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Results for “Legged locomotion”

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At least 19 recordsLinked to original sources

PubMed2005

An analytical estimation of the energy cost for legged locomotion.

Legged locomotion requires the determination of a number of parameters such as stride period, stride length, order of leg movements, leg trajectory, etc. How are these parameters determined? It has been reported that the locomotor patterns of many legged animals exhibit common characteristics, which suggests that there exists a basic strategy for legged locomotion. In this study we derive an equation to estimate the cost of transport for legged locomotion and examine a criterion of the minimization of the transport cost as a candidate of the strategy. The obtained optimal locomotor pattern that minimizes the cost suitably represents many characteristics of the pattern observed in legged animals. This suggests that the locomotor pattern of legged animals is well optimized with regard to the energetic cost. The result also suggests that the existence of specific gait patterns and the phase transition between them could be the result due to optimization; they are induced by the change in the distribution of ground reaction forces for each leg during locomotion.

Animals↗

PubMed1998

A neuro-mechanical model of legged locomotion: single leg control.

Most models of legged locomotion have concentrated on properties of either the mechanical or the neural system. Here a combined neuro-mechanical model of stepping in a single leg is presented, as the first step in the process of modeling and building a fast and dynamically stable quadruped. It is based on general principles of legged animals with special reference to vertebrates. The mechanical leg was first studied separately in order to take advantage of its inherent mechanical properties and avoid over-control during stepping generation. As a part of the design strategy it uses elastic actuators to increase shock tolerance and energy efficiency. The neural controller consists of a neural phase generator (NPG), a system of fast feedback pathways, and a single control neuron representing descending drive from higher centers in the brain. Sensory information directly influences the movements through the fast feedback pathways, but also entrains the NPG. The NPG has its own description of the state of the leg, which then enables it to set the feedback pathways so that only actions appropriate for the particular stage of the step cycle are undertaken. This preprogramming benefits from the NPG's ability to filter out any inconsistencies or gaps in the afferent input. In this way the model unites the use of central pattern generators and peripheral feedback systems for the generation of stepping movements. The neuro-mechanical system produced stable stepping patterns over a large velocity range and was adaptable to different body weights and landing from varying heights.

Animals↗

PubMed2002

Dynamics and stability of legged locomotion in the horizontal plane: a test case using insects.

Motivated by experimental studies of insects, we propose a model for legged locomotion in the horizontal plane. A three-degree-of freedom, energetically conservative, rigid-body model with a pair of compliant virtual legs in intermittent contact with the ground allows us to study how dynamics depends on parameters such as mass, moment of inertia, leg stiffness, and length. We find periodic gaits, and show that mechanics alone can confer asymptotic stability of relative heading and body angular velocity. We discuss the relevance of our idealized models to experiments and simulations on insect running, showing that their gait and force characteristics match observations reasonably well. We perform parameter studies and suggest that our model is relevant to the understanding of locomotion dynamics across species.

Animals↗

PubMed1998

Oscillatory network controlling six-legged locomotion. Optimization of model parameters.

The model of a legged locomotory system is optimized to ensure stable motion, reliable with respect to different initial conditions. The cost function suggested is based on the frequency of the model's loss of stability evaluated for randomly chosen initial leg positions. The optimized model can start from the majority of allowed leg configurations, demonstrating stable walking at low and moderate speeds. Furthermore, an acceleration procedure is designed to permit the model to pick up practically every speed and then walk successfully.

Journal Article↗

PubMed1999

Templates and anchors: neuromechanical hypotheses of legged locomotion on land.

