Mechanical work performed by the individual legs during uphill and downhill walking

Previous studies of the mechanical work performed during uphill and downhill walking have neglected the simultaneous negative and positive work performed by the leading and trailing legs during double support. Our goal was to quantify the mechanical work performed by the individual legs across a range of uphill and downhill grades. We hypothesized that during double support, (1) with steeper uphill grade, the negative work performed by the leading leg would become negligible and the trailing leg would perform progressively greater positive work to raise the center of mass (CoM), and (2) with steeper downhill grade, the leading leg would perform progressively greater negative work to lower the CoM and the positive work performed by the trailing leg would become negligible. 11 healthy young adults (6 M/5 F, 71.0±12.3 kg) walked at 1.25 m/s on a dual-belt force-measuring treadmill at seven grades (0, ±3, ±6, ±9°). We collected three-dimensional ground reaction forces (GRFs) and used the individual limbs method to calculate the mechanical work performed by each leg. As hypothesized, the trailing leg performed progressively greater positive work with steeper uphill grade, and the leading leg performed progressively greater negative work with steeper downhill grade (p<0.005). To our surprise, unlike level-ground walking, during double support the leading leg performed considerable positive work when walking uphill and the trailing leg performed considerable negative work when walking downhill (p<0.005). To understand how humans walk uphill and downhill, it is important to consider these revealing biomechanical aspects of individual leg function and interaction during double support.     

Asymmetric interlimb role-sharing in mechanical power during human sideways locomotion

Sideways movement at a wide variety of speeds is required in daily life and sports. The purpose of this study was to identify the characteristics of asymmetry in power output between lower limbs during sideways gait patterns. Seven healthy men performed steady-state sideways locomotion at various speeds. The mechanical external power of each limb was calculated and decomposed to the lateral and vertical components by the center of mass velocity and ground reaction force. We acquired data from 126 steps of sideways walking at 0.44–1.21 m/s, and from 41 steps of sideways galloping at 1.04–3.00 m/s. The results showed asymmetric power production between the limbs during sideways locomotion. During sideways walking, the trailing limb predominantly produced positive external power and the leading limb produced predominantly negative external power, and these amplitudes increased with step speed. In contrast, during sideways galloping, negative and subsequent positive power production was observed in both limbs. These differences in asymmetric interlimb role-sharing were mainly due to the vertical component. During sideways galloping, the trailing limb absorbs vertical power produced by the leading limb due to the longer flight time. This characteristic of vertical power production in the trailing limb may explain the presence of a double-support phase, which is not observed during forward running, even at high speeds. Our results will help to elucidate the asymmetric movements of the limbs in lateral directions at various speeds.     

Muscle mechanical work requirements during normal walking: the energetic cost of raising the body's center-of-mass is significant

Inverted pendulum models of walking predict that little muscle work is required for the exchange of body potential and kinetic energy in single-limb support. External power during walking (product of the measured ground reaction force and body center-of-mass (COM) velocity) is often analyzed to deduce net work output or mechanical energetic cost by muscles. Based on external power analyses and inverted pendulum theory, it has been suggested that a primary mechanical energetic cost may be associated with the mechanical work required to redirect the COM motion at the step-to-step transition. However, these models do not capture the multi-muscle, multi-segmental properties of walking, co-excitation of muscles to coordinate segmental energetic flow, and simultaneous production of positive and negative muscle work. In this study, a muscle-actuated forward dynamic simulation of walking was used to assess whether: (1). potential and kinetic energy of the body are exchanged with little muscle work; (2). external mechanical power can estimate the mechanical energetic cost for muscles; and (3.) the net work output and the mechanical energetic cost for muscles occurs mostly in double support. We found that the net work output by muscles cannot be estimated from external power and was the highest when the COM moved upward in early single-limb support even though kinetic and potential energy were exchanged, and muscle mechanical (and most likely metabolic) energetic cost is dominated not only by the need to redirect the COM in double support but also by the need to raise the COM in single support.     

Minimizing center of mass vertical movement increases metabolic cost in walking.

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.     

Individual limb work does not explain the greater metabolic cost of walking in elderly adults.

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.     

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.     

