Series Elasticity Research Articles

123 モータを付加した直列弾性アクチュエータシステムのインピーダンス制御(OS4-2 人を支援するメカトロニクス(2),OS4 人を支援するメカトロニクス)

123 モータを付加した直列弾性アクチュエータシステムのインピーダンス制御(OS4-2 人を支援するメカトロニクス(2),OS4 人を支援するメカトロニクス)

The role of series ankle elasticity in bipedal walking

The elastic stretch-shortening cycle of the Achilles tendon during walking can reduce the active work demands on the plantarflexor muscles in series. However, this does not explain why or when this ankle work, whether by muscle or tendon, needs to be performed during gait. We therefore employ a simple bipedal walking model to investigate how ankle work and series elasticity impact economical locomotion. Our model shows that ankle elasticity can use passive dynamics to aid push-off late in single support, redirecting the body's center-of-mass (COM) motion upward. An appropriately timed, elastic push-off helps to reduce dissipative collision losses at contralateral heelstrike, and therefore the positive work needed to offset those losses and power steady walking. Thus, the model demonstrates how elastic ankle work can reduce the total energetic demands of walking, including work required from more proximal knee and hip muscles. We found that the key requirement for using ankle elasticity to achieve economical gait is the proper ratio of ankle stiffness to foot length. Optimal combination of these parameters ensures proper timing of elastic energy release prior to contralateral heelstrike, and sufficient energy storage to redirect the COM velocity. In fact, there exist parameter combinations that theoretically yield collision-free walking, thus requiring zero active work, albeit with relatively high ankle torques. Ankle elasticity also allows the hip to power economical walking by contributing indirectly to push-off. Whether walking is powered by the ankle or hip, ankle elasticity may aid walking economy by reducing collision losses.

Elastic ankle exoskeletons reduce soleus muscle force but not work in human hopping

Inspired by elastic energy storage and return in tendons of human leg muscle-tendon units (MTU), exoskeletons often place a spring in parallel with an MTU to assist the MTU. However, this might perturb the normally efficient MTU mechanics and actually increase active muscle mechanical work. This study tested the effects of elastic parallel assistance on MTU mechanics. Participants hopped with and without spring-loaded ankle exoskeletons that assisted plantar flexion. An inverse dynamics analysis, combined with in vivo ultrasound imaging of soleus fascicles and surface electromyography, was used to determine muscle-tendon mechanics and activations. Whole body net metabolic power was obtained from indirect calorimetry. When hopping with spring-loaded exoskeletons, soleus activation was reduced (30-70%) and so was the magnitude of soleus force (peak force reduced by 30%) and the average rate of soleus force generation (by 50%). Although forces were lower, average positive fascicle power remained unchanged, owing to increased fascicle excursion (+4-5 mm). Net metabolic power was reduced with exoskeleton assistance (19%). These findings highlighted that parallel assistance to a muscle with appreciable series elasticity may have some negative consequences, and that the metabolic cost associated with generating force may be more pronounced than the cost of doing work for these muscles.

Hill-type muscle model parameters determined from experiments on single muscles show large animal-to-animal variation.

Models built using mean data can represent only a very small percentage, or none, of the population being modeled, and produce different activity than any member of it. Overcoming this "averaging" pitfall requires measuring, in single individuals in single experiments, all of the system's defining characteristics. We have developed protocols that allow all the parameters in the curves used in typical Hill-type models (passive and active force-length, series elasticity, force-activation, force-velocity) to be determined from experiments on individual stick insect muscles (Blümel et al. 2012a). A requirement for means to not well represent the population is that the population shows large variation in its defining characteristics. We therefore used these protocols to measure extensor muscle defining parameters in multiple animals. Across-animal variability in these parameters can be very large, ranging from 1.3- to 17-fold. This large variation is consistent with earlier data in which extensor muscle responses to identical motor neuron driving showed large animal-to-animal variability (Hooper etal. 2006), and suggests accurate modeling of extensor muscles requires modeling individual-by-individual. These complete characterizations of individual muscles also allowed us to test for parameter correlations. Two parameter pairs significantly co-varied, suggesting that a simpler model could as well reproduce muscle response.

Muscle co-contraction modulates damping and joint stability in a three-link biomechanical limb.

