Proximal versus distal control of two-joint planar reaching movements in the presence of neuromuscular noise

Determining how the human nervous system contends with neuro-motor noise is vital to understanding how humans achieve accurate goal-directed movements. Experimentally, people learning skilled tasks tend to reduce variability in distal joint movements more than in proximal joint movements. This suggests that they might be imposing greater control over distal joints than proximal joints. However, the reasons for this remain unclear, largely because it is not experimentally possible to directly manipulate either the noise or the control at each joint independently. Therefore, this study used a 2 degree-of-freedom torque driven arm model to determine how different combinations of noise and/or control independently applied at each joint affected the reaching accuracy and the total work required to make the movement. Signal-dependent noise was simultaneously and independently added to the shoulder and elbow torques to induce endpoint errors during planar reaching. Feedback control was then applied, independently and jointly, at each joint to reduce endpoint error due to the added neuromuscular noise. Movement direction and the inertia distribution along the arm were varied to quantify how these biomechanical variations affected the system performance. Endpoint error and total net work were computed as dependent measures. When each joint was independently subjected to noise in the absence of control, endpoint errors were more sensitive to distal (elbow) noise than to proximal (shoulder) noise for nearly all combinations of reaching direction and inertia ratio. The effects of distal noise on endpoint errors were more pronounced when inertia was distributed more toward the forearm. In contrast, the total net work decreased as mass was shifted to the upper arm for reaching movements in all directions. When noise was present at both joints and joint control was implemented, controlling the distal joint alone reduced endpoint errors more than controlling the proximal joint alone for nearly all combinations of reaching direction and inertia ratio. Applying control only at the distal joint was more effective at reducing endpoint errors when more of the mass was more proximally distributed. Likewise, controlling the distal joint alone required less total net work than controlling the proximal joint alone for nearly all combinations of reaching distance and inertia ratio. It is more efficient to reduce endpoint error and energetic cost by selectively applying control to reduce variability in the distal joint than the proximal joint. The reasons for this arise from the biomechanical configuration of the arm itself.     

Neuromuscular changes for hopping on a range of damped surfaces.

Humans hopping and running on elastic and damped surfaces maintain similar center-of-mass dynamics by adjusting stance leg mechanics. We tested the hypothesis that the leg transitions from acting like an energy-conserving spring on elastic surfaces to a power-producing actuator on damped surfaces during hopping due to changes in ankle mechanics. To test this hypothesis, we collected surface electromyography, video kinematics, and ground reaction force while eight male subjects (body mass: 76.2 +/- 1.7 kg) hopped in place on a range of damped surfaces. On the most damped surface, most of the mechanical work done by the leg appeared at the ankle (52%), whereas 23 and 25% appeared at the knee and hip, respectively. Hoppers extended all three joints during takeoff further than they flexed during landing and thereby did more net positive work on more heavily damped surfaces. Also, all three joints reached peak flexion sooner after touchdown on more heavily damped surfaces. Consequently, peak moment occurred during joint extension rather than at peak flexion as on elastic surfaces. These strategies caused the positive work during extension to exceed the negative work during flexion to a greater extent on more heavily damped surfaces. At the muscle level, surface EMG increased by 50-440% in ankle and knee extensors as surface damping increased to compensate for greater surface energy dissipation. Our findings, and those of previous studies of hopping on elastic surfaces, show that the ankle joint is the key determinant of both springlike and actuator-like leg mechanics during hopping in place.     

Joint development in the Drosophila leg: cell movements and cell populations

Flexible joints separate the rigid sections of the insect leg, allowing them to move. In Drosophila, the initial patterning of these joints is apparent in the larval imaginal discs from which the adult legs will develop. Here, we describe the later patterning and morphogenesis of the joints, which occurs after pupariation (AP). In the tibial/tarsal joint, the apodeme insertion site provides a fixed marker for the boundary between proximal and distal joint territories (the P/D boundary). Cells on either side of this boundary behave differently during morphogenesis. Morphogenesis begins with the apical constriction of distal joint cells, about 24 h AP. Distal cells then become columnar, causing distal tissue nearest the P/D boundary to fold into the leg. In the last stage of joint morphogenesis, the proximal joint cells closest to the P/D boundary align and elongate to form a "palisade" (a row of columnar cells) over the distal joint cells. The proximal and distal joint territories are characterised by the differential organisation of cytoskeletal and extracellular matrix proteins, and by the differential expression of enhancer trap lines and other gene markers. These markers also define a number of more localised territories within the pupal joint.     

