Compliant leg behaviour explains basic dynamics of walking and running

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

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s^-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.     

Bipedal walking and running with spring-like biarticular muscles

Compliant elements in the leg musculoskeletal system appear to be important not only for running but also for walking in human locomotion as shown in the energetics and kinematics studies of spring-mass model. While the spring-mass model assumes a whole leg as a linear spring, it is still not clear how the compliant elements of muscle-tendon systems behave in a human-like segmented leg structure. This study presents a minimalistic model of compliant leg structure that exploits dynamics of biarticular tension springs. In the proposed bipedal model, each leg consists of three leg segments with passive knee and ankle joints that are constrained by four linear tension springs. We found that biarticular arrangements of the springs that correspond to rectus femoris, biceps femoris and gastrocnemius in human legs provide self-stabilizing characteristics for both walking and running gaits. Through the experiments in simulation and a real-world robotic platform, we show how behavioral characteristics of the proposed model agree with basic patterns of human locomotion including joint kinematics and ground reaction force, which could not be explained in the previous models.     

How do low horizontal forces produce disproportionately high torques in human locomotion?

Although horizontal ground forces are only approximately 15% of vertical forces, they account for 47% and 33% of the metabolic cost in walking and running. To explain these disproportionately high metabolic costs, we hypothesized that low horizontal ground forces generate relatively high torques on body segments during locomotion and this is mediated by long moment arms. We compared external force moment arms and discreet torques applied to the body segments by horizontal and vertical forces during walking and running. Sixteen subjects (21.9+/-1.9 years) walked at 1.5m/s and ten subjects (23.2+/-2.0 years) ran at 3.83 m/s. Segmental torques in the sagittal plane were partitioned into components due to horizontal and vertical forces and quantified by their angular impulses. The mean (+/-S.E.) ratios of horizontal to vertical ground forces (GF ratio) and angular impulses (AI ratio) in walking were 0.131 (+/-0.003, 95% confidence interval (CI) 0.124-0.137) and 0.530 (+/-0.018, CI 0.497-0.569). Results were similar in running. In both gaits the AI ratios were significantly greater than the GF ratios because the respective CI's did not overlap. The horizontal forces produced 53% and 41% as much angular impulse on the body segments, as did the vertical forces in walking and running despite being only 13% as large. In the two movements the moment arms for the horizontal forces averaged across foot, leg, thigh, and trunk body segments were 3.8 fold larger than those for the vertical forces. The data supported the hypothesis and suggest that the relatively low horizontal vs. vertical forces accounted for a disproportionately higher percentage of the angular impulses placed on the body segments and this effect was due to relatively long moment arms for horizontal forces. These results partially explain the relatively large metabolic cost of generating relatively low horizontal forces.     

Metabolic energy and muscular activity required for leg swing in running.

The metabolic cost of leg swing in running is highly controversial. We investigated the cost of initiating and propagating leg swing at a moderate running speed and some of the muscular actions involved. We constructed an external swing assist (ESA) device that applied small anterior pulling forces to each foot during the first part of the swing phase. Subjects ran on a treadmill at 3.0 m/s normally and with ESA forces up to 4% body weight. With the greatest ESA force, net metabolic rate was 20.5% less than during normal running. Thus we infer that the metabolic cost of initiating and propagating leg swing comprises approximately 20% of the net cost of normal running. Even with the greatest ESA, mean electromyograph (mEMG) of the medial gastrocnemius and soleus muscles during later portions of stance phase did not change significantly compared with normal running, indicating that these muscles are not responsible for the initiation of leg swing. However, with ESA, rectus femoris mEMG during the early portions of swing phase was as much as 74% less than during normal running, confirming that it is responsible for the propagation of leg swing.     

Energy cost and muscular activity required for leg swing during walking.