Computational models of neuromotor control require forward models of limb movement that can replicate the natural relationships between muscle activation and joint dynamics without the burdens of excessive anatomical detail. We present a model of a three-link biomechanical limb that emphasizes the dynamics of limb movement within a simplified two-dimensional framework. Muscle co-contraction effects were incorporated into the model by flanking each joint with a pair of antagonist muscles that may be activated independently. Muscle co-contraction is known to alter the damping and stiffness of limb joints without altering net joint torque. Idealized muscle actuators were implemented using the Voigt muscle model which incorporates the parallel elasticity of muscle and tendon but omits series elasticity. The natural force-length-velocity relationships of contractile muscle tissue were incorporated into the actuators using ideal mathematical forms. Numerical stability analysis confirmed that co-contraction of these simplified actuators increased damping in the biomechanical limb consistent with observations of human motor control. Dynamic changes in joint stiffness were excluded by the omission of series elasticity. The analysis also revealed the unexpected finding that distinct stable (bistable) equilibrium positions can co-exist under identical levels of muscle co-contraction. We map the conditions under which bistability arises and prove analytically that monostability (equifinality) is guaranteed when the antagonist muscles are identical. Lastly we verify these analytic findings in the full biomechanical limb model.

Synthesis of mathematical model of two-mass electromechanical system with backlash in the form of modified recurrent neural network

Based on the equipment operating data the technique of mathematical model synthesis has been developed in the form of a modified recurrent neural network of the two-mass electromechanical system including a DC motor of series excitation, elasticity, damping and backlash in the mechanical transmission.

On the Biomimetic Design of Agile-Robot Legs

The development of functional legged robots has encountered its limits in human-made actuation technology. This paper describes research on the biomimetic design of legs for agile quadrupeds. A biomimetic leg concept that extracts key principles from horse legs which are responsible for the agile and powerful locomotion of these animals is presented. The proposed biomimetic leg model defines the effective leg length, leg kinematics, limb mass distribution, actuator power, and elastic energy recovery as determinants of agile locomotion, and values for these five key elements are given. The transfer of the extracted principles to technological instantiations is analyzed in detail, considering the availability of current materials, structures and actuators. A real leg prototype has been developed following the biomimetic leg concept proposed. The actuation system is based on the hybrid use of series elasticity and magneto-rheological dampers which provides variable compliance for natural motion. From the experimental evaluation of this prototype, conclusions on the current technological barriers to achieve real functional legged robots to walk dynamically in agile locomotion are presented.

Combining series elastic actuation and magneto-rheological damping for the control of agile locomotion

All-terrain robot locomotion is an active topic of research. Search and rescue maneuvers and exploratory missions could benefit from robots with the abilities of real animals. However, technological barriers exist to ultimately achieving the actuation system, which is able to meet the exigent requirements of these robots. This paper describes the locomotion control of a leg prototype, designed and developed to make a quadruped walk dynamically while exhibiting compliant interaction with the environment. The actuation system of the leg is based on the hybrid use of series elasticity and magneto-rheological dampers, which provide variable compliance for natural-looking motion and improved interaction with the ground. The locomotion control architecture has been proposed to exploit natural leg dynamics in order to improve energy efficiency. Results show that the controller achieves a significant reduction in energy consumption during the leg swing phase thanks to the exploitation of inherent leg dynamics. Added to this, experiments with the real leg prototype show that the combined use of series elasticity and magneto-rheological damping at the knee provide a 20 % reduction in the energy wasted in braking the knee during its extension in the leg stance phase.

Mechanisms underlying rhythmic locomotion: dynamics of muscle activation

We have studied the dynamical properties of tension development in leech longitudinal muscle during swimming. A new method is proposed for modeling muscle properties under functionally relevant conditions where the muscle is subjected to both periodic activation and rhythmic length changes. The 'dual-sinusoid' experiments were conducted on preparations of leech nerve cord and body wall. The longitudinal muscle was activated periodically by injection of sinusoidal currents into an identified motoneuron. Simultaneously, sinusoidal length changes were imposed on the body wall with prescribed phase differences (12 values equally spaced over 2π radians) with respect to the current injection. Through the singular value decomposition of appropriately constructed tension data matrices, the leech muscle was found to have a multiplicative structure in which the tension was expressed as the product of activation and length factors. The time courses of activation and length factors were determined from the tension data and were used to develop component models. The proposed modeling method is a general one and is applicable to contractile elements for which the effects of series elasticity are negligible.

