Mechanical energy oscillations of two brachiation gaits: measurement and simulation

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

Human crawling performance and technique revealed by inertial measurement units

Human crawling performance and technique are of broad interest to roboticists, biomechanists, and military personnel. This study explores the variables that define crawling performance in the context of an outdoor obstacle course used by military organizations worldwide to evaluate the effects of load and personal equipment on warfighter performance. Crawling kinematics, measured from four body-worn inertial measurement units (IMUs) attached to the upper arms and thighs, are recorded for thirty-three participants. The IMU data is distilled to four metrics of crawling performance; namely, crawl speed, crawl stride time, ipsilateral limb coordination, and contralateral limb coordination. We hypothesize that higher performance (as identified by higher crawl speeds) is associated with more coordinated limbs and lower stride times. A cluster analysis groups participants into high and low performers exhibiting statistically significant differences across the four performance metrics. In particular, high performers exhibit superior limb coordination associated with a “diagonal gait” in which contralateral limbs move largely in-phase to produce faster crawl speeds and shorter crawl stride times. In contrast, low performers crawl at slower speeds with longer crawl stride times and less limb coordination. Beyond these conclusions, a major contribution of this study is a method for deploying wearable IMUs to study crawling in contextually relevant (i.e. non-laboratory) environments.     

Simultaneous positive and negative external mechanical work in human walking.

In human walking, the center of mass motion is similar to an inverted pendulum. Viewing double support as a transition from one inverted pendulum to the next, we hypothesized that the leading leg performs negative work to redirect the center of mass velocity, while simultaneously, the trailing leg performs positive work to replace the lost energy. To test this hypothesis, we developed a method to quantify the external mechanical work performed by each limb (individual limbs method). Traditional measures of external mechanical work use the sum of the ground reaction forces acting on the limbs (combined limbs method) allowing for the mathematical cancellation of simultaneous positive and negative work during multiple support periods. We expected to find that the traditional combined limbs method underestimates external mechanical work by a substantial amount. We used both methods to measure the external mechanical work performed by humans walking over a range of speeds. We found that during double support, the legs perform a substantial amount of positive and negative external work simultaneously. The combined limbs measures of positive and negative external work were approximately 33% less than those calculated using the individual limbs method. At all speeds, the trailing leg performs greater than 97% of the double support positive work while the leading leg performs greater than 94% of the double support negative work.     

Human body proportions explained on the basis of biomechanical principles

On the basis of theoretical biomechanics and of experiments, we investigated the mechanical requirements to which the body of a bipedally walking primate is subject, and the possibilities to meet these requirements with a minimum amount of energy. The least energy-consuming adaptation is clearly a body shape favourable for the preferred locomotion. Some characteristics of human body shape, in particular its proportions, could be identified as advantageous for fulfilling obvious biological roles or mechanical necessities. The characteristic length and the extended position of human hindlimbs make walking faster without additional input of energy. Mass distribution on the hindlimbs reduces the energy necessary for accelerating the swing limb after liftoff and for decelerating the swing limb before the heelstrike. Length and mass distribution in the forelimb gives it a pendulum length comparable to that of the hindlimb, so that both extremities swing at the same frequency. This swinging of the forelimbs counters in part the movements exerted by the moved hindlimbs on the trunk. The elongate and slim shape of the trunk provides great mass moments of inertia and that means stability against being flexed ventrally and dorsally by the forward and rearward movements of the heavy and long hindlimbs. Shoulder breadth in combination with the shallow shape of the thorax yield higher mass moments of inertia against the rotation of the trunk about a vertical axis than a cylindrical trunk shape. Further elongation of the hindlimbs is limited by the energy necessary for acceleration and deceleration, as well as for lifting them during the swing phase. In addition, the reaction forces exerted by the hindlimbs would expose the trunk to undue excursions if the proportions trunk length/limb length or trunk mass/limb mass would decrease. The above-noted kinetic requirements are partly in line, partly in conflict with the requirements of statics.     