Jacobian Matrix Derived from Cross Product and its Application into High Power Joint Mechanism Analysis

The size and weight of an actuator tend to increase with actuator power because the actuator power-to-mass ratio is near constant for a given type of motor. Rapid motion such as jumping or running is difficult to realize by using simple actuator power. The aim of this research is to develop a high power joint mechanism that mimics the leg mechanism of a locust. The characteristics of the joint mechanism are evaluated using vector and dynamic analysis.The proposed high power joint mechanism consists of a closed link structure comprising four links and a spring. Linear actuators are attached to the top and bottom links, and the joint angle changes by controlling the lengths of the top and bottom links. A spring is located between two of the links, and is contracted using two linear actuators to provide stored force, which can be released instantaneously to produce a higher power response than that available directly from both actuators.The analysis demonstrates how the joint mechanism produces an output with a higher power than the rated input actuator power. The output characteristics of the joint mechanism depend on link length and link conditions.     

Segment interactions within the swing leg during unloaded and loaded running

In this study, designed to determine the effect of lower extremity inertia manipulation on joint kinetics and segment energetics during the swing phase, 15 male distance runners were filmed as they performed treadmill running (3.35 m s-1) under five load conditions: no added load and loads of 0.25 kg and 0.50 kg added to each thigh or each foot. Results of this study demonstrated that the energetics of the lower extremity movements during the swing phase of the running cycle were dominated by mechanical energy transfers between adjacent segments attributed to the joint reaction forces, which acted to redistribute mechanical energy within the system. These contributions were considerably greater than those of the net joint moments, which primarily reflected muscular generation and dissipation of mechanical energy. Lower extremity loading caused little change in the movement pattern of the swing leg. However, increases in the joint reaction forces and net moments and in the amount of work done and the energy transfer attributed to the reaction forces and moments were observed, but were limited to the joints proximal to the location of the added load. These results were consistent with the increased aerobic demand associated with increases in lower extremity inertia that have been reported elsewhere and also have implications for the manner in which the neuromuscular system controls the motion of the legs during running.     

Regulation of step frequency in transtibial amputee endurance athletes using a running-specific prosthesis

Running specific prostheses (RSP) are designed to replicate the spring-like behaviour of the human leg during running, by incorporating a real physical spring in the prosthesis. Leg stiffness is an important parameter in running as it is strongly related to step frequency and running economy. To be able to select a prosthesis that contributes to the required leg stiffness of the athlete, it needs to be known to what extent the behaviour of the prosthetic leg during running is dominated by the stiffness of the prosthesis or whether it can be regulated by adaptations of the residual joints. The aim of this study was to investigate whether and how athletes with an RSP could regulate leg stiffness during distance running at different step frequencies.Seven endurance runners with an unilateral transtibial amputation performed five running trials on a treadmill at a fixed speed, while different step frequencies were imposed (preferred step frequency (PSF) and −15%, −7.5%, +7.5% and +15% of PSF). Among others, step time, ground contact time, flight time, leg stiffness and joint kinetics were measured for both legs.In the intact leg, increasing step frequency was accompanied by a decrease in both contact and flight time, while in the prosthetic leg contact time remained constant and only flight time decreased. In accordance, leg stiffness increased in the intact leg, but not in the prosthetic leg. Although a substantial contribution of the residual leg to total leg stiffness was observed, this contribution did not change considerably with changing step frequency.Amputee athletes do not seem to be able to alter prosthetic leg stiffness to regulate step frequency during running. This invariant behaviour indicates that RSP stiffness has a large effect on total leg stiffness and therefore can have an important influence on running performance. Nevertheless, since prosthetic leg stiffness was considerably lower than stiffness of the RSP, compliance of the residual leg should not be ignored when selecting RSP stiffness.     