Locomotion results from complex, high-dimensional, non-linear, dynamically coupled interactions between an organism and its environment. Fortunately, simple models we call templates have been and can be made to resolve the redundancy of multiple legs, joints and muscles by seeking synergies and symmetries. A template is the simplest model (least number of variables and parameters) that exhibits a targeted behavior. For example, diverse species that differ in skeletal type, leg number and posture run in a stable manner like sagittal- and horizontal-plane spring-mass systems. Templates suggest control strategies that can be tested against empirical data. Templates must be grounded in more detailed morphological and physiological models to ask specific questions about multiple legs, the joint torques that actuate them, the recruitment of muscles that produce those torques and the neural networks that activate the ensemble. We term these more elaborate models anchors. They introduce representations of specific biological details whose mechanism of coordination is of interest. Since mechanisms require controls, anchors incorporate specific hypotheses concerning the manner in which unnecessary motion or energy from legs, joints and muscles is removed, leaving behind the behavior of the body in the low-degree-of-freedom template. Locating the origin of control is a challenge because neural and mechanical systems are dynamically coupled and both play a role. The control of slow, variable-frequency locomotion appears to be dominated by the nervous system, whereas during rapid, rhythmic locomotion, the control may reside more within the mechanical system. Anchored templates of many-legged, sprawled-postured animals suggest that passive, dynamic self-stabilization from a feedforward, tuned mechanical system can reject rapid perturbations and simplify control. Future progress would benefit from the creation of a field embracing comparative neuromechanics.

Animals↗

PubMed2004

Stability in legged locomotion.

Stability is a key element in a gait synthesis. Static stability margins are widely adopted in crawlers, while no similar approach has been developed for dynamically stable systems. Utilizing an analytical approach, we developed a set of easy-to-calculate stability indices to describe instantaneous static and dynamic (In)stability for a certain group of walking systems. The analysis is based on a thorough analysis of the interaction between ground reaction forces and the walking system. The indices are applicable to walking systems regardless of the number of legs or mechanical/biological design. We show that static and dynamic stability are independent of each other. We suggest a possible categorization of gait modes based on stability. Stability characteristics are analyzed in a healthy and highly pathological human gait. Finally, we discuss the applicability of the proposed methods.

Gait↗

PubMed2002

Biomechanical and physiological aspects of legged locomotion in humans.

Walking and running, the two basic gaits used by man, are very complex movements. They can, however, be described using two simple models: an inverted pendulum and a spring. Muscles must contract at each step to move the body segments in the proper sequence but the work done is, in part, relieved by the interplay of mechanical energies, potential and kinetic in walking, and elastic in running. This explains why there is an optimal speed of walking (minimal metabolic cost of about 2 J.kg(-1).m(-1) at about 1.11 m.s(-1)) and why the cost of running is constant and independent of speed (about 4 J.kg(-1).m(-1)). Historically, the mechanical work of locomotion has been divided into external and internal work. The former is the work done to raise and accelerate the body centre of mass (m) within the environment, the latter is the work done to accelerate the body segments with respect to the centre of m. The total work has been calculated, somewhat arbitrarily, as the sum of the two. While the changes of potential and kinetic energies can be accurately measured, the contribution of the elastic energy cannot easily be assessed, nor can the true work performed by the muscles. Many factors can affect the work of locomotion--the gradient of the terrain, body size (height and body m), and gravity. The partitioning of positive and negative work and their different efficiencies explain why the most economical gradient is about -10% (1.1 J.kg(-1).m(-1) at 1.3 m.s(-1) for walking, and 3.1 J.kg(-1).m(-1) at between 3 and 4 m.s(-1) for running). The mechanics of walking of children, pigmies and dwarfs, in particular the recovery of energy at each step, is not different from that of taller (normal sized) individuals when the speed is expressed in dynamically equivalent terms (Froude number). An extra load, external or internal (obesity) affects internal and external work according to the distribution of the added m. Different gravitational environments determine the optimal speed of walking and the speed of transition from walking to running: at more than 1 g it is easier to walk than to run, and it is the opposite at less than 1 g. Passive aids, such as skis or skates, allow an increase in the speed of progression, but the mechanics of the locomotion cannot be simply described using the models for walking and running because step frequency, the proportion of step duration during which the foot is in contact with the ground, the position of the limbs, the force exerted on the ground and the time of its application are all different.

Biomechanical Phenomena↗

PubMed1991

Mechanics of a rapid running insect: two-, four- and six-legged locomotion.