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected,off-centered curvy foot

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.     

Pendular activity of human upper limbs during slow and normal walking

When walking at normal and fast speeds, humans swing their upper limbs in alternation, each upper limb swinging in phase with the contralateral lower limb. However, at slow and very slow speeds, the upper limbs swing forward and back in unison, at twice the stride frequency of the lower limbs. The change from “single swinging” (in alternation) to “double swinging” (in unison) occurs consistently at a certain stride frequency for agiven individual, though different individuals may change at different stride frequencies. To explain this change in the way we use our upper limbs and individual variations in the occurrence of the change, the upper limb is modelled as a compound pendulum. Based on the kinematic properties of pendulums, we hypothesize that the stride frequency at which the change from “single swinging” to “double swinging” occurs will be at or slightly below the natural pendular frequency (NPF) of the upper limbs. Twenty-seven subjects were measured and then filmed while walking at various speeds. The mathematically derived NPF of each subject's upper limbs was compared to the stride frequency at which the subject changed from “single swinging” to “double swinging.” The results of the study conform very closely to the hypothesis, even when the NPF is artificially altered by adding weights to the subjects' hands. These results indicate that the pendulum model of the upper limb will be useful in further investigations of the function of the upper limbs in human walking. © 1994 Wiley-Liss, Inc.     

The oscillatory behavior of the CoM facilitates mechanical energy balance between push-off and heel strike

Humans use equal push-off and heel strike work during the double support phase to minimize the mechanical work done on the center of mass (CoM) during the gait. Recently, a step-to-step transition was reported to occur over a period of time greater than that of the double support phase, which brings into question whether the energetic optimality is sensitive to the definition of the step-to-step transition. To answer this question, the ground reaction forces (GRFs) of seven normal human subjects walking at four different speeds (1.1-2.4 m/s) were measured, and the push-off and heel strike work for three differently defined step-to-step transitions were computed based on the force, work, and velocity. To examine the optimality of the work and the impulse data, a hybrid theoretical-empirical analysis is presented using a dynamic walking model that allows finite time for step-to-step transitions and incorporates the effects of gravity within this period. The changes in the work and impulse were examined parametrically across a range of speeds. The results showed that the push-off work on the CoM was well balanced by the heel strike work for all three definitions of the step-to-step transition. The impulse data were well matched by the optimal impulse predictions (R(2)>0.7) that minimized the mechanical work done on the CoM during the gait. The results suggest that the balance of push-off and heel strike energy is a consistent property arising from the overall gait dynamics, which implies an inherited oscillatory behavior of the CoM, possibly by spring-like leg mechanics.     

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.     

Inefficient use of inverted pendulum mechanism during quadrupedal walking in the Japanese macaque

In animal walking, the gravitational potential and kinetic energy of the center of mass (COM) fluctuates out-of-phase to reduce the energetic cost of locomotion via an inverted pendulum mechanism, and, in canine quadrupedal walking, up to 70% of the mechanical energy can be recovered. However, the rate of energy recovery for quadrupedal walking in primates has been reported to be comparatively lower. The present study analyzed fluctuations in the potential and kinetic energy of the COM during quadrupedal walking in the Japanese macaque to clarify the mechanisms underlying this inefficient utilization of the inverted pendulum mechanism in primates. Monkeys walked on a wooden walkway at a self-selected speed, and ground reaction forces were measured, using a force platform, to calculate patterns of mechanical energy fluctuation and rates of energy recovery. Our results demonstrated that rates of energy recovery for quadrupedal walking in Japanese macaques were approximately 30–50%, much smaller than those reported for dogs. Comparisons of the patterns of mechanical energy fluctuation suggested that the potential and kinetic energies oscillated relatively more in-phase, and amplitudes did not attain near equality during quadrupedal walking in Japanese macaques, possibly because of greater weight support (reaction force) of the hindlimbs and more protracted forelimbs at touchdown in the Japanese macaque, two of the three commonly accepted locomotor characteristics distinguishing primates from non-primate mammals.     