What are the relations between mechanics, gait parameters, and energetics in terrestrial locomotion?

Are the different energy-conserving mechanics (i.e., pendulum and spring) used in different gaits reflected in differences in energetics and/or stride parameters? The analysis included published data from several species and new data from horses. When changing from pendulum to spring mechanics, there is a change in the slope of metabolic rate (MR) vs. speed in all species, in birds and quadrupeds there is no step increase, and in humans there are conflicting reports. At the trot-gallop transition, where quadrupeds are hypothesized to change from spring mechanics to some combination of spring and pendulum mechanics, there is a change in slope of MR vs. speed in horses but not in other species. Stride frequency (SF) is a logarithmic function of walking speed in all species, a linear function of trotting/running speed, and nearly independent of speed in galloping. In humans and horses there is a discontinuity in SF at the walk-trot (run) transition but not in birds. The slope of time of contact vs. speed does not change with mechanics in most species, but it does in humans. In horses and humans, there is a discontinuity at the walk-trot (run) transition and data for other species do not permit generalization. Duty factor (DF) in humans is greater than 0.5 in walking (pendulum mechanics) and less than 0.5 when running (spring mechanics). However, this is not true in many species that have DF>0.5 at the lowest speeds where they use spring mechanics. When trotting at low speeds, horses use forelimb DF>0.5 and hind limb DF<0.5. Thus, it is confusing to distinguish between walking and running by DF.     

Contributions of muscles to terminal-swing knee motions vary with walking speed

Many children with cerebral palsy walk with diminished knee extension during terminal swing, at speeds much slower than unimpaired children. Treatment of these gait abnormalities is challenging because the factors that extend the knee during normal walking, over a range of speeds, are not well understood. This study analyzed a series of three-dimensional, muscle-driven dynamic simulations to determine whether the relative contributions of individual muscles and other factors to angular motions of the swing-limb knee vary with walking speed. Simulations were developed that reproduced the measured gait dynamics of seven unimpaired children walking at self-selected, fast, slow, and very slow speeds (7 subjects×4 speeds=28 simulations). In mid-swing, muscles on the stance limb made the largest net contribution to extension of the swing-limb knee at all speeds examined. The stance-limb hip abductors, in particular, accelerated the pelvis upward, inducing reaction forces at the swing-limb hip that powerfully extended the knee. Velocity-related forces (i.e., Coriolis and centrifugal forces) also contributed to knee extension in mid-swing, though these contributions were diminished at slower speeds. In terminal swing, the hip flexors and other muscles on the swing-limb decelerated knee extension at the subjects’ self-selected, slow, and very slow speeds, but had only a minimal net effect on knee motions at the fastest speeds. Muscles on the stance limb helped brake knee extension at the subjects’ fastest speeds, but induced a net knee extension acceleration at the slowest speeds. These data—which show that the contributions of muscular and velocity-related forces to terminal-swing knee motions vary systematically with walking speed—emphasize the need for speed-matched control subjects when attempting to determine the causes of a patient's abnormal gait.     

Maximum walking speed and lower limb length in hominids

In 1984, Helene (Am. J. Physics 52:656) and Alexander (Am. Scientist 72:348–354) presented equations which purported to explain how lower limb length limited maximum walking speed in humans. The equations were based on a simplified model of human walking in which the center of mass (CoM) “vaults” over the supporting leg. Increasing walking speed by increasing stride frequency or stride length would increase the upward acceleration of the CoM in the first half of stance phase, to the point that it would be greater than the downward pull of gravity, and the individual would become airborne. This constitutes running by most definitions. While these models ignored various mechanical factors, such as knee flexion during midstance, that reduce the vertical movement of the CoM, the general idea is plausible inasmuch as the CoM of the body does oscillate vertically with each step. One hypothesis tested here is whether it is indeed the interaction between the pull of gravity and the individual's own upward acceleration that determines at what speed (or cadence) he changes from walking to running. Another hypothesis considered is that increased lower limb length (L) was selected for in early hominids, because of the locomotor advantages of longer lower limbs. Results indicate, however, that while L was clearly related to maximum possible walking speed, it was not an important factor in determining maximum “comfortable” walking speed. These and other results from the recent literature suggest that increased lower limb length provided no selective advantage in locomotion, and other explanations should be sought. © 1996 Wiley-Liss, Inc.     

