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At a given running speed, humans strongly prefer to use a stride frequency near their 'optimal' stride frequency that minimizes metabolic cost. Although there is no definitive explanation for why an optimal stride frequency exists, elastic energy usage has been implicated. Because the possibility for elastic energy storage and return may be impaired on slopes, we investigated whether and how the optimal stride frequency changes during uphill and downhill running. Presuming a smaller role of elastic energy, we hypothesized that altering stride frequency would change metabolic cost less during uphill and downhill running than during level running. To test this hypothesis, we collected force and metabolic data as nine male subjects ran at 2.8 m s(-1) on the level, 3 deg uphill and 3 deg downhill. Stride frequency was systematically varied above and below preferred stride frequency (PSF ±8% and ±15%). Ground reaction force data were used to calculate potential, kinetic and total mechanical energy, and to calculate the theoretical maximum possible and estimated actual elastic energy storage and return. Contrary to our hypothesis, we found that neither the overall relationship between metabolic cost and stride frequency nor the energetically optimal stride frequency changed substantially with slope. However, estimated actual elastic energy storage as a percentage of total positive power increased with increasing stride frequency on all slopes, indicating that muscle power decreases with increasing stride frequency. Combined with the increased cost of force production and internal work with increasing stride frequency, this leads to an intermediate optimal stride frequency and overall U-shaped curve.

When human hoppers are surprised by a change in surface stiffness, they adapt almost instantly by changing leg stiffness, implying that neural feedback is not necessary. The goal of this simulation study was first to investigate whether leg stiffness can change without neural control adjustment when landing on an unexpected hard or unexpected compliant (soft) surface, and second to determine what underlying mechanisms are responsible for this change in leg stiffness. The muscle stimulation pattern of a forward dynamic musculoskeletal model was optimized to make the model match experimental hopping kinematics on hard and soft surfaces. Next, only surface stiffness was changed to determine how the mechanical interaction of the musculoskeletal model with the unexpected surface affected leg stiffness. It was found that leg stiffness adapted passively to both unexpected surfaces. On the unexpected hard surface, leg stiffness was lower than on the soft surface, resulting in close-to-normal center of mass displacement. This reduction in leg stiffness was a result of reduced joint stiffness caused by lower effective muscle stiffness. Faster flexion of the joints due to the interaction with the hard surface led to larger changes in muscle length, while the prescribed increase in active state and resulting muscle force remained nearly constant in time. Opposite effects were found on the unexpected soft surface, demonstrating the bidirectional stabilizing properties of passive dynamics. These passive adaptations to unexpected surfaces may be critical when negotiating disturbances during locomotion across variable terrain.

Elderly adults consume more metabolic energy during walking than young adults. Our study tested the hypothesis that elderly adults consume more metabolic energy during walking than young adults because they perform more individual limb work on the center of mass. Thus we compared how much individual limb work young and elderly adults performed on the center of mass during walking. We measured metabolic rate and ground reaction force while 10 elderly and 10 young subjects walked at 5 speeds between 0.7 and 1.8 m/s. Compared with young subjects, elderly subjects consumed an average of 20% more metabolic energy (P=0.010), whereas they performed an average of 10% less individual limb work during walking over the range of speeds (P=0.028). During the single-support phase, elderly and young subjects both conserved approximately 80% of the center of mass mechanical energy by inverted pendulum energy exchange and performed a similar amount of individual limb work (P=0.473). However, during double support, elderly subjects performed an average of 17% less individual limb work than young subjects (P=0.007) because their forward speed fluctuated less (P=0.006). We conclude that the greater metabolic cost of walking in elderly adults cannot be explained by a difference in individual limb work. Future studies should examine whether a greater metabolic cost of stabilization, reduced muscle efficiency, greater antagonist cocontraction, and/or a greater cost of generating muscle force cause the elevated metabolic cost of walking in elderly adults.