Bionic ankle-foot prosthesis normalizes walking gait for persons with leg amputation

Over time, leg prostheses have improved in design, but have been incapable of actively adapting to different walking velocities in a manner comparable to a biological limb. People with a leg amputation using such commercially available passive-elastic prostheses require significantly more metabolic energy to walk at the same velocities, prefer to walk slower and have abnormal biomechanics compared with non-amputees. A bionic prosthesis has been developed that emulates the function of a biological ankle during level-ground walking, specifically providing the net positive work required for a range of walking velocities. We compared metabolic energy costs, preferred velocities and biomechanical patterns of seven people with a unilateral transtibial amputation using the bionic prosthesis and using their own passive-elastic prosthesis to those of seven non-amputees during level-ground walking. Compared with using a passive-elastic prosthesis, using the bionic prosthesis decreased metabolic cost by 8 per cent, increased trailing prosthetic leg mechanical work by 57 per cent and decreased the leading biological leg mechanical work by 10 per cent, on average, across walking velocities of 0.75-1.75 m s(-1) and increased preferred walking velocity by 23 per cent. Using the bionic prosthesis resulted in metabolic energy costs, preferred walking velocities and biomechanical patterns that were not significantly different from people without an amputation.     

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.     

Anthropomorphic Design of the Human-Like Walking Robot

In this paper, we present a new concept of the mechanical design of a humanoid robot. The goal is to build a humanoid robot utilizing a new structure which is more suitable for human-like walking with the characteristics of the knee stretch, heel-contact, and toe-off. Inspired by human skeleton, we made an anthropomorphic pelvis for the humanoid robot. In comparison with conventional humanoid robots, with such the anthropomorphic pelvis, our robot is capable of adjusting the center of gravity of the upper body by the motion of pelvic tilt, thus reducing the required torque at the ankle joint and the velocity variations in human-like walking. With more precise analysis of the foot mechanism, the fixed-length inverted pendulum can be used to describe the dynamics of biped walking, thus preventing redundant works and power consumption in length variable inverted pendulum system. As the result of the new structure we propose, a humanoid robot is able to walk with human-like gait.     

Muscle contributions to support and progression over a range of walking speeds

Muscles actuate walking by providing vertical support and forward progression of the mass center. To quantify muscle contributions to vertical support and forward progression (i.e., vertical and fore-aft accelerations of the mass center) over a range of walking speeds, three-dimensional muscle-actuated simulations of gait were generated and analyzed for eight subjects walking overground at very slow, slow, free, and fast speeds. We found that gluteus maximus, gluteus medius, vasti, hamstrings, gastrocnemius, and soleus were the primary contributors to support and progression at all speeds. With the exception of gluteus medius, contributions from these muscles generally increased with walking speed. During very slow and slow walking speeds, vertical support in early stance was primarily provided by a straighter limb, such that skeletal alignment, rather than muscles, provided resistance to gravity. When walking speed increased from slow to free, contributions to support from vasti and soleus increased dramatically. Greater stance-phase knee flexion during free and fast walking speeds caused increased vasti force, which provided support but also slowed progression, while contralateral soleus simultaneously provided increased propulsion. This study provides reference data for muscle contributions to support and progression over a wide range of walking speeds and highlights the importance of walking speed when evaluating muscle function.     

Balancing on a narrow ridge: biomechanics and control.

The balance of standing humans is usually explained by the inverted pendulum model. The subject invokes a horizontal ground-reaction force in this model and controls it by changing the location of the centre of pressure under the foot or feet. In experiments I showed that humans are able to stand on a ridge of only a few millimetres wide on one foot for a few minutes. In the present paper I investigate whether the inverted pendulum model is able to explain this achievement. I found that the centre of mass of the subjects sways beyond the surface of support, rendering the inverted pendulum model inadequate. Using inverse simulations of the dynamics of the human body, I found that hip-joint moments of the stance leg are used to vary the horizontal component of the ground-reaction force. This force brings the centre of mass back over the surface of support. The subjects generate moments of force at the hip-joint of the swing leg, at the shoulder-joints and at the neck. These moments work in conjunction with a hip strategy of the stance leg to limit the angular acceleration of the head-arms-trunk complex. The synchrony of the variation in moments suggests that subjects use a motor programme rather than long latency reflexes.     