Locomotion in the quail (Coturnix japonica): the kinematics of walking and increasing speed

Hindlimb segmental kinematics and stride characteristics are quantified in several quail locomoting on a treadmill over a six-fold increase in speed. These data are used to describe the kinematics of a walking stride and to identify which limb elements are used to change stride features as speed increases. In quail, the femur does not move during locomotion and the tarsometatarsus-phalangeal joint is a major moving joint; thus, quail have lost the most proximal moving joint and added one distally. The tibiotarsus and tarsometatarsus act together as a fixed strut swinging from the knee during stance phase (the ankle angle remains constant at a given speed) and the tarsometatarsus-phalangeal joint appears to have a major role in increasing limb length during the propulsive phase of the stride. Speed is increased with greater knee extension and by lengthening the tibiotarsus/tarsometatarsus via increased ankle extension at greater speeds. Because the femur is not moved and three distal elements are, quail move the limb segments through a stride and increase speed in a way fundamentally different from other nonavian vertebrates. However, the three moving joints in quail (the knee, ankle, and tarsometatarsophangeal joint) have strikingly similar kinematics to the analogous moving joints (the hip, knee, and ankle) in other vertebrates. Comparisons to other vertebrates indicate that birds appear to have two modes of limb function (three- and four-segment modes) that vary with speed and locomotory habits.     

The Influence of Dopaminergic Striatal Innervation on Upper Limb Locomotor Synergies

To determine the role of striatal dopaminergic innervation on upper limb synergies during walking, we measured arm kinematics in 13 subjects with Parkinson disease. Patients were recruited according to several inclusion criteria to represent the best possible in vivo model of dopaminergic denervation. Of relevance, we included only subjects with normal spatio-temporal parameters of the stride and gait speed to avoid an impairment of upper limbs locomotor synergies as a consequence of gait impairment per se. Dopaminergic innervation of the striatum was measured by FP-CIT and SPECT. All patients showed a reduction of gait-associated arms movement. No linear correlation was found between arm ROM reduction and contralateral dopaminergic putaminal innervation loss. Still, a partition analysis revealed a 80% chance of reduced arm ROM when putaminal dopamine content loss was >47%. A significant correlation was described between the asymmetry indices of the swinging of the two arms and dopaminergic striatal innervation. When arm ROM was reduced, we found a positive correlation between upper-lower limb phase shift modulation (at different gait velocities) and striatal dopaminergic innervation. These findings are preliminary evidence that dopaminergic striatal tone plays a modulatory role in upper-limb locomotor synergies and upper-lower limb coupling while walking at different velocities.     

How locomotion sub-functions can control walking at different speeds?

Inspired from template models explaining biological locomotory systems and Raibert׳s pioneering legged robots, locomotion can be realized by basic sub-functions: elastic axial leg function, leg swinging and balancing. Combinations of these three can generate different gaits with diverse properties. In this paper we investigate how locomotion sub-functions contribute to stabilize walking at different speeds. Based on this trilogy, we introduce a conceptual model to quantify human locomotion sub-functions in walking. This model can produce stable walking and also predict human locomotion sub-function control during swing phase of walking. Analyzing experimental data based on this modeling shows different control strategies which are employed to increase speed from slow to moderate and moderate to fast gaits.     