A human walker vaults up and over each stance limb like an inverted pendulum. This similarity suggests that the vertical motion of a walker's center of mass reduces metabolic cost by providing a mechanism for pendulum-like mechanical energy exchange. Alternatively, some researchers have hypothesized that minimizing vertical movements of the center of mass during walking minimizes the metabolic cost, and this view remains prevalent in clinical gait analysis. We examined the relationship between vertical movement and metabolic cost by having human subjects walk normally and with minimal center of mass vertical movement ("flat-trajectory walking"). In flat-trajectory walking, subjects reduced center of mass vertical displacement by an average of 69% (P = 0.0001) but consumed approximately twice as much metabolic energy over a range of speeds (0.7-1.8 m/s) (P = 0.0001). In flat-trajectory walking, passive pendulum-like mechanical energy exchange provided only a small portion of the energy required to accelerate the center of mass because gravitational potential energy fluctuated minimally. Thus, despite the smaller vertical movements in flat-trajectory walking, the net external mechanical work needed to move the center of mass was similar in both types of walking (P = 0.73). Subjects walked with more flexed stance limbs in flat-trajectory walking (P < 0.001), and the resultant increase in stance limb force generation likely helped cause the doubling in metabolic cost compared with normal walking. Regardless of the cause, these findings clearly demonstrate that human walkers consume substantially more metabolic energy when they minimize vertical motion.

During hopping in place and running, humans maintain similar center of mass dynamics by precisely adjusting leg mechanics to compensate for moderate changes in surface stiffness. We investigated the limits of this precise control by asking humans to hop in place on extremely soft elastic surfaces. We found that hoppers drastically altered leg mechanics and maintained similar center of mass dynamics despite a sevenfold change in surface stiffness (11-81 kN m(-1)). On the stiffest surfaces, the legs compressed in early stance and then extended in late stance in the pattern that is typical for normal bouncing gaits. On the softest surfaces, however, subjects reversed this pattern so that the legs extended up to 8 cm in early stance and then compressed by a similar distance in late stance. Consequently, the center of mass moved downward during stance by 5-7 cm less than the surface compressed and by a similar distance as on the stiffest surfaces. This unique leg action probably reduced extensor muscle pre-stretch because the joints first extended and then flexed during stance. This interpretation is supported by the observation that hoppers increased muscle activation by 50% on the softest surface despite similar joint moments and mechanical leg work as on the stiffest surface. Thus, the extreme adjustment to leg mechanics for very soft surfaces helps maintain normal center of mass dynamics but requires high muscle activation levels due to the loss of the normal extensor muscle stretch-shorten cycle.

The metabolic cost of walking is determined by many mechanical tasks, but the individual contribution of each task remains unclear. We hypothesized that the force generated to support body weight and the work performed to redirect and accelerate body mass each individually incur a significant metabolic cost during normal walking. To test our hypothesis, we measured changes in metabolic rate in response to combinations of simulated reduced gravity and added loading. We found that reducing body weight by simulating reduced gravity modestly decreased net metabolic rate. By calculating the metabolic cost per Newton of reduced body weight, we deduced that generating force to support body weight comprises approximately 28% of the metabolic cost of normal walking. Similar to previous loading studies, we found that adding both weight and mass increased net metabolic rate in more than direct proportion to load. However, when we added mass alone by using a combination of simulated reduced gravity and added load, net metabolic rate increased about one-half as much as when we added both weight and mass. By calculating the cost per kilogram of added mass, we deduced that the work performed on the center of mass comprises approximately 45% of the metabolic cost of normal walking. Our findings support the hypothesis that force and work each incur a significant metabolic cost. Specifically, the cost of performing work to redirect and accelerate the center of mass is almost twice as great as the cost of generating force to support body weight.

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.