Energetic costs of producing muscle work and force in a cyclical human bouncing task

Muscles expend energy to perform active work during locomotion, but they may also expend significant energy to produce force, for example when tendons perform much of the work passively. The relative contributions of work and force to overall energy expenditure are unknown. We therefore measured the mechanics and energetics of a cyclical bouncing task, designed to control for work and force. We hypothesized that near bouncing resonance, little work would be performed actively by muscle, but the cyclical production of force would cost substantial metabolic energy. Human subjects (n = 9) bounced vertically about the ankles at inversely proportional frequencies (1-4 Hz) and amplitudes (15-4 mm), such that the overall rate of work performed on the body remained approximately constant (0.30 ± 0.06 W/kg), but the forces varied considerably. We used parameter identification to estimate series elasticity of the triceps surae tendon, as well as the work performed actively by muscle and passively by tendon. Net metabolic energy expenditure for bouncing at 1 Hz was 1.15 ± 0.31 W/kg, attributable mainly to active muscle work with an efficiency of 24 ± 3%. But at 3 Hz (near resonance), most of the work was performed passively, so that active muscle work could account for only 40% of the net metabolic rate of 0.76 ± 0.28 W/kg. Near resonance, a cost for cyclical force that increased with both amplitude and frequency of force accounted for at least as much of the total energy expenditure as a cost for work. Series elasticity reduces the need for active work, but energy must still be expended for force production.

Afferent Contribution to Locomotor Muscle Activity During Unconstrained Overground Human Walking: An Analysis of Triceps Surae Muscle Fascicles

Plantar flexor series elasticity can be used to dissociate muscle-fascicle and muscle-tendon behavior and thus afferent feedback during human walking. We used electromyography (EMG) and high-speed ultrasonography concomitantly to monitor muscle activity and muscle fascicle behavior in 19 healthy volunteers as they walked across a platform. On random trials, the platform was dropped (8 cm, 0.9 g acceleration) or held at a small inclination (up to +/-3 degrees in the parasagittal plane) with respect to level ground. Dropping the platform in the mid and late phases of stance produced a depression in the soleus muscle activity with an onset latency of about 50 ms. The reduction in ground reaction force also unloaded the plantar flexor muscles. The soleus muscle fascicles shortened with a minimum delay of 14 ms. Small variations in platform inclination produced significant changes in triceps surae muscle activity; EMG increased when stepping on an inclined surface and decreased when stepping on a declined surface. This sensory modulation of the locomotor output was concomitant with changes in triceps surae muscle fascicle and gastrocnemius tendon length. Assuming that afferent activity correlates to these mechanical changes, our results indicate that within-step sensory feedback from the plantar flexor muscles automatically adjusts muscle activity to compensate for small ground irregularities. The delayed onset of muscle fascicle movement after dropping the platform indicates that at least the initial part of the soleus depression is more likely mediated by a decrease in force feedback than length-sensitive feedback, indicating that force feedback contributes to the locomotor activity in human walking.

Powered Ankle--Foot Prosthesis Improves Walking Metabolic Economy

At moderate to fast walking speeds, the human ankle provides net positive work at high-mechanical-power output to propel the body upward and forward during the stance period. On the contrary, conventional ankle-foot prostheses exhibit a passive-elastic response during stance, and consequently, cannot provide net work. Clinical studies indicate that transtibial amputees using conventional prostheses have higher gait metabolic rates than normal. Researchers believe that the main cause for these higher rates is due to the inability of conventional prostheses to provide sufficient positive power at terminal stance in the trailing leg to limit heel strike losses of the adjacent leading leg. In this investigation, we evaluate the hypothesis that a powered ankle-foot prosthesis, capable of providing human-like ankle work and power during stance, can decrease the metabolic cost of transport (COT) compared to a conventional passive-elastic prosthesis. To test the hypothesis, a powered prosthesis is built that comprises a unidirectional spring, configured in parallel with a force-controllable actuator with series elasticity. The prosthesis is shown to deliver the high mechanical power and net positive work observed in normal human walking. The rate of oxygen consumption and carbon dioxide production is measured as a determinant of metabolic rate on three unilateral transtibial amputees walking at self-selected speeds. We find that the powered prosthesis decreases the amputee's metabolic COT on average by 14% compared to the conventional passive-elastic prostheses evaluated (Flex-Foot Ceterusreg and Freedom Innovations Sierra), even though the powered system is over twofold heavier than the conventional devices. These results highlight the clinical importance of prosthetic interventions that closely mimic the mass distribution, kinetics, and kinematics of the missing limb.