Human leg model predicts ankle muscle-tendon morphology, state, roles and energetics in walking

A common feature in biological neuromuscular systems is the redundancy in joint actuation. Understanding how these redundancies are resolved in typical joint movements has been a long-standing problem in biomechanics, neuroscience and prosthetics. Many empirical studies have uncovered neural, mechanical and energetic aspects of how humans resolve these degrees of freedom to actuate leg joints for common tasks like walking. However, a unifying theoretical framework that explains the many independent empirical observations and predicts individual muscle and tendon contributions to joint actuation is yet to be established. Here we develop a computational framework to address how the ankle joint actuation problem is resolved by the neuromuscular system in walking. Our framework is founded upon the proposal that a consideration of both neural control and leg muscle-tendon morphology is critical to obtain predictive, mechanistic insight into individual muscle and tendon contributions to joint actuation. We examine kinetic, kinematic and electromyographic data from healthy walking subjects to find that human leg muscle-tendon morphology and neural activations enable a metabolically optimal realization of biological ankle mechanics in walking. This optimal realization (a) corresponds to independent empirical observations of operation and performance of the soleus and gastrocnemius muscles, (b) gives rise to an efficient load-sharing amongst ankle muscle-tendon units and (c) causes soleus and gastrocnemius muscle fibers to take on distinct mechanical roles of force generation and power production at the end of stance phase in walking. The framework outlined here suggests that the dynamical interplay between leg structure and neural control may be key to the high walking economy of humans, and has implications as a means to obtain insight into empirically inaccessible features of individual muscle and tendons in biomechanical tasks.     

BigDog-inspired studies in the locomotion of goats and dogs

Collision-based expenditure of mechanical energy and the compliance and geometry of the leg are fundamental, interrelated considerations in the mechanical design of legged runners. This article provides a basic context and rationale for experiments designed to inform each of these key areas in Boston Dynamic's BigDog robot. Although these principles have been investigated throughout the past few decades within different academic disciplines, BigDog required that they be considered together and in concert with an impressive set of control algorithms that are not discussed here. Although collision reduction is an important strategy for reducing mechanical cost of transport in the slowest and fastest quadrupedal gaits, walking and galloping, BigDog employed an intermediate-speed trotting gait without collision reduction. Trotting, instead, uses a spring-loaded inverted pendulum mechanism with potential for storage and return of elastic strain energy in appropriately compliant structures. Rather than tuning BigDog's built-in leg springs according to a spring-mass model-based virtual leg-spring constant , a much stiffer distal leg spring together with actuation of the adjacent joint provided good trotting dynamics and avoided functional limitations that might have been imposed by too much compliance in real-world terrain. Adjusting the directional compliance of the legs by adopting a knee-forward, elbow-back geometry led to more robust trotting dynamics by reducing perturbations about the pitch axis of the robot's center of mass (CoM). BigDog is the most successful large-scale, all-terrain trotting machine built to date and it continues to stimulate our understanding of legged locomotion in comparative biomechanics as well as in robotics.     

Gimbals in the insect leg

We studied the common kinematic features of the coxa and trochanter in cursorial and raptorial legs, which are the short size of the podomers, predominantly monoaxial joints, and the approximate orthogonality of adjacent joint axes. The chain coxa-trochanter with its short elements and serial orthogonality of joint axes resembles the gimbals which combine versatility and tolerance to external perturbations. The geometry of legs was studied in 23 insect species of 12 orders. Insects with monoaxial joints were selected. The joint between the trochanter and the femur (TFJ) is defined either by two vestigial condyles or by a straight anterior hinge. Direction of the joint axes in the two basal podomers was assessed by 3D measurements or by goniometry in two planes. Length of the coxa is <15% (mostly <8%) of the total length of the cursorial leg, that of the trochanter <10%. Angles between the proximal and distal joint axes in the middle coxa range from 124 to 84 degrees (mean 97+/-14 degrees ), in the trochanter (in all legs studied) from 125 to 72 degrees (mean 90+/-13 degrees ). Vectors of the distal axis in the coxa are concentrated about the normal to the plane defined by the proximal axis and the midpoint between the distal condyles. These vectors in the trochanter lie at various angles to the normal; angles are correlated with the direction of the TFJ relative to the femur. Range of reduction about the TFJ is over 60 degrees in the foreleg of Ranatra linearis, Mantispa lobata and the hind leg in Carabus coriaceus (confirming observations of previous authors), 40-60 degrees in the foreleg of Vespa crabro and in the middle one in Ammophila campestris, 10-30 degrees in other studied specimens. The special role of the trochanter in autotomy and in active propulsion in some insect groups is discussed. The majority of insects possess small trochanters and slightly movable TFJs with the joint axis laying in the femur-tibia plane. We pose the hypothesis that the TFJ damps external forces, the vectors of which lie off the femur-tibia plane, the reductor muscle acting as a spring. Thus the TFJ contributes to dynamic stability of legged locomotion.     