To investigate the metabolic cost and muscular actions required for the initiation and propagation of leg swing, we applied a novel combination of external forces to subjects walking on a treadmill. We applied a forward pulling force at each foot to assist leg swing, a constant forward pulling force at the waist to provide center of mass propulsion, and a combination of these foot and waist forces to evaluate leg swing. When the metabolic cost and muscle actions were at a minimum, the condition was considered optimal. We reasoned that the difference in energy consumption between the optimal combined waist and foot force trial and the optimal waist force-only trial would reflect the metabolic cost of initiating and propagating leg swing during normal walking. We also reasoned that a lower muscle activity with these assisting forces would indicate which muscles are normally responsible for initiating and propagating leg swing. With a propulsive force at the waist of 10% body weight (BW), the net metabolic cost of walking decreased to 58% of normal walking. With the optimal combination, a propulsive force at the waist of 10% BW plus a pulling force at the feet of 3% BW the net metabolic cost of walking further decreased to 48% of normal walking. With the same combination, the muscle activity of the iliopsoas and rectus femoris muscles during the swing phase was 27 and 60% lower, respectively, but the activity of the medial gastrocnemius and soleus before swing did not change. Thus our data indicate that approximately 10% of the net metabolic cost of walking is required to initiate and propagate leg swing. Additionally, the hip flexor muscles contribute to the initiation and propagation leg swing.     

Effective leg stiffness in running

Leg stiffness is a common parameter used to characterize leg function during bouncing gaits, like running and hopping. In the literature, different methods to approximate leg stiffness based on kinetic and kinematic parameters are described. A challenging point in estimating leg stiffness is the definition of leg compression during contact. In this paper four methods (methods A–D) based on ground reaction forces (GRF) and one method (method E) relying on temporal parameters are described. Leg stiffness calculated by these five methods is compared with running patterns, predicted by the spring mass model.The best and simplest approximation of leg stiffness is method E. It requires only easily accessible parameters (contact time, flight time, resting leg length, body mass and the leg's touch down angle). Method D is of similar quality but additionally requires the time-dependent progression of the GRF. The other three methods show clear differences from the model predictions by over- or underestimating leg stiffness, especially at slow speeds.Leg stiffness is derived from a conceptual model of legged locomotion and does not exist without this model. Therefore, it is important to prove which experimental method is suited best for approximating the stiffness in a specific task. This will help to interpret the predictions of the conceptual model in comparison with experimental data.     

Posture, gait and the ecological relevance of locomotor costs and energy-saving mechanisms in tetrapods

A reanalysis of locomotor data from functional, energetic, mechanical and ecological perspectives reveals that limb posture has major effects on limb biomechanics, energy-saving mechanisms and the costs of locomotion. Regressions of data coded by posture (crouched vs. erect) reveal nonlinear patterns in metabolic cost, limb muscle mass, effective mechanical advantage, and stride characteristics. In small crouched animals energy savings from spring and pendular mechanisms are inconsequential and thus the metabolic cost of locomotion is driven by muscle activation costs. Stride frequency appears to be the principal functional parameter related to the decreasing cost of locomotion in crouched animals. By contrast, the shift to erect limb postures invoked a series of correlated effects on the metabolic cost of locomotion: effective mechanical advantage increases, relative muscle masses decrease, metapodial limb segments elongate dramatically (as limbs shift from digitigrade to unguligrade designs) and biological springs increase in size and effectiveness. Each of these factors leads to decreases in the metabolic cost of locomotion in erect forms resulting from real and increasing contributions of pendular savings and spring savings. Comparisons of the relative costs and ecological relevance of different gaits reveal that running is cheaper than walking in smaller animals up to the size of dogs but running is more expensive than walking in horses. Animals do not necessarily use their cheapest gaits for their predominant locomotor activity. Therefore, locomotor costs are driven more by ecological relevance than by the need to optimize locomotor economy.     