To examine the effects of variation in body form on the mechanics of terrestrial locomotion, we used a miniature force platform to measure the ground reaction forces of the smallest and, relative to its mass, one of the fastest invertebrates ever studied, the American cockroach Periplaneta americana (mass = 0.83 g). From 0.44-1.0 ms-1, P. americana used an alternating tripod stepping pattern. Fluctuations in gravitational potential energy and horizontal kinetic energy of the center of mass were nearly in phase, characteristic of a running or bouncing gait. Aerial phases were observed as vertical ground reaction force approached zero at speeds above 1 ms-1. At the highest speeds (1.0-1.5 ms-1 or 50 body lengths per second), P. americana switched to quadrupedal and bipedal running. Stride frequency approached the wing beat frequencies used during flight (27 Hz). High speeds were attained by increasing stride length, whereas stride frequency showed little increase with speed. The mechanical power used to accelerate the center of mass increased curvilinearly with speed. The mass-specific mechanical energy used to move the center of mass a given distance was similar to that measured for animals five orders of magnitude larger in mass, but was only one-hundredth of the metabolic cost.

Analog-Digital Conversion↗

PubMed1990

The study of locomotion by finite state models.

A methodology to derive finite state models of legged locomotion is outlined. Background data for model derivation are joint angle functions and gait diagrams. The method is used to describe the walking of the cat in terms of an abstract automaton. The main features of finite state descriptions of legged locomotion are described. Such models are presenting locomotion invariants of a species in explicit form. It is emphasized that finite state models provide insight into structural features of motor control organization such as decomposition into subsystems, interaction between centralized and decentralized control, and the role of control levels. The finite state model of locomotion can be helpful in suggesting experiments pertinent to the study of motor control and interpretation of experimental results.

Animals↗

PubMed1988

Invariant structure in locomotion.

Biological systems are hypothesized to control behavior with reference to invariants, because this would allow the variable but robust accomplishment of tasks observed in biological behaviors. Invariants for legged locomotion are specified. Combined with observed properties of locomotion, they lead to predictions of forms of control for legged locomotion.

Animals↗

PubMed1994

The activity of interneurons during locomotion in the in vitro necturus spinal cord.

1. Less than two segments of the cervical spinal cord of the mudpuppy (Necturus maculatus) is sufficient to generate a locomotor rhythm with application of N-methyl-D-aspartic acid (NMDA). We have recorded intracellularly from rhythmically active interneurons in these segments and classified them according to their phase of firing within the step cycle and their afferent input. 2. Four classes of interneurons were found: flexor, flexor-->extensor, extensor, and extensor-->flexor. Interneurons that burst during the transition from flexion to extension or vice versa are referred to as "transitional" interneurons and represent the majority (68%) of rhythmically active interneurons studied in the mudpuppy spinal cord. 3. All flexor interneurons received only inhibitory input from cutaneous and dorsal root afferents, whereas the flexor-->extensor interneurons that responded received only excitatory input from dorsal root and cutaneous afferents. All extensor interneurons and all but one extensor-->flexor interneuron received no afferent input from the cutaneous or dorsal root afferents we stimulated. 4. Other interneurons have been classified as "tonic" cells. They fire continuously when the mudpuppy is walking and are silent when the mudpuppy is not walking. These interneurons receive no afferent input from the sources tested and may be responsible for turning locomotion on and off. 5. In conclusion, the presence of many transitional interneurons with specific patterns of afferent input may be required for the phasing of legged locomotion. We believe the in vitro preparation of the mudpuppy spinal cord and forelimb is an excellent model for studying the firing properties of interneurons during legged locomotion.

Afferent Pathways↗

PubMed2005

Blood flow in guinea fowl Numida meleagris as an indicator of energy expenditure by individual muscles during walking and running.

