Compliant ankle function results in landing-take off asymmetry in legged locomotion

The biomechanics of running and running styles: a synthesis

Running movements are parametrised using a wide variety of devices. Misleading interpretations can be avoided if the interdependencies and redundancies between biomechanical parameters are taken into account. In this synthetic review, commonly measured running parameters are discussed in relation to each other, culminating in a concise, yet comprehensive description of the full spectrum of running styles. Since the goal of running movements is to transport the body centre of mass (BCoM), and the BCoM trajectory can be derived from spatiotemporal parameters, we anticipate that different running styles are reflected in those spatiotemporal parameters. To this end, this review focuses on spatiotemporal parameters and their relationships with speed, ground reaction force and whole-body kinematics. Based on this evaluation, we submit that the full spectrum of running styles can be described by only two parameters, namely the step frequency and the duty factor (the ratio of stance time and stride time) as assessed at a given speed. These key parameters led to the conceptualisation of a so-called Dual-axis framework. This framework allows categorisation of distinctive running styles (coined 'Stick', 'Bounce', 'Push', 'Hop', and 'Sit') and provides a practical overview to guide future measurement and interpretation of running biomechanics.

Assessing spring-mass similarity in elite and recreational runners

The dynamic complexity and individualization of running biomechanics has challenged the development of objective and comparative gait measures. Here, we present and explore several novel biomechanical metrics for running that are informed by a canonical inter-species gait template-the spring-mass model. The measures assess running mechanics systemically against the template via quantifying characteristics of a runner's kinetics relative to the energy-conserving elastic system-i.e., their "spring-mass similarity". Applying these metrics in a retrospective cohort investigation, we studied the overground kinetics of two heterogenous populations of runners in two footwear conditions: elite and recreational athletes in shod and barefoot conditions. Across all measures and within foot strike types, the elite runners exhibited mechanics that were more similar to those of the ideally elastic spring-mass template. The elite runners had more symmetric bounces, less discrepancy (i.e., greater coordination) between horizontal and vertical kinetic changes, and better fit to a spring-mass vertical ground reaction force time series. Barefoot running elicited greater kinetic coordination in the recreational runners. At a faster speed, the elites further improved their similarity to the template. Overall, the more economical elite group exhibited greater likeness to the linearly elastic, energy-conserving spring-mass system than their recreational counterparts. This study introduces novel biomechanical measures related to performance in distance running. More broadly, it provides new, approachable metrics for systemic quantification of gait biomechanics in runners across all demographics. These metrics may be applied to assess a runner's global biomechanical response to a variety of interventions, including training adaptations, rehabilitation programs, and footwear conditions.

Biarticular muscles in light of template models, experiments and robotics: a review

Leg morphology is an important outcome of evolution. A remarkable morphological leg feature is the existence of biarticular muscles that span adjacent joints. Diverse studies from different fields of research suggest a less coherent understanding of the muscles' functionality in cyclic, sagittal plane locomotion. We structured this review of biarticular muscle function by reflecting biomechanical template models, human experiments and robotic system designs. Within these approaches, we surveyed the contribution of biarticular muscles to the locomotor subfunctions (stance, balance and swing). While mono- and biarticular muscles do not show physiological differences, the reviewed studies provide evidence for complementary and locomotor subfunction-specific contributions of mono- and biarticular muscles. In stance, biarticular muscles coordinate joint movements, improve economy (e.g. by transferring energy) and secure the zig-zag configuration of the leg against joint overextension. These commonly known functions are extended by an explicit role of biarticular muscles in controlling the angular momentum for balance and swing. Human-like leg arrangement and intrinsic (compliant) properties of biarticular structures improve the controllability and energy efficiency of legged robots and assistive devices. Future interdisciplinary research on biarticular muscles should address their role for sensing and control as well as non-cyclic and/or non-sagittal motions, and non-static moment arms.

