to test the hypothesis. It is found to be tenable in many cases when comparisons are confined to quadrupedal mammals of the type described by Jenkins (1971) as "cursorial". Most mammals of mass greater than 5 kg are of this type. Although the hypothesis applies less successfully to comparisons between cursorial and non-cursorial mammals it is shown to be a reasonable approximation even for such comparisons and for comparisons between quadrupedal mammals and bipedal mammals and birds.     

Optimal running speed and the evolution of hominin hunting strategies

Recent discussion of the selective pressures leading to the evolution of modern human postcranial morphology, seen as early as Homo erectus, has focused on the relative importance of walking versus running. Specifically, these conversations have centered on which gait may have been used by early Homo to acquire prey. An element of the debate is the widespread belief that quadrupeds are constrained to run at optimally efficient speeds within each gait, whereas humans are equally efficient at all running speeds. The belief in the lack of optimal running speeds in humans is based, however, on a number of early studies with experimental designs inadequate for the purpose of evaluating optimality. Here we measured the energetic cost of human running (n = 9) at six different speeds for five minutes at each speed, with careful replicates and controls. We then compared the fit of linear versus curvilinear models to the data within each subject. We found that individual humans do, in fact, have speeds at which running is significantly less costly than at other speeds (i.e., an optimal running speed). In addition, we demonstrate that the use of persistence hunting methods to gain access to prey at any running speed, even the optimum, would be extremely costly energetically, more so than a persistence hunt at optimal walking speed. We argue that neither extinct nor extant hominin populations are as flexible in the chosen speeds of persistence hunting pursuits as other researchers have suggested. Variations in the efficiency of human locomotion appear to be similar to those of terrestrial quadrupeds.     

Muscle mechanical advantage of human walking and running: implications for energy cost.

Muscular forces generated during locomotion depend on an animal's speed, gait, and size and underlie the energy demand to power locomotion. Changes in limb posture affect muscle forces by altering the mechanical advantage of the ground reaction force (R) and therefore the effective mechanical advantage (EMA = r/R, where r is the muscle mechanical advantage) for muscle force production. We used inverse dynamics based on force plate and kinematic recordings of humans as they walked and ran at steady speeds to examine how changes in muscle EMA affect muscle force-generating requirements at these gaits. We found a 68% decrease in knee extensor EMA when humans changed gait from a walk to a run compared with an 18% increase in hip extensor EMA and a 23% increase in ankle extensor EMA. Whereas the knee joint was extended (154-176 degrees) during much of the support phase of walking, its flexed position (134-164 degrees) during running resulted in a 5.2-fold increase in quadriceps impulse (time-integrated force during stance) needed to support body weight on the ground. This increase was associated with a 4.9-fold increase in the ground reaction force moment about the knee. In contrast, extensor impulse decreased 37% (P < 0.05) at the hip and did not change at the ankle when subjects switched from a walk to a run. We conclude that the decrease in limb mechanical advantage (mean limb extensor EMA) and increase in knee extensor impulse during running likely contribute to the higher metabolic cost of transport in running than in walking. The low mechanical advantage in running humans may also explain previous observations of a greater metabolic cost of transport for running humans compared with trotting and galloping quadrupeds of similar size.     

Energy cost of walking and gait instability in healthy 65- and 80-yr-olds.

This study tested whether the lower economy of walking in healthy elderly subjects is due to greater gait instability. We compared the energy cost of walking and gait instability (assessed by stride to stride changes in the stride time) in octogenarians (G80, n = 10), 65-yr-olds (G65, n = 10), and young controls (G25, n = 10) walking on a treadmill at six different speeds. The energy cost of walking was higher for G80 than for G25 across the different walking speeds (P < 0.05). Stride time variability at preferred walking speed was significantly greater in G80 (2.31 +/- 0.68%) and G65 (1.93 +/- 0.39%) compared with G25 (1.40 +/- 0.30%; P < 0.05). There was no significant correlation between gait instability and energy cost of walking at preferred walking speed. These findings demonstrated greater energy expenditure in healthy elderly subjects while walking and increased gait instability. However, no relationship was noted between these two variables. The increase in energy cost is probably multifactorial, and our results suggest that gait instability is probably not the main contributing factor in this population. We thus concluded that other mechanisms, such as the energy expenditure associated with walking movements and related to mechanical work, or neuromuscular factors, are more likely involved in the higher cost of walking in elderly people.     