Control of obstacle climbing in the cockroach, Blaberus discoidalis. I. Kinematics

An advantage of legged locomotion is the ability to climb over obstacles. We studied deathhead cockroaches as they climbed over plastic blocks in order to characterize the leg movements associated with climbing. Movements were recorded as animals surmounted 5.5-mm or 11-mm obstacles. The smaller obstacles were scaled with little change in running movements. The higher obstacles required altered gaits, leg positions and body posture. The most frequent sequence used was to first tilt the front of the body upward in a rearing stage, and then elevate the center of mass to the level of the top of the block. A horizontal running posture was re-assumed in a leveling-off stage. The action of the middle legs was redirected by rotations of the leg at the thoracal-coxal and the trochanteral-femoral joints. The subsequent extension movements of the coxal-trochanteral and femoral-tibial joints were within the range seen during horizontal running. The structure of proximal leg joints allows for flexibility in leg use by generating subtle, but effective changes in the direction of leg movement. This architecture, along with the resulting re-direction of movements, provides a range of strategies for both animals and walking machines.     

Bipedal walking and running with spring-like biarticular muscles

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

Mechanical analysis of the landing phase in heel-toe running.

Results of mechanical analyses of running may be helpful in the search for the etiology of running injuries. In this study a mechanical analysis was made of the landing phase of three trained heel-toe runners, running at their preferred speed and style. The body was modeled as a system of seven linked rigid segments, and the positions of markers defining these segments were monitored using 200 Hz video analysis. Information about the ground reaction force vector was collected using a force plate. Segment kinematics were combined with ground reaction force data for calculation of the net intersegmental forces and moments. The vertical component of the ground reaction force vector Fz was found to reach a first peak approximately 25 ms after touch-down. This peak occurs because, in the support leg, the vertical acceleration of the knee joint is not reduced relative to that of the ankle joint by rotation of the lower leg, so that the support leg segments collide with the floor. Rotation of the support upper leg, however, reduces the vertical acceleration of the hip joint relative to that of the knee joint, and thereby plays an important role in limiting the vertical forces during the first 40 ms. Between 40 and 100 ms after touch-down, the vertical forces are mainly limited by rotation of the support lower leg. At the instant that Fz reaches its first peak, net moments about ankle, knee and hip joints of the support leg are virtually zero. The net moment about the knee joint changed from -100 Nm (flexion) at touch-down to +200 Nm (extension) 50 ms after touch-down. These changes are too rapid to be explained by variations in the muscle activation levels and were ascribed to spring-like behavior of pre-activated knee flexor and knee extensor muscles. These results imply that the runners investigated had no opportunity to control the rotations of body segments during the first part of the contact phase, other than by selecting a certain geometry of the body and muscular (co-)activation levels prior to touch-down.     

The effect of speed on leg stiffness and joint kinetics in human running

The goals of this study were to examine the following hypotheses: (a) there is a difference between the theoretically calculated (McMahon and Cheng, 1990. Journal of Biomechanics 23, 65-78) and the kinematically measured length changes of the spring-mass model and (b) the leg spring stiffness, the ankle spring stiffness and the knee spring stiffness are influenced by running speed. Thirteen athletes took part in this study. Force was measured using a "Kistler" force plate (1000 Hz). Kinematic data were recorded using two high-speed (120 Hz) video cameras. Each athlete completed trials running at five different velocities (approx. 2.5, 3.5, 4.5, 5.5 and 6.5 m/s). Running velocity influences the leg spring stiffness, the effective vertical spring stiffness and the spring stiffness at the knee joint. The spring stiffness at the ankle joint showed no statistical difference (p < 0.05) for the five velocities. The theoretically calculated length change of the spring-mass model significantly (p < 0.05) overestimated the actual length change. For running velocities up to 6.5 m/s the leg spring stiffness is influenced mostly by changes in stiffness at the knee joint.     

Modeling the stance leg in two-dimensional analyses of sprinting: inclusion of the MTP joint affects joint kinetics

Two-dimensional analyses of sprint kinetics are commonly undertaken but often ignore the metatarsalphalangeal (MTP) joint and model the foot as a single segment. Due to the linked-segment nature of inverse dynamics analyses, the aim of this study was to investigate the effect of ignoring the MTP joint on the calculated joint kinetics at the other stance leg joints during sprinting. High-speed video and force platform data were collected from four to five trials for each of three international athletes. Resultant joint moments, powers, and net work at the stance leg joints during the first stance phase after block clearance were calculated using three different foot models. By ignoring the MTP joint, peak extensor moments at the ankle, knee, and hip were on average 35% higher (p < .05 for each athlete), 40% lower (p < .05), and 9% higher (p > .05), respectively, than those calculated with the MTP joint included. Peak ankle and knee joint powers and net work at all joints were also significantly (p < .05) different. By ignoring a genuine MTP joint plantar flexor moment, artificially high peak ankle joint moments are calculated, and these also affect the calculated joint kinetics at the knee.     