Humans running and hopping maintain similar center-of-mass motions, despite large changes in surface stiffness and damping. The goal of this study was to determine the contributions of anticipation and reaction when human hoppers encounter surprise, expected, and random changes from a soft elastic surface (27 kN/m) to a hard surface (411 kN/m). Subjects encountered the expected hard surface on every fourth hop and the random hard surface on an average of 25% of the hops in a trial. When hoppers on a soft surface were surprised by a hard surface, the ankle and knee joints were forced into greater flexion by passive interaction with the hard surface. Within 52 ms after subjects landed on the surprise hard surface, joint flexion increased, and the legs became less stiff than on the soft surface. These mechanical changes occurred before electromyography (EMG) first changed 68-188 ms after landing. Due to the fast mechanical reaction to the surprise hard surface, center-of-mass displacement and average leg stiffness were the same as on expected and random hard surfaces. This similarity is striking because subjects anticipated the expected and random hard surfaces by landing with their knees more flexed. Subjects also anticipated the expected hard surface by increasing the level of EMG by 24-76% during the 50 ms before landing. These results show that passive mechanisms alter leg stiffness for unexpected surface changes before muscle EMG changes and may be critical for adjustments to variable terrain encountered during locomotion in the natural world.

Walking involves a cyclic exchange of gravitational potential energy and kinetic energy of the center of mass. Our goal was to understand how the limbs of walking quadrupeds coordinate the vertical movements of the fore and hind quarters to produce these inverted pendulum-like movements. We collected kinematic and ground reaction force data from dogs walking over a range of speeds. We found that the fore and hind quarters of dogs behaved like two independent bipeds, each vaulting up and over its respective support limb. The center of mass moved up and down twice per stride, like a single walking biped, and up to 70% of the mechanical energy required to lift and accelerate the center of mass was recovered via the inverted pendulum mechanism. To understand how the limbs produce these center of mass movements, we created a simple model of two independent pendulums representing the movements of the fore and hind quarters. The model predicted that the fore and hind quarter movements would completely offset each other if the fore limb lagged the hind limb by 25% of the stride time and body mass was distributed equally between the fore and hind quarters. The primary reason that dogs did not walk with a flat trajectory of the center of mass was that each fore limb lagged its ipsilateral hind limb by only 15% of the stride time and thereby produced time periods when the fore and hind quarters moved up or down simultaneously. The secondary reason was that the fore limbs supported 63% of body mass. Consistent with these experimental results, the two-pendulum model predicts that the center of mass will undergo two fluctuations per stride cycle if limb phase is less than 25% and/or if the total mass is not distributed evenly between the fore or hind quarters.

Humans hopping and running on elastic and damped surfaces maintain similar center-of-mass dynamics by adjusting stance leg mechanics. We tested the hypothesis that the leg transitions from acting like an energy-conserving spring on elastic surfaces to a power-producing actuator on damped surfaces during hopping due to changes in ankle mechanics. To test this hypothesis, we collected surface electromyography, video kinematics, and ground reaction force while eight male subjects (body mass: 76.2 +/- 1.7 kg) hopped in place on a range of damped surfaces. On the most damped surface, most of the mechanical work done by the leg appeared at the ankle (52%), whereas 23 and 25% appeared at the knee and hip, respectively. Hoppers extended all three joints during takeoff further than they flexed during landing and thereby did more net positive work on more heavily damped surfaces. Also, all three joints reached peak flexion sooner after touchdown on more heavily damped surfaces. Consequently, peak moment occurred during joint extension rather than at peak flexion as on elastic surfaces. These strategies caused the positive work during extension to exceed the negative work during flexion to a greater extent on more heavily damped surfaces. At the muscle level, surface EMG increased by 50-440% in ankle and knee extensors as surface damping increased to compensate for greater surface energy dissipation. Our findings, and those of previous studies of hopping on elastic surfaces, show that the ankle joint is the key determinant of both springlike and actuator-like leg mechanics during hopping in place.