The Cost of Leg Forces in Bipedal Locomotion: A Simple Optimization Study

Simple optimization models show that bipedal locomotion may largely be governed by the mechanical work performed by the legs, minimization of which can automatically discover walking and running gaits. Work minimization can reproduce broad aspects of human ground reaction forces, such as a double-peaked profile for walking and a single peak for running, but the predicted peaks are unrealistically high and impulsive compared to the much smoother forces produced by humans. The smoothness might be explained better by a cost for the force rather than work produced by the legs, but it is unclear what features of force might be most relevant. We therefore tested a generalized force cost that can penalize force amplitude or its n-th time derivative, raised to the p-th power (or p-norm), across a variety of combinations for n and p. A simple model shows that this generalized force cost only produces smoother, human-like forces if it penalizes the rate rather than amplitude of force production, and only in combination with a work cost. Such a combined objective reproduces the characteristic profiles of human walking (R² = 0.96) and running (R² = 0.92), more so than minimization of either work or force amplitude alone (R² = −0.79 and R² = 0.22, respectively, for walking). Humans might find it preferable to avoid rapid force production, which may be mechanically and physiologically costly.     

Mechanical and metabolic determinants of the preferred step width in human walking

We studied the selection of preferred step width in human walking by measuring mechanical and metabolic costs as a function of experimentally manipulated step width (0.00-0.45L, as a fraction of leg length L). We estimated mechanical costs from individual limb external mechanical work and metabolic costs using open circuit respirometry. The mechanical and metabolic costs both increased substantially (54 and 45%, respectively) for widths greater than the preferred value (0.15-0.45L) and with step width squared (R(2) = 0.91 and 0.83, respectively). As predicted by a three-dimensional model of walking mechanics, the increases in these costs appear to be a result of the mechanical work required for redirecting the centre of mass velocity during the transition between single stance phases (step-to-step transition costs). The metabolic cost for steps narrower than preferred (0.10-0.00L) increased by 8%, which was probably as a result of the added cost of moving the swing leg laterally in order to avoid the stance leg (lateral limb swing cost). Trade-offs between the step-to-step transition and lateral limb swing costs resulted in a minimum metabolic cost at a step width of 0.12L, which is not significantly different from foot width (0.11L) or the preferred step width (0.13L). Humans appear to prefer a step width that minimizes metabolic cost.     

Mechanical energy and effective foot mass during impact loading of walking and running

The human heel pad is considered an important structure for attenuation of the transient force caused by heel-strike. Although the mechanical properties of heel pads are relatively well understood, the mechanical energy (Etot) absorbed by the heel pad during the impact phase has never been documented directly because data on the effective foot mass (Meff) was previously unavailable during normal forward locomotion. In this study, we use the impulse-momentum method (IMM) for calculating Meff from moving subjects. Mass-spring-damper models were developed to evaluate errors and to examine the effects of pad property, upper body mass, and effective leg spring on Meff. We simultaneously collected ground reaction forces, pad deformation, and lower limb kinematics during impact phase of barefoot walking, running, and crouched walking. The latter was included to examine the effect of knee angle on Meff. The magnitude of Meff as a percentage of body mass (M(B)) varies with knee angle at impact and significantly differs among gaits: 6.3%M(B) in walking, 5.3%M(B) in running, and 3.7%M(B) in crouched walking. Our modeling results suggested that Meff is insensitive to heel pad resilience and effective leg stiffness. At the instant prior to heel strike, Etot ranges from 0.24 to 3.99 J. The combination of video and forceplate data used in this study allows analyses of Etot and Etot as a function of heel-strike kinematics during normal locomotion. Relationship between Meff and knee angle provides insights into how changes in posture moderate impact transients at different gaits.     

Running in the real world: adjusting leg stiffness for 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.     

