Kinematic invariants during cyclical arm movements

It has been observed that the motion of the arm end-point (the hand, fingertip or the tip of a pen) is characterized by a number of regularities (kinematic invariants). Trajectory is usually straight, and the velocity profile has a bell shape during point-to-point movements. During drawing movements, a two-thirds power law predicts the dependence of the end-point velocity on the trajectory curvature. Although various principles of movement organization have been discussed as possible origins of these kinematic invariants, the nature of these movement trajectory characteristics remains an open question. A kinematic model of cyclical arm movements derived in the present study analytically demonstrates that all three kinematic invariants can be predicted from a two-joint approximation of the kinematic structure of the arm and from sinusoidal joint motions. With this approach, explicit expressions for two kinematic invariants, the two-thirds power law during drawing movements and the velocity profile during point-to-point movements are obtained as functions of arm segment lengths and joint motion parameters. Additionally, less recognized kinematic invariants are also derived from the model. The obtained analytical expressions are further validated with experimental data. The high accuracy of the predictions confirms practical utility of the model, showing that the model is relevant to human performance over a wide range of movements. The results create a basis for the consolidation of various existing interpretations of kinematic invariants. In particular, optimal control is discussed as a plausible source of invariant characteristics of joint motions and movement trajectories.     

Biomechanics and kinematics of limb-based locomotion in lizards: review, synthesis and prospectus.

The sprawling pattern of locomotion in lizards is kinematically intriguing and is underpinned by a distinctive pattern of appendicular morphology. The statics of the sprawling posture dictate fundamental design principles, and these place constraints on the three-dimensional kinematics of the limbs and body axis as locomotion is effected. The fore and hind limbs accommodate these constraints and dictates in fundamentally similar, but positionally different ways, resulting in different kinematic profiles for these two appendages. Recent kinematic investigations have helped to clarify earlier generalizations about lizard locomotion and have revealed that kinematic patterns are more variable than was previously supposed. Such analyses, and attendant detailed studies of the anatomy of the locomotor system, promise a new synthesis and enhanced understanding of evolutionary patterns of locomotion of lizards and adjustment to various locomotor substrata and modes of progression.     

The importance of the evolutionary heritage of locomotion on flat ground in small mammals for the development of arboreality

The earliest representatives of the mammalian stem line were small. Recent small mammals preserving their morphology possess rather similar kinematic and dynamic locomotor patterns, even if they are not closely related. For a small animal, the mechanics of locomotion on a large branch is comparable to locomotion on flat ground. Combining these informations, it seems sensible to start a discussion on the origins of arboreality with a detailed analysis of the locomotion of small mammals on flat ground. For this purpose, the kinematics of twelve species of mammals were observed using cineradiography, a "general limb" of small mammals was derived as a principle, and its interactions with the trunk were analyzed. These data form the basis for a theoretical upscaling of the motion patterns in arboreal animals, revealing that the transfer of torques between animal and branch becomes unavoidable, thus making the use of prehensile hands advantageous, which by their tendency of distal concentration of muscle masses force the need to change the basic kinematic patterns.     

Determination of toe-off event time during treadmill locomotion using kinematic data

Researchers collecting gait kinematic data during treadmill locomotion are often interested in determining the times of toe off and heel strike for each stride. In the absence of additional hardware, only position data collected with motion-capture equipment may be available. Others have published methods for using kinematic data for detecting overground gait events. However, during treadmill locomotion, especially running, overground methods may not possess sufficient accuracy. The purpose of this paper is to describe a method for using kinematic data to determine the time of toe off during treadmill locomotion. Ten subjects walked and ran on a treadmill while a motion-capture system collected positional data from heel and toe markers. The treadmill was equipped with force platforms that allowed an accurate determination of foot-ground contact. The time of toe off was determined using the vertical component of the toe marker, and this method was found to have greater accuracy for event detection than other published methods. Researchers can use the described method to determine times of heel strike and toe off during treadmill locomotion using only kinematic data.     

Kinematic of animal locomotion under various gravitational fields.

