Behaviour-based modelling of hexapod locomotion: linking biology and technical application

Walking in insects and most six-legged robots requires simultaneous control of up to 18 joints. Moreover, the number of joints that are mechanically coupled via body and ground varies from one moment to the next, and external conditions such as friction, compliance and slope of the substrate are often unpredictable. Thus, walking behaviour requires adaptive, context-dependent control of many degrees of freedom. As a consequence, modelling legged locomotion addresses many aspects of any motor behaviour in general. Based on results from behavioural experiments on arthropods, we describe a kinematic model of hexapod walking: the distributed artificial neural network controller walknet. Conceptually, the model addresses three basic problems in legged locomotion. (I) First, coordination of several legs requires coupling between the step cycles of adjacent legs, optimising synergistic propulsion, but ensuring stability through flexible adjustment to external disturbances. A set of behaviourally derived leg coordination rules can account for decentralised generation of different gaits, and allows stable walking of the insect model as well as of a number of legged robots. (II) Second, a wide range of different leg movements must be possible, e.g. to search for foothold, grasp for objects or groom the body surface. We present a simple neural network controller that can simulate targeted swing trajectories, obstacle avoidance reflexes and cyclic searching-movements. (III) Third, control of mechanically coupled joints of the legs in stance is achieved by exploiting the physical interactions between body, legs and substrate. A local positive displacement feedback, acting on individual leg joints, transforms passive displacement of a joint into active movement, generating synergistic assistance reflexes in all mechanically coupled joints.     

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.     

Stance leg control: variation of leg parameters supports stable hopping

The spring-loaded inverted pendulum describes the planar center-of-mass dynamics of legged locomotion. This model features linear springs with constant parameters as legs. In biological systems, however, spring-like properties of limbs can change over time. Therefore, in this study, it is asked how variation of spring parameters during ground contact would affect the dynamics of the spring-mass model. Neglecting damping initially, it is found that decreasing stiffness and increasing rest length of the leg during a stance phase are required for orbitally stable hopping. With damping, stable hopping is found for a larger region of rest-length rates and stiffness rates. Here, also increasing stiffness and decreasing rest length can result in stable hopping. Within the predicted range of leg parameter variations for stable hopping, there is no need for precise parameter tuning. Since hopping gaits form a subset of the running gaits (with vanishing horizontal velocity), these results may help to improve leg design in robots and prostheses.     

The type of leg lost affects habitat use but not survival in a non‐regenerating arthropod

Finding shelter and surviving encounters with predators are pervasive challenges for animals. These challenges may be exacerbated after individuals experience bodily damage. Certain forms of damage arise voluntarily in animals; for instance, some taxa release appendages (tails, legs, or other body parts) as a defensive strategy (“autotomy”). This behavior, however, may pose long‐term negative consequences for habitat use and survival. Additionally, these putative consequences are expected to vary according to the function of the lost body part. We tested the effects of losing different functional leg types (locomotor or sensory) on future habitat use and survival in a Neotropical species of Prionostemma harvestmen (Arachnida: Opiliones) that undergo frequent autotomy but do not regrow limbs. Daytime surveys revealed that both eight‐legged harvestmen and harvestmen missing legs roosted in similar frequencies across habitats (tree bark, mossy tree, or fern), and perched at similar heights. Mark–recapture data showed that harvestmen that lost sensory legs roosted in tree bark less frequently, but on mossy trees more frequently. On the contrary, we did not observe changes in habitat use for eight‐legged animals or animals that lost locomotor legs. This change might be related to sensory exploration and navigation. Lastly, we found that recapture rates across substrates were not affected by the type of legs lost, suggesting that leg loss does not impact survival. This potential lack of effect might play a role in why a defensive strategy like autotomy is so prevalent in harvestmen despite the lack of regeneration.     

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.     