Powered ankle-foot prosthesis

The minimum level of series compliance that adequately protects the transmission from damage during foot collision fails to satisfy bandwidth requirements. As a resolution to this difficulty, parallel motor elasticity is used to lower the forces borne by the SEA, enhancing system force bandwidth. To minimize prosthesis cost of transport (COT) and motor or transmission size, we select a parallel stiffness that supplies the necessary ankle stiffness during early stance period dorsiflexion, eliminating the need for SEA during that gait phase. In future investigations, we hope to apply the ankle-foot design to robotic, orthotic, and exoskeletal applications. In the design of biomimetic ankle-foot systems, we feel both series and parallel motor elasticity are of paramount importance.

Simulation of steady state and transient cardiac muscle response experiments with a Huxley-based contraction model

A cardiac muscle model is presented with the purpose of representing a wide range of mechanical experiments at constant and transient Ca 2+ concentration. Modifications of a previous model were: weak and power attached crossbridge states, a troponin system involving three consecutive regulatory troponin–tropomyosin units acting together in Ca 2+ kinetics and detachment constants depending on crossbridge length. This model improved cooperativity (Hill coefficient close to 4) and the force–velocity relationship, and incorporated the representation of the four phases of muscle response to length and force steps, isotonic shortening and isosarcometric contractions, preserving previous satisfactory results. Moreover, experimentally reported effects, such as length dependence on Ca 2+ affinity, the decreased cooperativity at higher Ca 2+ concentrations, temperature effects on the stiffness–frequency relationship and the isometric internal shortening due to series elasticity, were obtained. In conclusion, the model is more comprehensive than a previous version because it is able to represent a wider variety of steady state experiments, the mechanical variables in twitches can be adequately related to intracellular Ca 2+, and all the simulations were performed with the same set of parameters.

The extensor tibiae muscle of the stick insect: biomechanical properties of an insect walking leg muscle

We investigated the properties of the extensor tibiae muscle of the stick insect (Carausius morosus) middle leg. Muscle geometry of the middle leg was compared to that of the front and hind legs and to the flexor tibiae, respectively. The mean length of the extensor tibiae fibres is 1.41+/-0.23 mm and flexor fibres are 2.11+/-0.30 mm long. The change of fibre length with joint angle was measured and closely follows a cosine function. Its amplitude gives effective moment arm lengths of 0.28+/-0.02 mm for the extensor and 0.56+/-0.04 mm for the flexor. Resting extensor tibiae muscle passive tonic force increased from 2 to 5 mN in the maximum femur-tibia (FT)-joint working range when stretched by ramps. Active muscle properties were measured with simultaneous activation (up to 200 pulses s(-1)) of all three motoneurons innervating the extensor tibiae, because this reflects most closely physiological muscle activation during leg swing. The force-length relationship corresponds closely to the typical characteristic according to the sliding filament hypothesis: it has a plateau at medium fibre lengths, declines nearly linearly in force at both longer and shorter fibre lengths, and the muscle's working range lies in the short to medium fibre length range. Maximum contraction velocity showed a similar relationship. The force-velocity relationship was the traditional Hill curve hyperbola, but deviated from the hyperbolic shape in the region of maximum contraction force close to the isometric contraction. Step-like changes in muscle length induced by loaded release experiments characterised the non-linear series elasticity as a quadratic spring.