Notch signaling relieves the joint-suppressive activity of Defective proventriculus in the Drosophila leg

Segmentation plays crucial roles during morphogenesis. Drosophila legs are divided into segments along the proximal-distal axis by flexible structures called joints. Notch signaling is necessary and sufficient to promote leg growth and joint formation, and is activated in distal cells of each segment in everting prepupal leg discs. The homeobox gene defective proventriculus (dve) is expressed in regions both proximal and distal to the intersegmental folds at 4 h after puparium formation (APF). Dve-expressing region partly overlaps with the Notch-activated region, and they become a complementary pattern at 6 h APF. Interestingly, dve mutant legs resulted in extra joint formation at the center of each tarsal segment, and the forced expression of dve caused a jointless phenotype. We present evidence that Dve suppresses the potential joint-forming activity, and that Notch signaling represses Dve expression to form joints.     

Finger joint impedance during tapping on a computer keyswitch

We studied the dynamic behavior of finger joints during the contact period of tapping on a computer keyswitch, to characterize and parameterize joint function with a lumped-parameter impedance model. We tested the hypothesis that the metacarpophalangeal (MCP) and interphalangeal (IP) joints act similarly in terms of kinematics, torque, and energy production when tapping. Fifteen human subjects tapped with the index finger of the right hand on a computer keyswitch mounted on a two-axis force sensor, which measured forces in the vertical and sagittal planes. Miniature fiber-optic goniometers mounted across the dorsal side of each joint measured joint kinematics. Joint torques were calculated from endpoint forces and joint kinematics using an inverse dynamic algorithm. For each joint, a linear spring and damper model was fitted to joint torque, position, and velocity during the contact period of each tap (22 per subject on average). The spring-damper model could account for over 90% of the variance in torque when loading and unloading portions of the contact were separated, with model parameters comparable to those previously measured during isometric loading of the finger. The finger joints functioned differently, as illustrated by energy production during the contact period. During the loading phase of contact the MCP joint flexed and produced energy, whereas the proximal and distal IP joints extended and absorbed energy. These results suggest that the MCP joint does work on the interphalangeal joints as well as on the keyswitch.     

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

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

The antennal motor system of the stick insect Carausius morosus: anatomy and antennal movement pattern during walking

The stick insect Carausius morosus continuously moves its antennae during locomotion. Active antennal movements may reflect employment of antennae as tactile probes. Therefore, this study treats two basic aspects of the antennal motor system: First, the anatomy of antennal joints, muscles, nerves and motoneurons is described and discussed in comparison with other species. Second, the typical movement pattern of the antennae is analysed, and its spatio-temporal coordination with leg movements described. Each antenna is moved by two single-axis hinge joints. The proximal head-scape joint is controlled by two levator muscles and a three-partite depressor muscle. The distal scape-pedicel joint is controlled by an antagonistic abductor/ adductor pair. Three nerves innervate the antennal musculature, containing axons of 14-17 motoneurons, including one common inhibitor. During walking, the pattern of antennal movement is rhythmic and spatiotemporally coupled with leg movements. The antennal abduction/adduction cycle leads the protraction/retraction cycle of the ipsilateral front leg with a stable phase shift. During one abduction/adduction cycle there are typically two levation/depression cycles, however, with less strict temporal coupling than the horizontal component. Predictions of antennal contacts with square obstacles to occur before leg contacts match behavioural performance, indicating a potential role of active antennal movements in obstacle detection.     

The role of tendon elasticity in the locomotion of the camel (Camelus dromedarius)

Several ofthe distal leg muscles ofcamels have very short or even rudimentary muscle fibres. This makes it possible to calculate the elastic extensions of tendons that occur in running, from the leg positions observed in films. A series of experiments have been performed for this purpose on the dissected legs of a camel. The initial conclusions derived from them are modified in the light of estimates of the forces that act on the tendons, and of measurements of the elastic properties of one tendon. Evidence for movement at the intertarsal and tarso-metatarsal joints. and the corresponding joints of the fore leg, is examined. The importance of the various tendons as elastic energy stores in running is assessed.