A simple kinematic analysis of human locomotion under various gravitational fields is presented and a desirable way of locomotion is proposed. A comment on flight behaviors of insects in nongravity fields is also presented.     

A mechanical link model of two-toed sloths: no pendular mechanics during suspensory locomotion

Sloths are morphologically specialized in suspensory quadrupedal locomotion and posture. During steady-state locomotion they utilize a trot-like footfall sequence. Contrasting the growing amount of published accounts of the functional morphology and kinematics of sloth locomotion, no study concerned with the dynamics of their quadrupedal suspensory locomotion has been conducted. Brachiating primates have been shown to travel at low mechanical costs using pendular mechanics, but this is associated with considerable dynamic forces exerted onto the support. To test whether sloth locomotion can be described by simple connected pendulum mechanics, we analyzed the dynamics of sloth locomotion with use of a mechanical segment link model. The model integrates the body segment parameters and is driven by kinematic data with both segment parameters and kinematic data obtained from the same sloth individual. No simple pendular mechanics were present. We then used the model to carry out an inverse dynamic analysis. The analysis allowed us to estimate net limb joint torques and substrate reaction forces during the contact phases. Predominant flexing limb joint torque profiles in the shoulder, elbow, hip, and knee are in stark contrast to published dominant extensor torques in the limb joints of pronograde quadrupedal mammals. This dissimilarity likely reflects the inverse orientation of the sloth towards the gravity vector. Nevertheless, scapular pivot and shoulder seem to provide the strongest torque for progression as expected based on unchanged basic kinematic pattern previously described. Our model predicts that sloths actively reduce the dynamical forces and moments that are transmitted onto the support. We conclude that these findings reflect the need to reduce the risk of breaking supports because in this case sloths would likely be unable to react quickly enough to prevent potentially lethal falls. To achieve this, sloths seem to avoid the dynamical consequences of effective pendular mechanics.     

Locomotion Generation and Motion Library Design for an Anguilliform Robotic Fish

In this paper, modeling, locomotion generation, motion library design and path planning for a real prototype of an Anguilliform robotic fish are presented. The robotic fish consists of four links and three joints, and the driving forces are the torques applied to the joints. Considering kinematic constraints and hydrodynamic forces, Lagrangian formulation is used to obtain the dynamic model of the fish. Using this model, three major locomotion patterns of Anguilliform fish, including forward locomotion, backward locomotion and turning locomotion are investigated. It is found that the fish exhibits different locomotion patterns by giving different reference joint angles, such as adding reversed phase difference, or adding deflections to the original reference angles. The results are validated by both simulations and experiments. Furthermore, the relations among the speed of the fish, angular frequency, undulation amplitude, phase difference, as well as the relationship between the turning radius and deflection angle are investigated. These relations provide an elaborated motion library that can be used for motion planning of the robotic fish.     

Kinematic Analysis and Experimental Verification on the Locomotion of Gecko

This paper presents a kinematic analysis of the locomotion of a gecko,and experimental verification of the kinematicmodel.Kinematic analysis is important for parameter design,dynamic analysis,and optimization in biomimetic robot research.The proposed kinematic analysis can simulate,without iteration,the locomotion of gecko satisfying the constraint conditionsthat maintain the position of the contacted feet on the surface.So the method has an advantage for analyzing the climbing motionof the quadruped mechanism in a real time application.The kinematic model of a gecko consists of four legs based on 7-degreesof freedom spherical-revolute-spherical joints and two revolute joints in the waist.The motion of the kinematic model issimulated based on measurement data of each joint.The motion of the kinematic model simulates the investigated real gecko’smotion by using the experimental results.The analysis solves the forward kinematics by considering the model as a combinationof closed and open serial mechanisms under the condition that maintains the contact positions of the attached feet on the ground.The motions of each joint are validated by comparing with the experimental results.In addition to the measured gait,three othergaits are simulated based on the kinematic model.The maximum strides of each gait are calculated by workspace analysis.Theresult can be used in biomimetic robot design and motion planning.     

Artificial neural network model for the generation of muscle activation patterns for human locomotion.