Effects of Series Elasticity on the Human Knee Extension Torque-Angle Relationship in Vivo

Effects of Series Elasticity on the Human Knee Extension Torque-Angle Relationship in Vivo

Effects of Series Elasticity on the Human Knee Extension Torque-Angle Relationship in Vivo

The purpose of this study was to investigate the effects of series elasticity on the torque-angle relationship of the knee extensors in vivo. Forty-two men volunteered to take part in the present study. The participants performed maximal voluntary isometric contractions at eight knee-joint angles (40, 50, 60, 70, 80, 90, 100, 110°). The elongation of the tendon and aponeurosis of the vastus lateralis muscle was directly measured by ultrasonography, while the participants performed ramp isometric knee extensions to the voluntary maximum at 80° of knee angle. There was no significant difference in the torque value between 50° and 100°, although there was variation in the shape of the “torque-angle” relationship. The variability in the torqueangle curve was not affected by the activation level of agonist and antagonist muscles and the moment arm length. The ratio of torque at 100° compared to that at 50° was significantly (r2 = 18–23%) correlated to the maximal elongation and strain (to initial length) of the tendon structures. These results suggest that increased compliance of tendon structures of the knee extensors may contribute to variations in the torque-angle curves of the knee extensors.

Muscle activation assessment: Effects of method, stimulus number, and joint angle

Activation capacity has traditionally been assessed using the interpolated twitch technique (ITT) and central activation ratio (CAR). However, the quantitative agreement of the two methods and the physiological mechanisms underpinning any possible differences have not been fully elucidated. The aim of this study was to compare and assess the sensitivity of the ITT and CAR to potential errors introduced by (1) evoking inadequate force, by manipulating the number of stimuli, and (2) neglecting differences in series elasticity between conditions, by manipulating joint angle. Ten subjects performed knee extension contractions at 30 degrees and 90 degrees knee-joint angles during which the ITT and CAR methods were applied using 1, 2, 4, and 8 electrical stimuli. Joint angle influenced the ITT outcome with higher values taken at 90 degrees (P < 0.05), while the number of stimuli influenced the CAR outcome with a higher number of stimuli yielding lower values (P < 0.05). For any given joint angle and stimulus number, the CAR method produced higher activation values than the ITT method by 8%-16%. Therefore, in the quantification of voluntary drive with the ITT and CAR methods consideration should be given not only to the number of stimuli applied but also to the effect of series elasticity due to joint-angle differences, since these factors may differently affect the outcome of the calculation, depending on the approach followed.

The effect of series elasticity on actuator power and work output: Implications for robotic and prosthetic joint design

Evidence from biomechanics research suggests that tendon series elasticity allows muscle to act in an optimal range of its force–length and force–velocity curves to achieve work and power amplification. In this investigation we put forth a simple model to quantify the capacity of series elasticity to increase work and power output from an actuator. We show that an appropriate spring constant increases the energy that an actuator can deliver to a mass by a factor of 4. The series elasticity changes the actuator operating point along its force–velocity curve and therefore affects the actuator work output over a fixed stroke length. In addition, the model predicts that a series spring can store energy and deliver peak powers greater than the power limit of the source by a factor of 1.4. Preliminary experiments are performed to test model predictions. We find qualitative agreement between the model and experimental data, highlighting the importance of series elasticity for actuator work and power amplification across a fixed stroke length. We present several non-dimensional relations that can aid designers in the fabrication of robotic and prosthetic limbs optimized for work and power delivery.

Contribution of Muscle Series Elasticity to Maximum Performance in Drop Jumping

The contribution of muscle in-series compliance on maximum performance of the muscle tendon complex was investigated using a forward dynamic computer simulation. The model of the human body contains 8 Hill-type muscles of the lower extremities. Muscle activation is optimized as a function of time, so that maximum drop jump height is achieved by the model. It is shown that the muscle series elastic energy stored in the downward phase provides a considerable contribution (32%) to the total muscle energy in the push-off phase. Furthermore, by the return of stored elastic energy all muscle contractile elements can reduce their shortening velocity up to 63% during push-off to develop a higher force due to their force velocity properties. The additional stretch taken up by the muscle series elastic element allows only m. rectus femoris to work closer to its optimal length, due to its force length properties. Therefore the contribution of the series elastic element to muscle performance in maximum height drop jumping is to store and return energy, and at the same time to increase the force producing ability of the contractile elements during push-off.