Running and walking are mechanically complex activities. Leg muscles must exert forces to support weight and provide stability, do work to accelerate the limbs and body centre of mass, and absorb work to act as brakes. Current understanding of energy use during legged locomotion has been limited by the lack of measurements of energy use by individual muscles. Our study is based on the correlation between blood flow and aerobic energy expenditure in active skeletal muscle during locomotion. This correlation is strongly supported by the available evidence concerning control of blood flow to active muscle, and the relationship between blood flow and the rate of muscle oxygen consumption. We used injectable microspheres to measure the blood flow to the hind-limb muscles, and other body tissues, in guinea fowl (Numida meleagris) at rest, and across a range of walking and running speeds. Combined with data concerning the various mechanical functions of the leg muscles, this approach has enabled the first direct estimates of the energetic costs of some of these functions. Cardiac output increased from 350 ml min(-1) at rest, to 1700 ml min(-1) at a running speed ( approximately 2.6 m s(-1)) eliciting a of 90% of . The increase in cardiac output was achieved via approximately equal factorial increases in heart rate and stroke volume. Approximately 90% of the increased cardiac output was directed to the active muscles of the hind limbs, without redistribution of blood flow from the viscera. Values of mass-specific blood flow to the ventricles, approximately 15 ml min(-1) g(-1), and one of the hind-limb muscles, approximately 9 ml min(-1) g(-1), were the highest yet recorded for blood flow to active muscle. The patterns of increasing blood flow with increasing speed varied greatly among different muscles. The increases in flow correlated with the likely fibre type distribution of the muscles. Muscles expected to have many high-oxidative fibres preferentially increased flow at low exercise intensities. We estimated substantial energetic costs associated with swinging the limbs, co-contraction to stabilize the knee and work production by the hind-limb muscles. Our data provide a basis for evaluating hypotheses relating the mechanics and energetics of legged locomotion.

Animals↗

PubMed2004

Running on water: Three-dimensional force generation by basilisk lizards.

Water provides a unique challenge for legged locomotion because it readily yields to any applied force. Previous studies have shown that static stability during locomotion is possible only when the center of mass remains within a theoretical region of stability. Running across a highly yielding surface could move the center of mass beyond the edges of the region of stability, potentially leading to tripping or falling. Yet basilisk lizards are proficient water runners, regularly dashing across bodies of water to evade predators. We present here direct measurements of time-averaged force produced by juvenile plumed basilisk lizards (Basiliscus plumifrons) while running across water. By using digital particle image velocimetry to visualize fluid flow induced by foot movement, we show that sufficient support force is generated for a lizard to run across water and that novel strategies are also required to run across a highly yielding surface. Juvenile basilisk lizards produce greatest support and propulsive forces during the first half of the step, when the foot moves primarily vertically downwards into the water; they also produce large transverse reaction forces that change from medial (79% body weight) to lateral (37% body weight) throughout the step. These forces may act to dynamically stabilize the lizards during water running. Our results give insight into the mechanics of how basilisk lizards run across water and, on a broader scale, provide a conceptual basis for how locomotor surface properties can challenge established rules for the mechanics of legged locomotion.

Animals↗

PubMed2005

Neuromusculoskeletal computer modeling and simulation of upright, straight-legged, bipedal locomotion of Australopithecus afarensis (A.L. 288-1).

The skeleton of Australopithecus afarensis (A.L. 288-1, better known as "Lucy") is by far the most complete record of locomotor morphology of early hominids currently available. Even though researchers agree that the postcranial skeleton of Lucy shows morphological features indicative of bipedality, only a few studies have investigated Lucy's bipedal locomotion itself. Lucy's energy expenditure during locomotion has been the topic of much speculation, but has not been investigated, except for several estimates derived from experimental data collected on other animals. To gain further insights into how Lucy may have walked, we generated a full three-dimensional (3D) reconstruction and forward-dynamic simulation of upright bipedal locomotion of this ancient human ancestor. Laser-scanned 3D bone geometries were combined with state-of-the-art neuromusculoskeletal modeling and simulation techniques from computational biomechanics. A detailed full 3D neuromusculoskeletal model was developed that encompassed all major bones, joints (10), and muscles (52) of the lower extremity. A model of muscle force and heat production was used to actuate the musculoskeletal system, and to estimate total energy expenditure during locomotion. Neural activation profiles for each of the 52 muscles that produced a single step of locomotion, while at the same time minimizing the energy consumed per meter traveled, were searched through numerical optimization. The numerical optimization resulted in smooth locomotor kinematics, and the predicted energy expenditure was appropriate for upright bipedal walking in an individual of Lucy's body size.