The scaling or ontogeny of human gait kinetics and walk-run transition: The implications of work vs. peak power minimization

A simple model is developed to find vertical force profiles and stance durations that minimize either limb mechanical work or peak power demands during bipedal locomotion. The model predicts that work minimization is achieved with a symmetrical vertical force profile, consistent with previous models and observations of adult humans, and data for 487 participants (predominantly 11-18 years old) required to walk at a range of speeds at a Science Fair. Work minimization also predicts the discrete walk-run transition, familiar for adult humans. In contrast, modeled peak limb mechanical power demands are minimized with an early skew in vertical ground reaction force that increases with speed, and stance durations that decrease steadily with speed across the work minimizing walk-run transition speed. The peak power minimization model therefore predicts a continuous walk-run gait transition that is quantitatively consistent with measurements of younger children (1.1-4.7 years) required to locomote at a range of speeds but free to select their own gaits.

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected, off-centered curvy foot

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.

Children and adults minimise activated muscle volume by selecting gait parameters that balance gross mechanical power and work demands

Terrestrial locomotion on legs is energetically expensive. Compared with cycling, or with locomotion in swimming or flying animals, walking and running are highly uneconomical. Legged gaits that minimise mechanical work have previously been identified and broadly match walking and running at appropriate speeds. Furthermore, the ‘cost of muscle force’ approaches are effective in relating locomotion kinetics to metabolic cost. However, few accounts have been made for why animals deviate from either work-minimising or muscle-force-minimising strategies. Also, there is no current mechanistic account for the scaling of locomotion kinetics with animal size and speed. Here, we report measurements of ground reaction forces in walking children and adult humans, and their stance durations during running. We find that many aspects of gait kinetics and kinematics scale with speed and size in a manner that is consistent with minimising muscle activation required for the more demanding between mechanical work and power: spreading the duration of muscle action reduces activation requirements for power, at the cost of greater work demands. Mechanical work is relatively more demanding for larger bipeds – adult humans – accounting for their symmetrical M-shaped vertical force traces in walking, and relatively brief stance durations in running compared with smaller bipeds – children. The gaits of small children, and the greater deviation of their mechanics from work-minimising strategies, may be understood as appropriate for their scale, not merely as immature, incompletely developed and energetically sub-optimal versions of adult gaits.

Highlighted Article: The gross mechanics of walking and running children and adults support a new model for the costs dominating level terrestrial locomotion – muscle activation for mechanical work or power.

Running, hopping and trotting: tuning step frequency to the resonant frequency of the bouncing system favors larger more compliant animals

A long-lasting challenge in comparative physiology is to understand why the efficiency of the mechanical work done to maintain locomotion increases with body mass. It has been suggested that this is due to a more elastic step in larger animals. Here we show that in running, hopping trotting animals and in human running during growth the resonant frequency of the bouncing system decreases with increasing body mass with the same trend surprisingly independent of different animal species and gaits. Step frequency about equals the resonant frequency in trotting and running whereas it is about half the resonant frequency in hopping. The energy loss by elastic hysteresis during loading-unloading the bouncing system from its equilibrium position decreases with increasing body mass. Similarity to a symmetric bounce increases with increasing body mass and, for a given body mass, seems to be maximal in hopping, intermediate in trotting and minimal in running. We conclude that: i) tuning step frequency to the resonant frequency of the bouncing system coincides with a lower hysteresis loss in larger more compliant animals, ii) the mechanism of gait per se affects similarity with a symmetric bounce independent of hysteresis and iii) the greater efficiency in larger animals may be due, at least in part, to a lower hysteresis loss.