Stick insects walking on a wheel: Perturbations induced by obstruction of leg protraction

Summary Stick insects (Carausius morosus) walking on a wheel were perturbed by restricting the forward protraction of individual legs. A barrier placed before a single middle or rear leg prevented that leg from reaching its normal protraction endpoint but allowed it unimpeded retraction. Upon striking the barrier, the protracting leg attempted to get past it and thereby prolonged protraction. This prolongation increased with the extent to which the obstruction infringed upon the leg's normal step range. Barriers placed near the midpoint of this range elicited large perturbations: the blocked leg often continued its protraction throughout many step cycles of the other legs (Fig. 1 E, F). For the most part walking was irregular and smooth forward progression was disrupted. Nevertheless, the infrequent steps by the affected leg usually were coordinated with those of the adjacent ipsilateral legs.More rostral barrier positions elicited smaller perturbations: the blocked leg usually made one step in each step cycle of the other legs (Fig. 1 B, C, D, G). Measurements for these regular step sequences showed quantitatively that protraction duration increased in proportion to the severity of the infringement on normal leg movement (Figs. 3, 4). The fraction of the step period occupied by protraction increased from ca. 10% for normal walking to ca. 50% for caudal barrier positions. This proportionality is interpreted to show the importance of spatial components of the walking program.When one leg was obstructed, its extended protraction influenced the stepping of the three adjacent legs as follows. First, the ipsilateral rostral leg showed the largest change: its protraction onset was regularly delayed for the duration of the extended protraction (Figs. 4, 7, 8), demonstrating a strong, centrally mediated inhibition. The presence of a further delay of up to 100 to 140 ms suggests that peripheral input from the protracting leg may be important for releasing this inhibition. Second, steps by an adjacent caudal leg were not measurably affected. However, the method may not have sufficed to reveal such effects because during regular walking middle leg protractions rarely lasted long enough to conflict with subsequent steps by the ipsilateral rear leg. Third, contralateral effects differed between middle and rear leg obstructions. If the obstructed leg was a middle leg, its extended protraction had little effect upon stepping by the contralateral middle leg: the latter leg frequently protracted while the blocked leg continued its protraction and there was no consistent change in the phase relation of these two legs (Table 1). In contrast, if the obstructed leg was a rear leg, protractions by the contralateral rear leg tended to be delayed (Table 1).     

The contralateral coordination of walking legs in the crayfish Astacus leptodactylus

The coupling mechanisms which coordinate the movement of ipsilateral walking legs in the crayfish have been described in earlier investigations. Concerning the coupling between contralateral legs it was only known that these influences are weaker than those acting between ipsilateral legs. The nature of these coupling mechanisms between contralateral legs of the crayfish are investigated here by running left and right legs on separate walking belts at different speeds. The results show that coordination is performed by a phase-dependent shift of the anterior extreme position of the influenced leg. This backward shift leads to a shortening of both the return stroke and the following power stroke. As the coupling influence is only weak, several steps might be necessary to retain normal coordination after a disturbance. This corresponds to v. Holst's relative coordination. The influences act in both directions, from left to right and vice versa. However, one side may be more or less dominant. A gradient was found in the way that anterior leg pairs show less strong coordination than posterior legs. In some cases the coupling between diagonally neighbouring legs was found to be stronger than between contralateral legs of the same segment. The interpretation of this result is still open.     