Swimming speed, respiration rate, and estimated cost of transport in adult killer whales

The physiology of free-ranging cetaceans is difficult to study and as a consequence, data on the energetics of these animals are limited. To better understand the energetic cost of swimming in killer whales, total cost of transport ( COT ) was estimated from swimming speeds and respiration rates from wild adult northern resident killer whales ( Orcinus orca ) and reported values of oxygen consumption in captive whales. Respiration rate (breaths per minute) was positively correlated with swimming speed (meters per second), while mass-specific COT (Joules per kilogram per meter) decreased with speed. Lack of data on very fast-swimming animals hindered assessment of the exact speed at which COT was minimal. However, minimum mass-specific COT for killer whales in the present study approached those predicted by a previously published allometric equation for marine mammals, and corresponded to "optimal" swimming speeds of 2.6–3 m/s. Interestingly, the observed average swimming speed (1.6 m/s) was lower than predicted optimal swimming speed. Finally, females with dependent calves had higher respiration rates than females without calves. These findings could be due to synchronous breathing with calves or could result from increased costs of lactation and swimming with a calf in echelon formation. Consequently, females with calves may have much greater COT at optimal swimming speeds than females without calves.     

The metabolic cost of walking in humans, chimpanzees, and early hominins

Bipedalism is a defining feature of the hominin lineage, but the nature and efficiency of early hominin walking remains the focus of much debate. Here, we investigate walking cost in early hominins using experimental data from humans and chimpanzees. We use gait and energetics data from humans, and from chimpanzees walking bipedally and quadrupedally, to test a new model linking locomotor anatomy and posture to walking cost. We then use this model to reconstruct locomotor cost for early, ape-like hominins and for the A.L. 288 Australopithecus afarensis specimen. Results of the model indicate that hind limb length, posture (effective mechanical advantage), and muscle fascicle length contribute nearly equally to differences in walking cost between humans and chimpanzees. Further, relatively small changes in these variables would decrease the cost of bipedalism in an early chimpanzee-like biped below that of quadrupedal apes. Estimates of walking cost in A.L. 288, over a range of hypothetical postures from crouched to fully extended, are below those of quadrupedal apes, but above those of modern humans. These results indicate that walking cost in early hominins was likely similar to or below that of their quadrupedal ape-like forebears, and that by the mid-Pliocene, hominin walking was less costly than that of other apes. This supports the hypothesis that locomotor energy economy was an important evolutionary pressure on hominin bipedalism.     

Multiple walking speed-frequency relations are predicted by constrained optimization

A person constrained to walk at a given speed v on a treadmill, chooses a particular step frequency f and step length d=v/f. Testing over a range of speeds generates a speed-frequency (v-f) relationship. This relationship is commonly posited as a basic feature of human gait. It is often further posited that this curve follows from minimum energy cost strategy. We observed that individuals walking under different constraint circumstances--walking to a range of fixed metronome frequencies (fixed f) or over a range of spaced markers (fixed d)--produce speed-frequency relations distinct from the constrained v relation. We show here that three distinct speed-frequency curves, similar to those observed, are predicted by the assumption that a walking person optimizes an underlying objective function F (v, f) that has a minimum at the preferred gait. Further, the metabolic cost of transport is a reasonable approximate candidate for the function F.     

The cost of walking downhill: Is the preferred gait energetically optimal?