Contributions of muscles and passive dynamics to swing initiation over a range of walking speeds

Stiff-knee gait is a common walking problem in cerebral palsy characterized by insufficient knee flexion during swing. To identify factors that may limit knee flexion in swing, it is necessary to understand how unimpaired subjects successfully coordinate muscles and passive dynamics (gravity and velocity-related forces) to accelerate the knee into flexion during double support, a critical phase just prior to swing that establishes the conditions for achieving sufficient knee flexion during swing. It is also necessary to understand how contributions to swing initiation change with walking speed, since patients with stiff-knee gait often walk slowly. We analyzed muscle-driven dynamic simulations of eight unimpaired subjects walking at four speeds to quantify the contributions of muscles, gravity, and velocity-related forces (i.e. Coriolis and centrifugal forces) to preswing knee flexion acceleration during double support at each speed. Analysis of the simulations revealed contributions from muscles and passive dynamics varied systematically with walking speed. Preswing knee flexion acceleration was achieved primarily by hip flexor muscles on the preswing leg with assistance from biceps femoris short head. Hip flexors on the preswing leg were primarily responsible for the increase in preswing knee flexion acceleration during double support with faster walking speed. The hip extensors and abductors on the contralateral leg and velocity-related forces opposed preswing knee flexion acceleration during double support.     

The mechanics of hopping by kangaroos (Macropodidae)

Force platform records and films have been made of kangaroos and a wallaby hopping.
The maximum forces exerted on the ground were about six times body weight. The force exerted on the ground changes direction, throughout the period when the feet are on the ground, so that it is always more or less in line with the centre of mass. Consequently the animal decelerates a little and then accelerates again, during the contact phase.
The fluctuations of potential energy which occur in each hop are slightly smaller at high speeds than at low ones. Fluctuations of external kinetic energy increase with speed and account for most of the energy cost of hopping at high speeds. Fluctuations of internal kinetic energy (due to acceleration and deceleration of the limbs) are relatively small. While the feet are on the ground the extensor muscles of the hip do positive work, those of the knee negative work and those of the ankle negative work followed by positive work. The energy cost of hopping is reduced substantially by elastic storage of energy in the Achilles tendon. In the case of a wallaby hopping at moderate speed the calculated saving was 40%. The maximum stresses developed in leg muscles, tendons and the tibia have been calculated and are discussed in relation to the known properties of muscle, tendon and bone. The trunk pitches as the animal hops because the two legs swing forwards and back simultaneously. Appropriate tail movements reduce, but do not eliminate, this effect. A mathematical theory of hopping is presented and used to investigate the merits of different hopping techniques.
Dawson & Taylor's (1973) discovery that the rate of oxygen consumption of kangaroos decreases a little, as hopping speed increases, is probably to be explained by the increased role of elastic storage of energy at high speeds.     

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.     

Contributions of muscles to mediolateral ground reaction force over a range of walking speeds

Impaired control of mediolateral body motion during walking is an important health concern. Developing treatments to improve mediolateral control is challenging, partly because the mechanisms by which muscles modulate mediolateral ground reaction force (and thereby modulate mediolateral acceleration of the body mass center) during unimpaired walking are poorly understood. To investigate this, we examined mediolateral ground reaction forces in eight unimpaired subjects walking at four speeds and determined the contributions of muscles, gravity, and velocity-related forces to the mediolateral ground reaction force by analyzing muscle-driven simulations of these subjects. During early stance (0-6% gait cycle), peak ground reaction force on the leading foot was directed laterally and increased significantly (p<0.05) with walking speed. During early single support (14-30% gait cycle), peak ground reaction force on the stance foot was directed medially and increased significantly (p<0.01) with speed. Muscles accounted for more than 92% of the mediolateral ground reaction force over all walking speeds, whereas gravity and velocity-related forces made relatively small contributions. Muscles coordinate mediolateral acceleration via an interplay between the medial ground reaction force contributed by the abductors and the lateral ground reaction forces contributed by the knee extensors, plantarflexors, and adductors. Our findings show how muscles that contribute to forward progression and body-weight support also modulate mediolateral acceleration of the body mass center while weight is transferred from one leg to another during double support.