Special section on biomimetics of movement

Movement in biology is an essential aspect of survival for many organisms, animals and plants. Implementing movement efficiently to meet specific needs is a key attribute of natural living systems, and can provide ideas for man-made developments. If we had to find a subtitle able to essentially convey the aim of this special section, it could read as follows: 'taking inspiration from nature for new materials, actuators, structures and controls for systems that move'. Our world is characterized by a huge variety of technical, engineering systems that move. They surround us in countless products that integrate actuators for different kinds of purposes. Basically, any kind of mechatronic system, such as those used for consumer products, machines, vehicles, industrial systems, robots, etc, is based on one or more devices that move, according to different implementations and motion ranges, often in response to external and internal stimuli. Despite this, technical solutions to develop systems that move do not evolve very quickly as they rely on traditional and well consolidated actuation technologies, which are implemented according to known architectures and with established materials. This fact limits our capability to overcome challenges related to the needs continuously raised by new fields of application, either at small or at large scales. Biomimetics-based approaches may provide innovative thinking and technologies in the field, taking inspiration from nature for smart and effective solutions. In an effort to disseminate current advances in this field, this special section collects some papers that cover different topics. A brief synopsis of the content of each contribution is presented below. The first paper, by Lienhard et al [1], deals with bioinspiration for the realization of structural parts in systems that passively move. It presents a bioinspired hingeless flapping mechanism, considered as a solution to the kinematics of deployable systems for architectural structures. The approach relies on structural elasticity to replace the need for local hinges. To this end, the authors have used fibre-reinforced polymers combining high tensile strength with low bending stiffness. The solution favours lower structural complexity as well as higher design versatility. Bioinspiration from the elastic kinetics of plants is a central pillar of the paper, which highlights the interrelation of form, actuation and kinematics in those natural systems. The second paper, by Nakata et al [2], deals with bioinspired systems that actively move, and, more specifically, fly. The paper is about the aerodynamics of a bio-inspired flexible flapping-wing micro air vehicle conceived to fly in a Reynolds number regime used by most natural flyers, including insects, bats and birds. The paper presents a study of the flexible wing aerodynamics of the flapping vehicle by combining an in-house computational fluid dynamic model with wind tunnel experiments. In particular, the developed model is shown to be able to predict unsteady aerodynamics in terms of vortex and wake structures and their relationship with aerodynamic force generation. Simulations are validated by wind tunnel experiments, confirming the effectiveness of the adopted design solutions, as well as the importance of wing flexibility in designing small flapping-wing vehicles. The third paper, by Annunziata et al [3], deals with bioinspired control strategies for systems that move. In particular, the paper describes approaches to increase the stiffness variability in multi-muscle driven joints. Different strategies for simultaneous control of torque and stiffness in a hinge joint actuated by two antagonistic muscle pairs are presented. The proposed strategies combine torque and stiffness control by co-activation with approaches based on activation overflow and inverse modelling. Extensive simulations are performed and described to assess the control efficacy. In the fourth paper, Merker et al [4] present a study on stable walking with asymmetric legs. The authors are concerned with the need to clarify to what extent differences in the leg function of contralateral limbs can be tolerated during walking or running. A bipedal spring-mass model simulating walking with compliant legs is used to show that even remarkable differences between contralateral legs can not only be tolerated, but may also introduce advantages to the robustness of the system dynamics. This study might contribute to shedding light on the stability of asymmetric leg walking, including the potential benefits of asymmetry, with possible implications for design of prosthetic or orthotic systems. The last two papers of this special section deal with active bioinspired systems driven by new actuators made of smart materials. In particular, the paper authored by Rossi et al [5] presents an underwater fish-like robot based on bending structures driven by shape memory alloys. These kinds of actuators are used to bend the backbone of the fish, which in turn causes a change in the curvature of the fish body. The paper describes the mechanisms by which standard swimming patterns can be reproduced with the proposed design, and show characterizations in terms of the actuation speed and position accuracy of prototype systems. The last paper, by Carpi et al [6], presents an overview on ionic- and electronic-type electromechanically active polymer actuators as artificial muscles for bioinspired applications. The electrical responsiveness and numerous functional and structural properties that these materials and actuators have in common with natural muscles are shown to be the key motivation by which they are studied as artificial muscles for a huge variety of possible uses. The authors describe the fundamental aspects of relevant technologies and emphasize how after several years of basic research, electromechanically active polymer actuators are today facing their important initial transition from academia into commercialization. In conclusion, we hope that the selection of papers in this special section might help to provide readers with a balanced overview, through examples on the relevant fundamental aspects, materials, actuators, structures, controls and on their effective integration, in order to develop approaches which will be successful in 'taking inspiration from nature for systems that move'. References [1] Lienhard J, Schleicher S, Poppinga S, Masselter T, Milwich M, Speck T and Knippers J 2011 Flectofin: a hingeless flapping mechanism inspired by nature Bioinsp. Biomim. 6 045001 [2] Nakata T, Liu H, Tanaka Y, Nishihashi N, Wang X and Sato A 2011 Aerodynamics of a bio-inspired flexible flapping-wing micro air vehicle Bioinsp. Biomim. 6 045002 [3] Annunziata S, Paskarbeit J and Schneider A 2011 Novel bioinspired control approaches to increase the stiffness variability in multi-muscle driven joints Bioinsp. Biomim. 6 045003 [4] Merker A, Rummel J and Seyfarth A 2011 Stable walking with asymmetric legs Bioinsp. Biomim. 6 045004 [5] Rossi C, Colorado J, Coral W and Barrientos A 2011 Bending continuous structures with SMAs: a novel robotic fish design Bioinsp. Biomim. 6 045005 [6] Carpi F, Kornbluh R, Sommer-Larsen P and Alici G 2011 Electroactive polymer actuators as artificial muscles: are they ready for bioinspired applications? Bioinsp. Biomim. 6 045006.     