Humans tend to prefer walking patterns that minimize energetic cost, but must also maintain stability to avoid falling over. The relative importance of these two goals in determining the preferred gait pattern is not currently clear. We investigated the relationship between energetic cost and stability during downhill walking, a context in which gravitational energy will assist propulsion but may also reduce stability. We hypothesized that humans will not minimize energetic cost when walking downhill, but will instead prefer a gait pattern that increases stability. Simulations of a dynamic walking model were used to determine whether stable downhill gaits could be achieved using a simple control strategy. Experimentally, twelve healthy subjects walked downhill at 1.25 m/s (0, 0.05, 0.10, and 0.15 gradients). For each slope, subjects performed normal and relaxed trials, in which they were instructed to reduce muscle activity and allow gravity to maximally assist their gait. We quantified energetic cost, stride timing, and leg muscle activity. In our model simulations, increase in slope reduced the required actuation but also decreased stability. Experimental subjects behaved more like the model when using the relaxed rather than the normal walking strategy; the relaxed strategy decreased energetic cost at the steeper slopes but increased stride period variability, an indicator of instability. These results indicate that subjects do not take optimal advantage of the propulsion provided by gravity to decrease energetic cost, but instead prefer a more stable and more costly gait pattern.     

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.     

Gait modification when decreasing double support percentage

Much is still unknown about walking stability, including which aspects of gait contribute to higher stability. Walking stability appears to be related to walking speed, although the exact relationship is unclear. As walking speed decreases, the double support (DS) period of gait increases both in time and as a percentage of the gait cycle. Because humans have more control over their center of mass movement during DS, increasing DS duration may alter stability. This study examined how human gait is affected by changing DS percentage independent of walking speed. Sixteen young, healthy adults walked on a treadmill at a single speed for six one-minute trials. These trials included normal gait as well as longer- and shorter-than-normal DS percentage gaits. Subjects were consistently able to decrease DS percentage but had difficulty increasing DS percentage. In some cases, subjects altered their cadence when changing DS percentage, particularly when attempting to increase DS percentage. The changes to gait when decreasing DS percentage were similar to changes when increasing walking speed but occurred mainly during the swing period. These changes include increased hip and knee flexion during the swing period, increased swing foot height, and larger magnitude peaks in ground reaction forces. The changes in gait when attempting to increase DS percentage trended toward changes when decreasing walking speed. Altering DS percentage induced gait changes that were similar to, yet clearly distinct from, gait changes due to walking speed. Further, the difficulty of increasing DS percentage when walking at a constant speed suggests that people walk more slowly when they want to increase time spent in DS.     

Effects of obesity and sex on the energetic cost and preferred speed of walking.

The metabolic energy cost of walking is determined, to a large degree, by body mass, but it is not clear how body composition and mass distribution influence this cost. We tested the hypothesis that walking would be most expensive for obese women compared with obese men and normal-weight women and men. Furthermore, we hypothesized that for all groups, preferred walking speed would correspond to the speed that minimized the gross energy cost per distance. We measured body composition, maximal oxygen consumption, and preferred walking speed of 39 (19 class II obese, 20 normal weight) women and men. We also measured oxygen consumption and carbon dioxide production while the subjects walked on a level treadmill at six speeds (0.50-1.75 m/s). Both obesity and sex affected the net metabolic rate (W/kg) of walking. Net metabolic rates of obese subjects were only approximately 10% greater (per kg) than for normal-weight subjects, and net metabolic rates for women were approximately 10% greater than for men. The increase in net metabolic rate at faster walking speeds was greatest in obese women compared with the other groups. Preferred walking speed was not different across groups (1.42 m/s) and was near the speed that minimized gross energy cost per distance. Surprisingly, mass distribution (thigh mass/body mass) was not related to net metabolic rate, but body composition (% fat) was (r2= 0.43). Detailed biomechanical studies of walking are needed to investigate whether obese individuals adopt novel energy saving mechanisms during walking.