Skilled locomotor behaviour requires information from various levels within the central nervous system (CNS). Mathematical models have permitted researchers to simulate various mechanisms in order to understand the organization of the locomotor control system. While it is difficult to adequately characterize the numerous inputs to the locomotor control system, an alternative strategy may be to use a kinematic movement plan to represent the complex inputs to the locomotor control system based on the possibility that the CNS may plan movements at a kinematic level. We propose the use of artificial neural network (ANN) models to represent the transformation of a kinematic plan into the necessary motor patterns. Essentially, kinematic representation of the actual limb movement was used as the input to an ANN model which generated the EMG activity of 8 muscles of the lower limb and trunk. Data from a wide variety of gait conditions was necessary to develop a robust model that could accommodate various environmental conditions encountered during everyday activity. A total of 120 walking strides representing normal walking and ten conditions where the normal gait was modified in terms of cadence, stride length, stance width or required foot clearance. The final network was assessed on its ability to predict the EMG activity on individual walking trials as well as its ability to represent the general activation pattern of a particular gait condition. The predicted EMG patterns closely matched those recorded experimentally, exhibiting the appropriate magnitude and temporal phasing required for each modification. Only 2 of the 96 muscle/gait conditions had RMS errors above 0.10, only 5 muscle/gait conditions exhibited correlations below 0.80 (most were above 0.90) and only 25 muscle/gait conditions deviated outside the normal range of muscle activity for more than 25% of the gait cycle. These results indicate the ability of single network ANNs to represent the transformation between a kinematic movement plan and the necessary muscle activations for normal steady state locomotion but they were also able to generate muscle activation patterns for conditions requiring changes in walking speed, foot placement and foot clearance. The abilities of this type of network have implications towards both the fundamental understanding of the control of locomotion and practical realizations of artificial control systems for use in rehabilitation medicine.     

Octopuses use a human-like strategy to control precise point-to-point arm movements

One of the key problems in motor control is mastering or reducing the number of degrees of freedom (DOFs) through coordination. This problem is especially prominent with hyper-redundant limbs such as the extremely flexible arm of the octopus. Several strategies for simplifying these control problems have been suggested for human point-to-point arm movements. Despite the evolutionary gap and morphological differences, humans and octopuses evolved similar strategies when fetching food to the mouth. To achieve this precise point-to-point-task, octopus arms generate a quasi-articulated structure based on three dynamic joints. A rotational movement around these joints brings the object to the mouth . Here, we describe a peripheral neural mechanism-two waves of muscle activation propagate toward each other, and their collision point sets the medial-joint location. This is a remarkably simple mechanism for adjusting the length of the segments according to where the object is grasped. Furthermore, similar to certain human arm movements, kinematic invariants were observed at the joint level rather than at the end-effector level, suggesting intrinsic control coordination. The evolutionary convergence to similar geometrical and kinematic features suggests that a kinematically constrained articulated limb controlled at the level of joint space is the optimal solution for precise point-to-point movements.     

Locomotion studies as an aid in clinical assessment of childhood gait.

A clinical locomotion laboratory has been developed to provide quantitative information in the management of gait disorders. The biomedical engineering development of this system identified two major clinical constraints: (a) the need for instrumentation that would not alter the natural gait of the patient and (b) the need for data-processing techniques that would permit analysis and correlation of the large volume of electromyographic (EMg) and kinematic information. The net result has been a unit that incorporates a multichannel telemetry system to capture the EMG and foot-switch information and a television computer system to handle the kinematic information. Gait studies on children with hemiparesis, muscular dystrophy and cerebral palsy have yielded quantitative EMG and kinematic information on the pathomechanics of ambulation in these disorders. Because the information obtained is quantitative, an accurate measure of improvement (or lack of it) after treatment can be documented. Therefore, the locomotion laboratory may have an important role in the preoperative and postoperative evaluation of children whose abnormal gait may require surgical corrective procedures or rehabilitative treatment including the use of prostheses or orthoses.     

Kinematic parameters of terrestrial locomotion in cursorial (ratites), swimming (ducks), and striding birds (quail and guinea fowl).