Bioenergetics and the origin of hominid bipedalism

Compared to most quadrupedal mammals, humans are energetically inefficient when running at high speeds. This fact can be taken to mean that human bipedalism evolved for reasons other than to reduce relative energy cost during locomotion. Recalculation of the energy expended during human walking at normal speeds shows that (1) human bipedalism is at least as efficient as typical mammalian quadrupedalism and (2) human gait is much more efficient than bipedal or quadrupedal locomotion in the chimpanzee. We conclude that bipedalism bestowed an energetic advantage on the Miocene hominoid ancestors of the Hominidae.     

Trunk orientation causes asymmetries in leg function in small bird terrestrial locomotion

In contrast to the upright trunk in humans, trunk orientation in most birds is almost horizontal (pronograde). It is conceivable that the orientation of the heavy trunk strongly influences the dynamics of bipedal terrestrial locomotion. Here, we analyse for the first time the effects of a pronograde trunk orientation on leg function and stability during bipedal locomotion. For this, we first inferred the leg function and trunk control strategy applied by a generalized small bird during terrestrial locomotion by analysing synchronously recorded kinematic (three-dimensional X-ray videography) and kinetic (three-dimensional force measurement) quail locomotion data. Then, by simulating quail gaits using a simplistic bioinspired numerical model which made use of parameters obtained in in vivo experiments with real quail, we show that the observed asymmetric leg function (left-skewed ground reaction force and longer leg at touchdown than at lift-off) is necessary for pronograde steady-state locomotion. In addition, steady-state locomotion becomes stable for specific morphological parameters. For quail-like parameters, the most common stable solution is grounded running, a gait preferred by quail and most of the other small birds. We hypothesize that stability of bipedal locomotion is a functional demand that, depending on trunk orientation and centre of mass location, constrains basic hind limb morphology and function, such as leg length, leg stiffness and leg damping.     

Gait selection in the ostrich: mechanical and metabolic characteristics of walking and running with and without an aerial phase

It has been argued that minimization of metabolic-energy costs is a primary determinant of gait selection in terrestrial animals. This view is based predominantly on data from humans and horses, which have been shown to choose the most economical gait (walking, running, galloping) for any given speed. It is not certain whether a minimization of metabolic costs is associated with the selection of other prevalent forms of terrestrial gaits, such as grounded running (a widespread gait in birds). Using biomechanical and metabolic measurements of four ostriches moving on a treadmill over a range of speeds from 0.8 to 6.7 m s(-1), we reveal here that the selection of walking or grounded running at intermediate speeds also favours a reduction in the metabolic cost of locomotion. This gait transition is characterized by a shift in locomotor kinetics from an inverted-pendulum gait to a bouncing gait that lacks an aerial phase. By contrast, when the ostrich adopts an aerial-running gait at faster speeds, there are no abrupt transitions in mechanical parameters or in the metabolic cost of locomotion. These data suggest a continuum between grounded and aerial running, indicating that they belong to the same locomotor paradigm.     

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.     

Optimal muscle fascicle length and tendon stiffness for maximising gastrocnemius efficiency during human walking and running

Muscles generate force to resist gravitational and inertial forces and/or to undertake work, e.g. on the centre of mass. A trade-off in muscle architecture exists in muscles that do both; the fibres should be as short as possible to minimise activation cost but long enough to maintain an appropriate shortening velocity. Energetic cost is also influenced by tendon compliance which modulates the timecourse of muscle mechanical work. Here we use a Hill-type muscle model of the human medial gastrocnemius to determine the muscle fascicle length and Achilles tendon compliance that maximise efficiency during the stance phase of walking (1.2 m/s) and running (3.2 and 3.9 m/s). A broad range of muscle fascicle lengths (ranging from 45 to 70 mm) and tendon stiffness values (150-500 N/mm) can achieve close to optimal efficiency at each speed of locomotion; however, efficient walking requires shorter muscle fascicles and a more compliant tendon than running. The values that maximise efficiency are within the range measured in normal populations. A non-linear toe-region region of the tendon force-length properties may further influence the optimal values, requiring a stiffer tendon with slightly longer muscle fascicles; however, it does not alter the main results. We conclude that muscle fibre length and tendon compliance combinations may be tuned to maximise efficiency under a given gait condition. Efficiency is maximised when the required volume of muscle is minimised, which may also help reduce limb inertia and basal metabolic costs.     