Kinematic and kinetic changes in obese gait in bariatric surgery-induced weight loss

This study examines the effects of a radical bariatric surgery-induced weight loss on the gait of obese subjects. We performed a three-dimensional motion analysis of lower limbs, and collected force platform data in the gait laboratory to calculate knee and hip joint moments. Subjects (n=13) performed walking trials in the laboratory before and 8.8 months (SD 4.2) after the surgical procedure at two gait speeds (1.2m/s and 1.5m/s). The average weight loss was 26.7kg (SD 9.2kg), corresponding to 21.5% (SD 6.8%) of the initial weight. We observed a decrease in step width at both gait speeds, but no changes in relative double support or swing time or stride length. A significant decrease was noted in the absolute values of peak knee abductor, peak knee flexor and peak hip extensor moments. However, the moment values normalized by the body weight and height remained unchanged in most cases. Thus, we conclude that weight loss reduces hip and knee joint moments in proportion to the amount of weight lost.     

How close to a pendulum is human upper limb movement during walking?

The aim of this work was to investigate how close to pendulum-like behaviour the periodic motion of the human upper limb (or upper extremity) is, during normal walking at a comfortable speed of locomotion. Twenty-five healthy young persons (males and females) participated in the experiment. Biomechanical testing was undertaken (mass and centre of mass of each segment of the total upper extremity). Participants were walking on a treadmill with a standardised velocity of 1.1 ms(-1) (comfortable speed for all of them). A video analysis system with Silicon software was used to measure the different angles of the arm and forearm. The theoretical period of motion and maximal angular velocity were computed for the centre of mass of the total upper limb from the measured phases of the arm swing and associated positional potential energies. Actual measured periods of motion, in comparison, represented a level of similarity to a lightly damped simple pendulum. Using this assumption, the "damping factor" was calculated from the ratio between theoretical and measured values. A vast majority of people exhibited an actual angular velocity exceeding the expected theoretical angular velocity calculated for a virtual pendulum of similar mass and length characteristics. This may be due to muscle forces that are contributing to the motion of the upper limb during walking rather than simple gravity force acting alone. The observed positional potential energy of the dominant limb was greater than that of the non-dominant limb for the vast majority of participants.     

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.     

Resonant frequencies of arms and legs identify different walking patterns

The present study is aimed at investigating changes in the coordination of arm and leg movements in young healthy subjects. It was hypothesized that with changes in walking velocity there is a change in frequency and phase coupling between the arms and the legs. In addition, it was hypothesized that the preferred frequencies of the different coordination patterns can be predicted on the basis of the resonant frequencies of arms and legs with a simple pendulum model. The kinematics of arms and legs during treadmill walking in seven healthy subjects were recorded with accelerometers in the sagittal plane at a wide range of different velocities (i.e., 0.3-1. 3m/s). Power spectral analyses revealed a statistically significant change in the frequency relation between arms and legs, i.e., within the velocity range 0.3-0.7m/s arm movement frequencies were dominantly synchronized with the step frequency, whereas from 0.8m/s onwards arm frequencies were locked onto stride frequency. Significant effects of walking speed on mean relative phase between leg and arm movements were found. All limb pairs showed a significantly more stable coordination pattern from 0.8 to 1.0m/s onwards. Results from the pendulum modelling demonstrated that for most subjects at low-velocity preferred movement frequencies of the arms are predicted by the resonant frequencies of individual arms (about 0.98Hz), whereas at higher velocities these are predicted on the basis of the resonant frequencies of the individual legs (about 0.85Hz). The results support the above-mentioned hypotheses, and suggest that different patterns of coordination, as shown by changes in frequency coupling and phase relations, can exist within the human walking mode.     