Warum Spinnen (nur) acht Beine haben

Why spiders have (only) eight legs The difference in leg number between insects and spiders serves as a model for the study of the genetics and evolution of bodyplan differences. In this context the Hox genes are important factors: especially the Hox gene Antennapedia has apparently changed its function and interactions with so far unidentified factors to result in the eight‐legged spider bodyplan.     

Intersegmental transfer of sensory signals in the stick insect leg muscle control system

Intersegmental coordination during locomotion in legged animals arises from mechanical couplings and the exchange of neuronal information between legs. Here, the information flow from a single leg sense organ of the stick insect Cuniculina impigra onto motoneurons and interneurons of other legs was investigated. The femoral chordotonal organ (fCO) of the right middle leg, which measures posture and movement of the femur-tibia joint, was stimulated, and the responses of the tibial motoneuron pools of the other legs were recorded. In resting animals, fCO signals did not affect motoneuronal activity in neighboring legs. When the locomotor system was activated and antagonistic motoneurons were bursting in alternation, fCO stimuli facilitated transitions from flexor to extensor activity and vice versa in the contralateral leg. Following pharmacological treatment with picrotoxin, a blocker of GABA-ergic inhibition, the tibial motoneurons of all legs showed specific responses to signals from the middle leg fCO. For the contralateral middle leg we show that fCO signals encoding velocity and position of the tibia were processed by those identified local premotor nonspiking interneurons known to contribute to posture and movement control during standing and voluntary leg movements. Interneurons received both excitatory and inhibitory inputs, so that the response of some interneurons supported the motoneuronal output, while others opposed it. Our results demonstrate that sensory information from the fCO specifically affects the motoneuronal activity of other legs and that the layer of premotor nonspiking interneurons is a site of interaction between local proprioceptive sensory signals and proprioceptive signals from other legs.     

Leg skin temperature and thigh sweat output: possible central influence of local thermal inputs

To demonstrate whether or not the skin temperature of one lower limb can have an influence on the sweat rate of the contralateral leg, the two legs of five subjects were exposed inside leg-chambers to specific local thermal conditions while sweat rates were measured on both limbs. Three experiments (C I,II,III) of 3 h were carried out: each included two phases A and B. During A, the right leg was not ventilated, while the left leg was (C I) or was not (C II–III) ventilated. During B, the legs were either removed from the leg-chambers (C I) or ventilated inside the chambers at differently controlled levels of leg skin temperature (C II–III). At all times, sweat capsules on both legs measured the sweat rates of local areas of the thigh which were also temperature-controlled. Results showed that, at constant or slightly increased mean skin and core temperatures, the sweat output of one leg could be decreased at constant (C II) or higher local skin temperature (C III) probably due to a decrease in the temperature of the opposite leg. This finding is interpreted as a consequence of a central negative effect, originating from contralateral thermal inputs.     