The energetic cost of locomotion: humans and primates compared to generalized endotherms

A wide range of selective pressures have been advanced as possible causes for the adoption of bipedalism in the hominin lineage. One suggestion has been that because modern human walking is relatively efficient compared to that of a typical quadruped, the ancestral quadruped may have reaped an energetic advantage when it walked on two legs. While it has become clear that human walking is relatively efficient and human running inefficient compared to "generalized endotherms", workers differ in their opinion of how the cost of human bipedal locomotion compares to that of a generalized primate walking quadrupedally. One view is that human walking is particularly efficient in comparison to other primates. The present study addresses this by comparing the cost of human walking and running to that of the eight primate species for which data are available and by comparing cost in primates to that of a "generalized endotherm". There is no evidence that primate locomotion is more costly than that of a generalized endotherm, although more data on adult Old World monkeys and apes would be useful. Further, human locomotion does not appear to be particularly efficient relative to that of other primates.     

The evolution of human running: effects of changes in lower-limb length on locomotor economy

Previous studies have differed in expectations about whether long limbs should increase or decrease the energetic cost of locomotion. It has recently been shown that relatively longer lower limbs (relative to body mass) reduce the energetic cost of human walking. Here we report on whether a relationship exists between limb length and cost of human running. Subjects whose measured lower-limb lengths were relatively long or short for their mass (as judged by deviations from predicted values based on a regression of lower-limb length on body mass) were selected. Eighteen human subjects rested in a seated position and ran on a treadmill at 2.68 ms(-1) while their expired gases were collected and analyzed; stride length was determined from videotapes. We found significant negative relationships between relative lower-limb length and two measures of cost. The partial correlation between net cost of transport and lower-limb length controlling for body mass was r=-0.69 (p=0.002). The partial correlation between the gross cost of locomotion at 2.68 ms(-1) and lower-limb length controlling for body mass was r=-0.61 (p=0.009). Thus, subjects with relatively longer lower limbs tend to have lower locomotor costs than those with relatively shorter lower limbs, similar to the results found for human walking. Contrary to general expectation, a linear relationship between stride length and lower-limb length was not found.     

Kinetics of individual limbs during level and slope walking with a unilateral transtibial bone-anchored prosthesis in the cat

Ongoing animal preclinical studies on transcutaneous bone-anchored prostheses have aimed to improve biomechanics of prosthetic locomotion in people with limb loss. It is much less common to translate successful developments in human biomechanics and prosthetic research to veterinary medicine to treat animals with limb loss. Current standard of care in veterinary medicine is amputation of the whole limb if a distal segment cannot be salvaged. Bone-anchored transcutaneous prostheses, developed for people with limb loss, could be beneficial for veterinary practice. The aim of this study was to examined if and how cats utilize the limb with a bone-anchored passive transtibial prosthesis during level and slope walking. Four cats were implanted with a porous titanium implant into the right distal tibia. Ground reaction forces and full-body kinematics were recorded during level and slope (±50%) walking before and 4–6 months after implantation and prosthesis attachment. The duty factor of the prosthetic limb exceeded zero in all cats and slope conditions (p < 0.05) and was in the range of 45.0–60.6%. Thus, cats utilized the prosthetic leg for locomotion instead of walking on three legs. Ground reaction forces, power and work of the prosthetic limb were reduced compared to intact locomotion, whereas those of the contralateral hind- and forelimbs increased (p < 0.05). This asymmetry was likely caused by insufficient energy generation for propulsion by the prosthetic leg, as no signs of pain or discomfort were observed in the animals. We concluded that cats could utilize a unilateral bone-anchored transtibial prosthesis for quadrupedal level and slope locomotion.