Steps to Take to Enhance Gait Stability: The Effect of Stride Frequency,Stride Length,and Walking Speed on Local Dynamic Stability and Margins of Stability

The purpose of the current study was to investigate whether adaptations of stride length, stride frequency, and walking speed, independently influence local dynamic stability and the size of the medio-lateral and backward margins of stability during walking. Nine healthy subjects walked 25 trials on a treadmill at different combinations of stride frequency, stride length, and consequently at different walking speeds. Visual feedback about the required and the actual combination of stride frequency and stride length was given during the trials. Generalized Estimating Equations were used to investigate the independent contribution of stride length, stride frequency, and walking speed on the measures of gait stability. Increasing stride frequency was found to enhance medio-lateral margins of stability. Backward margins of stability became larger as stride length decreased or walking speed increased. For local dynamic stability no significant effects of stride frequency, stride length or walking speed were found. We conclude that adaptations in stride frequency, stride length and/or walking speed can result in an increase of the medio-lateral and backward margins of stability, while these adaptations do not seem to affect local dynamic stability. Gait training focusing on the observed stepping strategies to enhance margins of stability might be a useful contribution to programs aimed at fall prevention.     

Activity of upper limb muscles during human walking

The EMG activity of upper limb muscles during human gait has rarely been studied previously. It was examined in 20 normal volunteers in four conditions: walking on a treadmill (1) with unrestrained natural arm swing (Normal), (2) while volitionally holding the arms still (Held), (3) with the arms immobilized (Bound), and (4) with the arms swinging in phase with the ipsilateral legs, i.e. opposite-to-normal phasing (Anti-Normal). Normal arm swing involved weak rhythmical lengthening and shortening contractions of arm and shoulder muscles. Phasic muscle activity was needed to keep the unrestricted arms still during walking (Held), indicating a passive component of arm swing. An active component, possibly programmed centrally, existed as well, because some EMG signals persisted when the arms were immobilized during walking (Bound). Anti-Normal gait involved stronger EMG activity than Normal walking and was uneconomical. The present results indicate that normal arm swing has both passive and active components.     

Effects of arm swing on mechanical parameters of human gait

The aim of this study was to investigate the influence of the upper limb swing on human gait. Measurements were performed on 52 subjects by using the Elite system with two cameras and a Kistler force platform. The recording of trajectories of characteristic body points on the subjects and the measurement of ground reaction forces have been performed at normal walking and at walking with emphasised rhythmic upper limb swing. The trajectory of the whole body mass centre, central dynamic moments of inertia and ground reaction forces have been calculated for every subject and mean curves of the entire group have been determined for walking with the natural and the emphasised upper limb swing. The determined mean values of normalised mechanical parameters have been compared and differences between the gait with the natural and the emphasised upper limb swing have been described.     

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.     

Control of lateral weight transfer is associated with walking speed in individuals post-stroke

Restoring functional gait speed is an important goal for rehabilitation post-stroke. During walking, transferring of one’s body weight between the limbs and maintaining balance stability are necessary for independent functional gait. Although it is documented that individuals post-stroke commonly have difficulties with performing weight transfer onto their paretic limbs, it remains to be determined if these deficits contributed to slower walking speeds. The primary purpose of this study was to compare the weight transfer characteristics between slow and fast post-stroke ambulators. Participants (N = 36) with chronic post-stroke hemiparesis walked at their comfortable and maximal walking speeds on a treadmill. Participants were stratified into 2 groups based on their comfortable walking speeds (≥0.8 m/s or <0.8 m/s). Minimum body center of mass (COM) to center of pressure (COP) distance, weight transfer timing, step width, lateral foot placement relative to the COM, hip moment, peak vertical and anterior ground reaction forces, and changes in walking speed were analyzed. Results showed that slow walkers walked with a delayed and deficient weight transfer to the paretic limb, lower hip abductor moment, and more lateral paretic limb foot placement relative to the COM compared to fast walkers. In addition, propulsive force and walking speed capacity was related to lateral weight transfer ability. These findings demonstrated that deficits in lateral weight transfer and stability could potentially be one of the limiting factors underlying comfortable walking speeds and a determinant of chronic stroke survivors’ ability to increase walking speed.     

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.