Trunk orientation causes asymmetries in leg function in small bird terrestrial locomotion

In contrast to the upright trunk in humans, trunk orientation in most birds is almost horizontal (pronograde). It is conceivable that the orientation of the heavy trunk strongly influences the dynamics of bipedal terrestrial locomotion. Here, we analyse for the first time the effects of a pronograde trunk orientation on leg function and stability during bipedal locomotion. For this, we first inferred the leg function and trunk control strategy applied by a generalized small bird during terrestrial locomotion by analysing synchronously recorded kinematic (three-dimensional X-ray videography) and kinetic (three-dimensional force measurement) quail locomotion data. Then, by simulating quail gaits using a simplistic bioinspired numerical model which made use of parameters obtained in in vivo experiments with real quail, we show that the observed asymmetric leg function (left-skewed ground reaction force and longer leg at touchdown than at lift-off) is necessary for pronograde steady-state locomotion. In addition, steady-state locomotion becomes stable for specific morphological parameters. For quail-like parameters, the most common stable solution is grounded running, a gait preferred by quail and most of the other small birds. We hypothesize that stability of bipedal locomotion is a functional demand that, depending on trunk orientation and centre of mass location, constrains basic hind limb morphology and function, such as leg length, leg stiffness and leg damping.

Scaling of the spring in the leg during bouncing gaits of mammals

Trotting, bipedal running, and especially hopping have long been considered the principal bouncing gaits of legged animals. We use the radial-leg spring constant [Formula: see text] to quantify the stiffness of the physical leg during bouncing gaits. The radial-leg is modeled as an extensible strut between the hip and the ground and [Formula: see text] is determined from the force and deflection of this strut in each instance of stance. A Hookean spring is modeled in-series with a linear actuator and the stiffness of this spring [Formula: see text] is determined by minimizing the work of the actuator while reproducing the measured force-deflection dynamics of an individual leg during trotting or running, and of the paired legs during hopping. Prior studies have estimated leg stiffness using [Formula: see text], a metric that imagines a virtual-leg connected to the center of mass. While [Formula: see text] has been applied extensively in human and comparative biomechanics, we show that [Formula: see text] more accurately models the spring in the leg when actuation is allowed, as is the case in biological and robotic systems. Our allometric analysis of [Formula: see text] in the kangaroo rat, tammar wallaby, dog, goat, and human during hopping, trotting, or running show that [Formula: see text] scales as body mass to the two-third power, which is consistent with the predictions of dynamic similarity and with the scaling of [Formula: see text]. Hence, two-third scaling of locomotor spring constants among mammals is supported by both the radial-leg and virtual-leg models, yet the scaling of [Formula: see text] emerges from work-minimization in the radial-leg model instead of being a defacto result of the ratio of force to length used to compute [Formula: see text]. Another key distinction between the virtual-leg and radial-leg is that [Formula: see text] is substantially greater than [Formula: see text], as indicated by a 30-37% greater scaling coefficient for [Formula: see text]. We also show that the legs of goats are on average twice as stiff as those of dogs of the same mass and that goats increase the stiffness of their legs, in part, by more nearly aligning their distal limb-joints with the ground reaction force vector. This study is the first allometric analysis of leg spring constants in two decades. By means of an independent model, our findings reinforce the two-third scaling of spring constants with body mass, while showing that springs in-series with actuators are stiffer than those predicted by energy-conservative models of the leg.

Relative accuracy evaluation

The quality of data plays an important role in business analysis and decision making, and data accuracy is an important aspect in data quality. Thus one necessary task for data quality management is to evaluate the accuracy of the data. And in order to solve the problem that the accuracy of the whole data set is low while a useful part may be high, it is also necessary to evaluate the accuracy of the query results, called relative accuracy. However, as far as we know, neither measure nor effective methods for the accuracy evaluation methods are proposed. Motivated by this, for relative accuracy evaluation, we propose a systematic method. We design a relative accuracy evaluation framework for relational databases based on a new metric to measure the accuracy using statistics. We apply the methods to evaluate the precision and recall of basic queries, which show the result's relative accuracy. We also propose the method to handle data update and to improve accuracy evaluation using functional dependencies. Extensive experimental results show the effectiveness and efficiency of our proposed framework and algorithms.