The importance of size, functional features and morphological features in adaptation for walking in birds were studied. The time and space kinematic parameters of locomotion were compared in two running birds, the ratites (rhea, kiwi, Paleognatiforms), in two swimming birds, (ducks) and two striding birds, (quail and Guinea fowl). The results showed that in the two phases, stance and swing, the time and space parameters worked in opposite ways: the duration of the swing was constant, but its length increased with speed. In contrast, the duration of the stance was correlated to speed, while its length was not (except in ducks). In all the birds, a higher speed was achieved by a decrease of the stance duration, and an increase of the swing length. The kinematic parameters were not used in the same way in all species: There is a size effect and large birds increase their speed mainly by increasing the frequency of their movements and the small species increase mainly their amplitude. Nevertheless, it is not the main factor and morphology, such as swimming adaptation features of the ducks, and behaviour, are important because they modify the mechanical constraints and influence the kinematics parameters.     

Gait Study and Pattern Generation of a Starfish-Like Soft Robot with Flexible Rays Actuated by SMAs

This paper presents the design and development of a starfish-like soft robot with flexible rays and the implementation of multi-gait locomotion using Shape Memory Alloy （SMA） actuators. The design principle was inspired by the starfish, which possesses a remarkable symmetrical structure and soft internal skeleton. A soft robot body was constructed by using 3D printing technology. A kinematic model of the SMA spring was built and developed for motion control according to displacement and force requirements. The locomotion inspired from starfish was applied to the implementation of the multi-ray robot through the flexible actuation induced multi-gait movements in various environments. By virtue of the proposed ray control patterns in gait transition, the soft robot was able to cross over an obstacle approximately twice of its body height. Results also showed that the speed of the soft robot was 6.5 times faster on sand than on a clammy rough terrain. These experiments demonstrated that the bionic soft robot with flexible rays actuated by SMAs and multi-gait locomotion in proposed patterns can perform successfully and smoothly in various terrains.     

Bridging “Romer’s Gap”: Limb Mechanics of an Extant Belly-Dragging Lizard Inform Debate on Tetrapod Locomotion During the Early Carboniferous

Devonian stem tetrapods are thought to have used ‘crutching’ on land, a belly-dragging form of synchronous forelimb action-powered locomotion. During the Early Carboniferous, early tetrapods underwent rapid radiation, and the terrestrial locomotion of crown-group node tetrapods is believed to have been hindlimb-powered and ‘raised’, involving symmetrical gaits similar to those used by modern salamanders. The fossil record over this period of evolutionary transition is remarkably poor (Romer’s Gap), but we hypothesize a phase of belly-dragging sprawling locomotion combined with symmetrical gaits. Since belly-dragging sprawling locomotion has differing functional demands from ‘raised’ sprawling locomotion, we studied the limb mechanics of the extant belly-dragging blue-tongued skink. We used X-ray reconstruction of moving morphology to quantify the three-dimensional kinematic components, and simultaneously recorded single limb substrate reaction forces (SRF) in order to calculate SRF moment arms and the external moments acting on the proximal limb joints. In the hindlimbs, stylopodal long-axis rotation is more emphasized than in the forelimbs, and much greater vertical and propulsive forces are exerted. The SRF moment arm acting on the shoulder is at a local minimum at the instant of peak force. The hindlimbs display patterns that more closely resemble ‘raised’ sprawling species. External moment at the shoulder of the skink is smaller than in ‘raised’ sprawlers. We propose an evolutionary scenario in which the locomotor mechanics of belly-dragging early tetrapods were gradually modified towards hindlimb-powered, raised terrestrial locomotion with symmetrical gait. In accordance with the view that limb evolution was an exaptation for terrestrial locomotion, the kinematic pattern of the limbs for the generation of propulsion preceded, in our scenario, the evolution of permanent body weight support.     