Righting kinematics in beetles (Insecta: Coleoptera)

Twenty modes of stereotyped righting motions were observed in 116 representative species of coleoptera. Methods included cine and stereocine recording with further frame by frame analysis, stereogrammetry, inverse kinematic reconstruction of joint angles, stroboscopic photography, recording of electromyograms, 3D measurements of the articulations, etc. The basic mode consists of a search phase, ending up with grasping the substrate, and a righting, overturning phase. Leg coordination within the search cycle differs from the walking cycle with respect to phasing of certain muscle groups. Search movements of all legs appear chaotic, but the tendency to move in antiphase is still present in adjacent ipsilateral and contralateral leg pairs. The system of leg coordination might be split: legs of one side might search, while contralateral legs walk, or fore and middle legs walk while hind legs search. Elaborated types of righting include somersaults with the aid of contralateral or diagonal legs, pitch on elytra, jumps with previous energy storage with the aid of unbending between thoracic segments (well-known for Elateridae), or quick folding of elytra (originally described in Histeridae). Righting in beetles is compared with righting modes known in locusts and cockroaches. Search in a righting beetle is directed dorsad, while a walking insect searches for the ground downwards. Main righting modes were schematized for possible application to robotics.     

Evolution of the arthropod neuromuscular system. 1. Arrangement of muscles and innervation in the walking legs of a scorpion: Vaejovis spinigerus (Wood, 1863) Vaejovidae, Scorpiones, Arachnida

(1) The musculature of the walking legs is analysed with regard to both morphology and function in the scorpion, Vaejovis spinigerus (Wood, 1863) (Vaejovidae, Scorpiones, Arachnida), and selected other species. Conspicuous features are multipartite muscles, muscles spanning two joints, and partial lack of antagonistic muscles. The muscle arrangement is compared to that in the walking limbs of other Arthropoda and possible phylogenetic implications are discussed. (2). Histochemical characterisation of selected leg muscles indicates that these are composed of layers of slow, intermediate and fast muscle fibres. Anti-GABA immunohistochemistry shows that mainly the intermediate fibres receive innervation from putative inhibitory motoneurons. (3). Intracellular recording from muscle fibres reveals both excitatory and inhibitory muscle innervation. Individual muscle fibres may receive input from more than one inhibitory motoneuron, as indicated by different IPSP amplitudes. (4). The motoneuron supply of the leg muscles is analysed by retrograde fills of motor nerves. The general arrangement of leg motoneurons in the central nervous system and motoneuron anatomy conforms to the situation in pterygote insects and decapod crustaceans. For example, there are an anterior and a posterior group of leg motoneurons in each hemineuromere, and two contralateral somata near the ganglion midline. Between 12 and 20 motoneurons are found to supply each muscle. Most motoneuron cell bodies supplying a given muscle are arranged in a single cluster with a specific location.     

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.     

Skeletal adaptations for forwards and sideways walking in three species of decapod crustaceans

Crustaceans have been successfully employed to study legged locomotion for decades. Most studies have focused on either forwards-walking macrurans, or sideways-walking brachyurans. Libinia emarginata is a Majoid crab (Brachyura) and as such belongs to the earliest group to have evolved the crab form from homoloid ancestors. Unlike most brachyurans, Libinia walks forwards 80% of the time. We employed standard anatomical techniques and motion analysis to compare the skeleton, stance, and the range of motion of the legs of Libinia to the sideways-walking green shore crab (Carcinus maenas), and to the forwards-walking crayfish (Procambarus clarkii). We found animals tended to have greater ranges of motion for joints articulating in the preferred direction of locomotion. Leg segments proximal to such joints were comparatively longer. Thorax elongation, leg length and placement at rest also reflected walking preference. Comparative studies of walking in Libinia and other brachyurans may shed light on the neuroethology of legged locomotion, and on the anatomical and physiological changes necessary for sideways-walking in crustaceans.     

