Series Elastic Element Research Articles

Relationship between resting medial gastrocnemius stiffness and drop jump performance

Although the influence of the series elastic element of the muscle–tendon unit on jump performance has been investigated, the corresponding effect of the parallel elastic element remains unclear. This study examined the relationship between the resting calf muscle stiffness and drop jump performance. Twenty-four healthy men participated in this study. The shear moduli of the medial gastrocnemius and the soleus were measured at rest as an index of muscle stiffness using ultrasound shear wave elastography. The participants performed drop jumps from a 15 cm high box. The Spearman rank correlation coefficient was used to examine the relationships between shear moduli of the muscles and drop jump performance. The medial gastrocnemius shear modulus showed a significant correlation with the drop jump index (jump height/contact time) (r = 0.414, P = 0.044) and jump height (r = 0.411, P = 0.046), but not with contact time (P > 0.05). The soleus shear modulus did not correlate with these jump parameters (P > 0.05). These results suggest that the resting medial gastrocnemius stiffness can be considered as one of the factors that influence drop jump performance. Therefore, increase in resting muscle stiffness should enhance explosive athletic performance in training regimens.

Muscle-Tendon Behavior and Kinetics in Gastrocnemius Medialis During Forefoot and Rearfoot Strike Running.

The present study aimed to clarify the effect of the foot strike pattern on muscle-tendon behavior and kinetics of the gastrocnemius medialis during treadmill running. Seven male participants ran with 2 different foot strike patterns (forefoot strike [FFS] and rearfoot strike [RFS]), with a step frequency of 2.50Hz and at a speed of 2.38m/s for 45seconds on a treadmill with an instrumented force platform. The fascicle behavior of gastrocnemius medialis was captured using a B-mode ultrasound system with a sampling rate of 75Hz, and the mechanical work done and power exerted by the fascicle and tendon were calculated. At the initial contact, the fascicle length was significantly shorter in the FFS than in the RFS (P = .001). However, the fascicular velocity did not differ between strike patterns. Higher tendon stretch and recoil were observed in the FFS (P < .001 and P = .017, respectively) compared with the RFS. The fascicle in the positive phase performed the same mechanical work in both the FFS and RFS; however, the fascicle in the negative phase performed significantly greater work in the FFS than in the RFS (P = .001). RFS may be advantageous for requiring less muscular work and elastic energy in the series elastic element compared with the FFS.

Design and optimisation of load-adaptive actuator with variable stiffness for compact ankle exoskeleton

To overcome the limitations of linear series elastic actuators (SEAs) with constant stiffness, a novel load-adaptive actuator with variable stiffness is proposed for actuating ankle exoskeletons through an inverted slider-crank mechanism. Using the proposed actuator, the stiffness of the exoskeleton can be adjusted passively based on the external load and joint angle. To achieve compactness, a novel nonlinear spring mechanism with user-defined load–deflection behaviour is designed by combining a cam mechanism with parabolic beams; this proposed mechanism is used as the series elastic element of the proposed actuator. Dimensional optimisation of the ankle exoskeleton, including the actuator, is subsequently performed for maximising the energy efficiency based on gait biomechanics and considering the constraints of the inverted slider-crank mechanism, electric motor, and the nonlinear spring mechanism. Simulation and experimental results show that the energy efficiency is improved by using the proposed load-adaptive actuator-powered ankle exoskeleton compared with using an exoskeleton driven by linear SEAs.

Force variability is mostly not motor noise: Theoretical implications for motor control.