Animals↗

PubMed2002

Joint stiffness of the ankle and the knee in running.

The spring-mass model is a valid fundament to understand global dynamics of fast legged locomotion under gravity. The underlying concept of elasticity, implying leg stiffness as a crucial parameter, is also found on lower motor control levels, i.e. in muscle-reflex and muscle-tendon systems. Therefore, it seems reasonable that global leg stiffness emerges from local elasticity established by appropriate joint torques. A recently published model of an elastically operating, segmented leg predicts that proper adjustment of joint elasticities to the leg geometry and initial conditions of ground contact provides internal leg stability. Another recent study suggests that in turn the leg segmentation and the initial conditions may be a consequence of metabolic and bone stress constraints. In this study, the theoretical predictions were verified experimentally with respect to initial conditions and elastic joint characteristics in human running. Kinematics and kinetics were measured and the joint torques were estimated by inverse dynamics. Stiffnesses and elastic nonlinearities describing the resulting joint characteristics were extracted from parameter fits. Our results clearly support the theoretical predictions: the knee joint is always stiffer and more extended than the ankle joint. Moreover, the knee torque characteristic on the average shows the higher nonlinearity. According to literature, the leg geometry is a consequence of metabolic and material stress limitations. Adapted to this given geometry, the initial joint angle conditions in fast locomotion are a compromise between metabolic and control effort minimisation. Based on this adaptation, an appropriate joint stiffness ratio between ankle and knee passively safeguards the internal leg stability. The identified joint nonlinearities contribute to the linearisation of the leg spring.

Adult↗

PubMed2005

A collisional model of the energetic cost of support work qualitatively explains leg sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition.

Terrestrial legged locomotion requires repeated support forces to redirect the body's vertical velocity component from down to up. We assume that the redirection is accomplished by impulsive leg forces that cause small-angle glancing collisions of a point-mass model of the animal. We estimate the energetic costs of these collisions by assuming a metabolic cost proportional to positive muscle work involved in generating the impulses. The cost of bipedal running estimated from this collisional model becomes less than that of walking at a Froude number (v2/gl) of about 0.7. Two strategies to reduce locomotion costs associated with the motion redirection are: (1) having legs simulate purely elastic springs, as is observed in human running; and (2) sequencing the leg forces during the redirection phase; examples of this sequencing are the ba-da-dump pattern of a horse gallop and having push-off followed by heel-strike in human walking.

Animals↗

PubMed1991

Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment.

A new principle of sensorimotor control of legged locomotion in an unpredictable environment is proposed on the basis of neurophysiological knowledge and a theory of nonlinear dynamics. Stable and flexible locomotion is realized as a global limit cycle generated by a global entrainment between the rhythmic activities of a nervous system composed of coupled neural oscillators and the rhythmic movements of a musculo-skeletal system including interaction with its environment. Coordinated movements are generated not by slaving to an explicit representation of the precise trajectories of the movement of each part but by dynamic interactions among the nervous system, the musculo-skeletal system and the environment. The performance of a bipedal model based on the above principle was investigated by computer simulation. Walking movements stable to mechanical perturbations and to environmental changes were obtained. Moreover, the model generated not only the walking movement but also the running movement by changing a single parameter nonspecific to the movement. The transitions between the gait patterns occurred with hysteresis.

Animals↗

PubMed2000

Mechanical models for insect locomotion: dynamics and stability in the horizontal plane I. Theory.

We study the dynamics and stability of legged locomotion in the horizontal plane. Motivated by experimental studies of insects, we develop two- and three-degree-of freedom rigid body models with pairs of 'virtual' elastic legs in intermittent contact with the ground. We focus on conservative compliant-legged models, but we also consider prescribed forces, prescribed leg displacements, and combined strategies. The resulting mechanical systems exhibit periodic gaits whose stability characteristics are due to intermittent foot contact, and are largely determined by geometrical criteria. Most strikingly, we show that mechanics alone can confer asymptotic stability in heading and body orientation. In a companion paper, we apply our results to rapidly running cockroaches.

Algorithms↗