Fast-moving legged animals bounce along the ground with spring-like legs and agilely traverse variable terrain. Previous research has shown that hopping and running humans maintain the same bouncing movement of the body's centre of mass on a range of elastic surfaces by adjusting their spring-like legs to exactly offset changes in surface stiffness. This study investigated human hopping on damped surfaces that dissipated up to 72% of the hopper's mechanical energy. On these surfaces, the legs did not act like pure springs. Leg muscles performed up to 24-fold more net work to replace the energy lost by the damped surface. However, considering the leg and surface together, the combination appeared to behave like a constant stiffness spring on all damped surfaces. By conserving the mechanics of the leg-surface combination regardless of surface damping, hoppers also conserved centre-of-mass motions. Thus, the normal bouncing movements of the centre of mass in hopping are not always a direct result of spring-like leg behaviour. Conserving the trajectory of the centre of mass by maintaining spring-like mechanics of the leg-surface combination may be an important control strategy for fast-legged locomotion on variable terrain.

The Hoffmann (H-) reflex is an electrical analogue of the monosynaptic stretch reflex, elicited by bypassing the muscle spindle and directly stimulating the afferent nerve. Studying H-reflex modulation provides insight into how the nervous system centrally modulates stretch reflex responses.A common measure of H-reflex gain is the slope of the relationship between H-reflex amplitude and EMG amplitude. To examine soleus H-reflex gain across a range of EMG levels during human locomotion, we used simulated reduced gravity to reduce muscle activity. We hypothesised that H-reflex gain would be independent of gravity level.We recorded EMG from eight subjects walking (1.25 m s-1) and running (3.0 m s-1) at four gravity levels (1.0, 0.75, 0.5 and 0.25 G (Earth gravity)). We normalised the stimulus M-wave and resulting H-reflex to the maximal M-wave amplitude (Mmax) elicited throughout the stride to correct for movement of stimulus and recording electrodes relative to nerve and muscle fibres. Peak soleus EMG amplitude decreased by ~30% for walking and for running over the fourfold change in gravity. As hypothesised, slopes of linear regressions fitted to H-reflex versus EMG data were independent of gravity for walking and running (ANOVA, P > 0.8). The slopes were also independent of gait (P > 0.6), contrary to previous studies. Walking had a greater y-intercept (19.9% Mmax) than running (-2.5% Mmax; P < 0.001). At all levels of EMG, walking H-reflex amplitudes were higher than running H-reflex amplitudes by a constant amount. We conclude that the nervous system adjusts H-reflex threshold but not H-reflex gain between walking and running. These findings provide insight into potential neural mechanisms responsible for spinal modulation of the stretch reflex during human locomotion.

Recent advances in integrative studies of locomotion have revealed several general principles. Energy storage and exchange mechanisms discovered in walking and running bipeds apply to multilegged locomotion and even to flying and swimming. Nonpropulsive lateral forces can be sizable, but they may benefit stability, maneuverability, or other criteria that become apparent in natural environments. Locomotor control systems combine rapid mechanical preflexes with multimodal sensory feedback and feedforward commands. Muscles have a surprising variety of functions in locomotion, serving as motors, brakes, springs, and struts. Integrative approaches reveal not only how each component within a locomotor system operates but how they function as a collective whole.

Walking is often modeled as an inverted pendulum system in which the center of mass vaults over the rigid stance limb. Running is modeled as a simple spring-mass system in which the center of mass bounces along on the compliant stance limb. In these models, differences in stance-limb behavior lead to nearly opposite patterns of vertical movements of the center of mass in the two gaits. Our goal was to quantify the importance of stance-limb behavior and other factors in determining the trajectory of the center of mass during walking and running. We collected kinematic and force platform data during human walking and running. Virtual stance-limb compression (i.e. reduction in the distance between the point of foot-ground contact and the center of mass during the first half of the stance phase) was only 26% lower for walking (0.091 m) than for running (0.123 m) at speeds near the gait transition speed. In spite of this relatively small difference, the center of mass moved upwards by 0.031 m during the first half of the stance phase during walking and moved downwards by 0.073 m during the first half of the stance phase during running. The most important reason for this difference was that the stance limb swept through a larger angle during walking (30.4 degrees) than during running (19.2 degrees). We conclude that stance-limb touchdown angle and virtual stance-limb compression both play important roles in determining the trajectory of the center of mass and whether a gait is a walk or a run.