Variability in muscle force is a hallmark of healthy and pathological human behavior. Predominant theories of sensorimotor control assume ‘motor noise’ leads to force variability and its ‘signal dependence’ (variability in muscle force whose amplitude increases with intensity of neural drive). Here, we demonstrate that the two proposed mechanisms for motor noise (i.e. the stochastic nature of motor unit discharge and unfused tetanic contraction) cannot account for the majority of force variability nor for its signal dependence. We do so by considering three previously underappreciated but physiologically important features of a population of motor units: 1) fusion of motor unit twitches, 2) coupling among motoneuron discharge rate, cross-bridge dynamics, and muscle mechanics, and 3) a series-elastic element to account for the aponeurosis and tendon. These results argue strongly against the idea that force variability and the resulting kinematic variability are generated primarily by ‘motor noise.’ Rather, they underscore the importance of variability arising from properties of control strategies embodied through distributed sensorimotor systems. As such, our study provides a critical path toward developing theories and models of sensorimotor control that provide a physiologically valid and clinically useful understanding of healthy and pathologic force variability.

Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Muscle contraction is a fundamental biological process where molecular interactions between the myosin molecular motor and actin filaments result in contraction of a whole muscle, a process spanning size scales differing in eight orders of magnitude. Since unique behavior is observed at every scale in between these two extremes, to fully understand muscle function it is vital to develop multi-scale models. Based on simulations of classic measurements of muscle heat generation as a function of work, and shortening rate as a function of applied force, we hypothesize that a model based on molecular measurements must be modified to include a weakly-bound interaction between myosin and actin in order to fit measurements at the muscle fiber or whole muscle scales. This hypothesis is further supported by the model's need for a weakly-bound state in order to qualitatively reproduce the force response that occurs when a muscle fiber is rapidly stretched a small distance. We tested this hypothesis by measuring steady-state force as a function of shortening velocity, and the force transient caused by a rapid length step in Drosophila jump muscle fibers. Then, by performing global parameter optimization, we quantitatively compared the predictions of two mathematical models, one lacking a weakly-bound state and one with a weakly-bound state, to these measurements. Both models could reproduce our force-velocity measurements, but only the model with a weakly-bound state could reproduce our force transient measurements. However, neither model could concurrently fit both measurements. We find that only a model that includes weakly-bound cross-bridges with force-dependent detachment and an elastic element in series with the cross-bridges is able to fit both of our measurements. This result suggests that the force response after stretch is not a reflection of distinct steps in the cross-bridge cycle, but rather arises from the interaction of cross-bridges with a series elastic element. Additionally, the model suggests that the curvature of the force-velocity relationship arises from a combination of the force-dependence of weakly- and strongly-bound cross-bridges. Overall, this work presents a minimal cross-bridge model that has predictive power at the fiber level.

Design, Control and Evaluation of the Electro-Hydrostatic Actuator, PREHydrA, for Gait Restoration Exoskeleton Technology

A preliminary design for the PREHydrA (passive return, electro-hydrostatic actuator) concept; a high force density, remote actuator, is tested to requirements for wearable robotics technology intended for gait restoration; one of the most demanding tasks for wearable robotics. While the concept offers good wearability properties, it has never been used in wearable robotics for full support. This work shows that the combination of electro-hydrostatic actuators with a return force and series elastic element offers a good alternative to other actuation types. Custom and small commercial components are used in a design for the knee joint. An experimental setup with a pendulum representing a swinging lower leg was used to show force and angle tracking performance. The results of a maximum zero force (-400-1100 N actuator force range) tracking mean absolute error of 61 N (6.79 Nm joint torque error) at 5.5 Hz excitation and a full swing (70°) within 0.35 s (0.8 m/s actuator velocity), match or exceed current state of the art exoskeleton actuation and control and show that the PREHydrA concept is very well suited for application in exoskeleton technology, especially when the cylinder design is optimized.

Gastrocnemius Medialis Contractile Behavior Is Preserved During 30% Body Weight Supported Gait Training.