The control of walking movements in the leg of the rock lobster

1. Experiments with rock lobsters walking on a treadmill were undertaken to obtain information upon the system controlling the movement of the legs. Results show that the position of the leg is an important parameter affecting the cyclic movement of the walking leg. Stepping can be interrupted when the geometrical conditions for terminating either a return stroke or a power stroke are not fullfilled. 2. The mean value of anterior and posterior extreme positions (AEP and PEP respectively) of the walking legs do not depend on the walking speed (Fig. 1). 3. When one leg is isolated from the other walking legs by placing it on a platform the AEPs and PEPs of the other legs show a broader distribution compared to controls (Figs. 2 and 3). 4. Force measurements (Fig. 4) are in agreement with the hypothesis that the movement of the leg is controlled by a position servomechanism. 5. When one leg stands on a stationary force transducer this leg develops forces which oscillate with the step rhythm of the other legs (Fig. 5). 6. A posteriorly directed influence is found, by which the return stroke of a leg can be started when the anterior leg performs a backward directed movement. 7. Results are compared with those obtained from stick insects. The systems controlling the movement of the individual leg are similar in both, lobster and stick insect but the influences between the legs seem to be considerably different.     

Side-to-side comparisons of bone mineral density in upper and lower limbs of collegiate athletes

This cross-sectional study investigated the effects of participation in various sports on side-to-side (contralateral) differences in bone mineral density (BMD) of the upper and lower limbs. The BMD of the arms and legs was measured using dual energy X-ray absorptiometry. The subjects were 184 collegiate athletes, both men and women, who participated in NCAA Division I-A baseball, basketball, football, golf, soccer, tennis, cross-country, indoor/outdoor track, and volleyball. Results revealed greater BMD of the right arms compared with the left arms for all teams, with the most pronounced differences observed in men's and women's tennis and men's baseball. Differences in the lower limbs were less common. No significant differences in lower limb BMD were found in the women. In men, differences in lower limb BMD were found in the football and tennis teams, with the nondominant leg having greater bone mass. Recognition of contralateral differences in bone density may be of particular interest to strength and conditioning professionals as they consider the need to include bilateral and unilateral training programs in an effort to maximize performance and minimize stress-related injuries.     

A model of leg coordination in the stick insect,Carausius morosus

Mechanisms dependent upon leg position coordinate the alternate stepping of adjacent ipsilateral and contralateral legs in the stick insect. In this insect, swing duration and step amplitude are independent of walking speed. A simple geometrical model of the leg controller is used here to test different mechanisms for compatibility with these two invariant features. Leg position is the state variable of a relaxation oscillator and position thresholds determine the transitions between swing and stance. The coordination mechanisms alter these thresholds. The position-dependent mechanisms considered differ either in the form or the speed-dependence of the function relating the shift in the posterior threshold of the receiving leg to the position of the sending leg. The results identify parameter combinations leading to alternate stepping with symmetric or asymmetric phase distributions, to shifts in the posterior extreme position as a function of speed, to double stepping or to in-phase stepping. An optimal position-dependent excitatory mechanism is described. Finally the consequences of adding either inhibitory influences or time-dependent excitatory influences are analyzed.     

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.     

Zur Beeinflussung der Bewegungsweise eines Beines von Carausius morosus durch Amputation anderer Beine

Amputation of a leg alters the amplitude of the adjacent ipsilateral legs during walking: Amputation of a middle leg encreases the amplitude of the foreleg especially by changing the rear extreme position. Amputation of a foreleg reduces the amplitude of the middle leg especially by changing the front extreme position. There is no significant influence observable on contralateral legs.