When humans hop in place or run forward, leg stiffness is increased to offset reductions in surface stiffness, allowing the global kinematics and mechanics to remain the same on all surfaces. The purpose of the present study was to determine the mechanism for adjusting leg stiffness. Seven subjects hopped in place on surfaces of different stiffnesses (23-35,000 kN/m) while force platform, kinematic, and electromyographic data were collected. Leg stiffness approximately doubled between the most stiff surface and the least stiff surface. Over the same range of surfaces, ankle torsional stiffness increased 1.75-fold, and the knee became more extended at the time of touchdown (2.81 vs. 2.65 rad). We used a computer simulation to examine the sensitivity of leg stiffness to the observed changes in ankle stiffness and touchdown knee angle. Our model consisted of four segments (foot, shank, thigh, head-arms-trunk) interconnected by three torsional springs (ankle, knee, hip). In the model, an increase in ankle stiffness 1.75-fold caused leg stiffness to increase 1.7-fold. A change in touchdown knee angle as observed in the subjects caused leg stiffness to increase 1.3-fold. Thus both joint stiffness and limb geometry adjustments are important in adjusting leg stiffness to allow similar hopping on different surfaces.

A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal's leg stiffness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg stiffness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered different surfaces in the natural world. We found that human runners adjust their leg stiffness to accommodate changes in surface stiffness, allowing them to maintain similar running mechanics on different surfaces. These results provide important insight into mechanics and control of animal locomotion and suggest that incorporating an adjustable leg stiffness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.

This study tested the hypothesis that there has been an evolutionary increase in locomotor performance capacity at low temperature in nocturnal lizards. Nocturnal lizards are often active at low and suboptimal body temperatures. An evolutionary decrease in the minimum cost of locomotion could increase endurance capacity at low temperature, partially offsetting the thermal handicap of nocturnality. In support of the nocturnality hypothesis, we discovered that minimum cost of locomotion of a nocturnal gecko, Coleonyx variegatus (4.2 g), was only 58% of the minimum cost of locomotion of Phrynosoma douglassii, a diurnal lizard (4.5 g). As a result, maximum aerobic speed was 2.3 times as great in the nocturnal lizard compared to the diurnal lizard. By using the method of phylogenetically independent contrasts at the species level, we showed that the relationship between mass and minimum cost of locomotion in diurnal lizards was similar to that of the ahistorical standard allometry and that low minimum cost of locomotion in geckos represents a significant evolutionary change from the ancestral diurnal pattern. The decrease in the minimum cost of locomotion concordant with the evolution of nocturnality suggests that geckos evolved a greater capacity for sustained locomotion at low temperature.

The goal of the present study was to test the hypothesis that maximum running speed is limited by how much mechanical power the muscular system can produce. To test this hypothesis, two species of lizards, Coleonyx variegatus and Eumeces skiltonianus, sprinted on hills of different slopes. According to the hypothesis, maximum speed should decrease on steeper uphill slopes but mechanical power output at maximum speed should be independent of slope. For level sprinting, the external mechanical power output was determined from force platform data. For uphill sprinting, the mechanical power output was approximated as the power required to lift the center of mass vertically. When the slope increased from level to 40 degrees uphill, maximum speed decreased by 28% in C. variegatus and by 16% in E. skiltonianus. At maximum speed on a 40 degrees uphill slope in both species, the mechanical power required to lift the body vertically was approximately 3.9 times greater than the external mechanical power output at maximum speed on the level. Because total limb mass is small in both species (6-16% of body mass) and stride frequency is similar at maximum speed on all slopes, the internal mechanical power output is likely to be small and similar in magnitude on all slopes. I conclude that the muscular system is capable of producing substantially more power during locomotion than it actually produces during level sprinting. Thus, the capacity of the muscular system to produce power does not limit maximum running speed.