Functional divergence between morphs of a dwarf chameleon: differential locomotor kinematics in relation to habitat structure

Arboreal lizards are extremely effective at moving in structurally complex habitats, including surfaces of varying diameter and incline. Chameleons exemplify this by exhibiting a number of morphological specializations for moving in these habitats, including the use of prehensile feet and tail to grasp branches. Despite their unique morphology and behaviour, little is known about how locomotor movements vary between species. In addition, some species, such as the Cape Dwarf Chameleon, Bradypodion pumilum, consist of two morphs that differ in ecology, morphology, and behaviour. The two morphs can be found in either closed canopy woodland habitat or relatively open fynbos habitat. The morph that occupies the woodland habitat tends to be larger and utilizes larger diameter perches. Although their ecological and morphological divergence is established, whether this translates into differences in three‐dimensional kinematics of locomotion is not known. Given the potentially strong selective pressures from structurally different habitats, kinematic differences might reveal the functional basis of incipient speciation. We determined that the two morphs diverge significantly in multidimensional kinematic space, and that this occurs for the forelimb and hindlimb independently. These differences outweigh the effects of substrate within each morph, although the differences between morphs were more pronounced on the vertical treatments.     

Conservation rules, their breakdown, and optimality in Caenorhabditis sinusoidal locomotion

Undulatory locomotion is common to nematodes as well as to limbless vertebrates, but its control is not understood in spite of the identification of hundred of genes involved in Caenorhabditis elegans locomotion. To reveal the mechanisms of nematode undulatory locomotion, we quantitatively analysed the movement of C. elegans with genetic perturbations to neurons, muscles, and skeleton (cuticle). We also compared locomotion of different Caenorhabditis species. We constructed a theoretical model that combines mechanics and biophysics, and that is constrained by the observations of propulsion and muscular velocities, as well as wavelength and amplitude of undulations. We find that normalized wavelength is a conserved quantity among wild-type C. elegans individuals, across mutants, and across different species. The velocity of forward propulsion scales linearly with the velocity of the muscular wave and the corresponding slope is also a conserved quantity and almost optimal; the exceptions are in some mutants affecting cuticle structure. In theoretical terms, the optimality of the slope is equivalent to the exact balance between muscular and visco-elastic body reaction bending moments. We find that the amplitude and frequency of undulations are inversely correlated and provide a theoretical explanation for this fact. These experimental results are valid both for young adults and for all larval stages of wild-type C. elegans. In particular, during development, the amplitude scales linearly with the wavelength, consistent with our theory. We also investigated the influence of substrate firmness on motion parameters, and found that it does not affect the above invariants. In general, our biomechanical model can explain the observed robustness of the mechanisms controlling nematode undulatory locomotion.     

Limb kinematics during locomotion in the two-toed sloth (Choloepus didactylus,Xenarthra) and its implications for the evolution of the sloth locomotor apparatus

In order to gain insight into the function of the extant sloth locomotion and its evolution, we conducted a detailed videoradiographic analysis of two-toed sloth locomotion (Xenarthra: Choloepus didactylus). Both unrestrained as well as steady-state locomotion was analyzed. Spatio-temporal gait parameters, data on interlimb coordination, and limb kinematics are reported. Two-toed sloths displayed great variability in spatio-temporal gait parameters over the observed range of speeds. They increase speed by decreasing the durations of contact and swing phases, as well as by increasing step length. Gait utilization also varies with no strict gait sequence or interlimb timing evident in slow movements, but a tendency to employ diagonal sequence, diagonal couplet gaits in fast movements. In contrast, limb kinematics were highly conserved with respect to ‘normal’ pronograde locomotion. Limb element and joint angles at touch down and lift off, element and joint excursions, and contribution to body progression of individual elements are similar to those reported for non-cursorial mammals of small to medium size. Hands and feet are specialized to maintain firm connection to supports, and do not contribute to step length or progression. In so doing, the tarsometatarsus lost its role as an individual propulsive element during the evolution of suspensory locomotion. Conservative kinematic behavior of the remaining limb elements does not preclude that muscle recruitment and neuromuscular control for limb pro- and retraction are also conserved. The observed kinematic patterns of two-toed sloths improve our understanding of the convergent evolution of quadrupedal suspensory posture and locomotion in the two extant sloth lineages.