Lizards bend their trunks laterally with each step of locomotion and, as a result, their locomotion appears to be fundamentally different from mammalian locomotion. The goal of the present study was to determine whether lizards use the same two basic gaits as other legged animals or whether they use a mechanically unique gait due to lateral trunk bending. Force platform and kinematic measurements revealed that two species of lizards, Coleonyx variegatus and Eumeces skiltonianus, used two basic gaits similar to mammalian walking and trotting gaits. In both gaits, the kinetic energy fluctuations due to lateral movements of the center of mass were less than 5% of the total external mechanical energy fluctuations. In the walking gait, both species vaulted over their stance limbs like inverted pendulums. The fluctuations in kinetic energy and gravitational potential energy of the center of mass were approximately 180 degrees out of phase. The lizards conserved as much as 51% of the external mechanical energy required for locomotion by the inverted pendulum mechanism. Both species also used a bouncing gait, similar to mammalian trotting, in which the fluctuations in kinetic energy and gravitational potential energy of the center of mass were nearly exactly in phase. The mass-specific external mechanical work required to travel 1 m (1.5 J kg-1) was similar to that for other legged animals. Thus, in spite of marked lateral bending of the trunk, the mechanics of lizard locomotion is similar to the mechanics of locomotion in other legged animals.

When mammals run, the overall musculoskeletal system behaves as a single linear "leg spring". We used force platform and kinematic measurements to determine whether leg spring stiffness (k(leg)) is adjusted to accommodate changes in surface stiffness (ksurf) when humans hoop in place, a good experimental model for examining adjustments to k(leg) in bouncing gaits. We found that k(leg) was greatly increased to accommodate surfaces of lower stiffnesses. The series combination of k(leg) and ksurf [total stiffness (ktot)] was independent of ksurf at a given hopping frequency. For example, when humans hopped at a frequency of 2 Hz, they tripled their k(leg) on the least stiff surface (ksurf = 26.1 kN/m; k(leg) = 53.3 kN/m) compared with the most stiff surface (ksurf = 35,000 kN/m; k(leg) = 17.8 kN/m). Values for ktot were not significantly different on the least stiff surface (16.7 kN/m) and the most stiff surface (17.8 kN/m). Because of the k(leg) adjustment, many aspects of the hopping mechanics (e.g., ground-contact time and center of mass vertical displacement) remained remarkably similar despite a > 1,000-fold change in ksurf. This study provides insight into how k(leg) adjustments can allow similar locomotion mechanics on the variety of terrains encountered by runners in the natural world.

Trotting and hopping animals use muscles, tendons and ligaments to store and return elastic energy as they bounce along the ground. We examine how the musculoskeletal spring system operates at different speeds and in animals of different sizes. We model trotting and hopping as a simple spring-mass system which consists of a leg spring and a mass. We find that the stiffness of the leg spring (k(leg)) is nearly independent of speed in dogs, goats, horses and red kangaroos. As these animals trot or hop faster, the leg spring sweeps a greater angle during the stance phase, and the vertical excursion of the center of mass during the ground contact phase decreases. The combination of these changes to the spring system causes animals to bounce off the ground more quickly at higher speeds. Analysis of a wide size range of animals (0.1-140 kg) at equivalent speeds reveals that larger animals have stiffer leg springs (k(leg) [symbol: see text] M0.67, where M is body mass), but that the angle swept by the leg spring is nearly independent of body mass. As a result, the resonant period of vertical vibration of the spring-mass system is longer in larger animals. The length of time that the feet are in contact with the ground increases with body mass in nearly the same way as the resonant period of vertical vibration.

It is widely thought that animals switch gaits at speeds that minimize energetic cost. Horses naturally switched from a trot to a gallop at a speed where galloping required more energy than trotting, and thus, the gait transition actually increased the energetic cost of running. However, by galloping at this speed, the peak forces on the muscles, tendons, and bones, and presumably the chance of injury, are reduced. When the horses carried weights, they switched from a trot to a gallop at a lower speed but at the same critical level of force. These findings suggest that the trot-gallop transition is triggered when musculoskeletal forces reach a critical level.