Rehabilitative body weight supported gait training aims at restoring walking function as a key element in activities of daily living. Studies demonstrated reductions in muscle and joint forces, while kinematic gait patterns appear to be preserved with up to 30% weight support. However, the influence of body weight support on muscle architecture, with respect to fascicle and series elastic element behavior is unknown, despite this having potential clinical implications for gait retraining. Eight males (31.9 ± 4.7 years) walked at 75% of the speed at which they typically transition to running, with 0% and 30% body weight support on a lower-body positive pressure treadmill. Gastrocnemius medialis fascicle lengths and pennation angles were measured via ultrasonography. Additionally, joint kinematics were analyzed to determine gastrocnemius medialis muscle–tendon unit lengths, consisting of the muscle's contractile and series elastic elements. Series elastic element length was assessed using a muscle–tendon unit model. Depending on whether data were normally distributed, a paired t-test or Wilcoxon signed rank test was performed to determine if body weight supported walking had any effects on joint kinematics and fascicle–series elastic element behavior. Walking with 30% body weight support had no statistically significant effect on joint kinematics and peak series elastic element length. Furthermore, at the time when peak series elastic element length was achieved, and on average across the entire stance phase, muscle–tendon unit length, fascicle length, pennation angle, and fascicle velocity were unchanged with respect to body weight support. In accordance with unchanged gait kinematics, preservation of fascicle–series elastic element behavior was observed during walking with 30% body weight support, which suggests transferability of gait patterns to subsequent unsupported walking.

Finite-difference and integral schemes for Maxwell viscous stress calculation in immersed boundary simulations of viscoelastic membranes.

The immersed boundary method (IBM) has been frequently utilized to simulate the motion and deformation of biological cells and capsules in various flow situations. Despite the convenience in dealing with flow-membrane interaction, direct implementation of membrane viscosity in IBM suffers severe numerical instability. It has been shown that adding an artificial elastic element in series to the viscous component in the membrane mechanics can efficiently improve the numerical stability in IBM membrane simulations. Recently Li and Zhang (Int J Numer Methods Biomed Eng 35:e3200, 2019) proposed a finite-difference method for calculating membrane viscous stress. In the present paper, two new schemes are developed based on the convolution integral expression of the Maxwell viscoelastic element. We then conduct several tests for the accuracy, stability, and efficiency performances of these three viscous stress schemes. By studying the behavior of a one-dimensional Maxwell element under sinusoidal deformation, we find that a good accuracy can be achieved by selecting an appropriate relaxation time. The twisting sphere tests confirm that, compared to the numerical errors induced by other components in capsule simulations, such as the finite element method for membrane discretization and IBM for flow-membrane interaction, the errors from the viscous stress calculation are negligible. Moreover, extensive simulations are conducted for the dynamic deformation of a spherical capsule in shear flow, using different numerical schemes and various combinations of the artificial spring constants and calculation frequency for the membrane viscous stress calculation. No difference is observed among the results from the three schemes; and these viscous stress schemes require very little extra computation time compared to other components in IBM simulations. The simulation results converge gradually with the increase in the artificial spring stiffness; however, a threshold value exists for the spring stiffness to maintain the numerical stability. The viscous stress calculation frequency has noapparent influence on the calculation results, but a large frequency number can cause the simulation to collapse. We therefore suggest to calculate the membrane viscous stress at each simulation time step, such that a better numerical stabilitycan be achieved. The three numerical schemes have nearly identical performances in all aspects, and they can all be utilized in future IBM simulations of viscoelastic membranes.

A Case Study on Influence of Utilizing Hill-Type Muscles on Mechanical Efficiency of Biped Running Gait

The presence of compliant elements in biped running mechanisms generates a smoother motion and decreases the impact forces. Biological creatures that have a complicated actuation system with parallel and series elastic elements in their muscles demonstrate very efficient and robust bipedal gaits. The main difficulty of implementing these systems is duplicating their complicated dynamics and control. This paper studies the effects of an actuation system, including Hill-type muscles on the running efficiency of a kneed biped robot model with point feet. In this research, we implement arbitrary trajectories compatible with the initial condition of the robot, and we calculate the necessary muscle forces using an analytical inverse dynamics model. To verify the results, we execute the direct dynamics of the robot with the calculated control inputs to generate the robot’s trajectory. Finally, we calculate the contractile element force of the muscles and its cost of transport, and we investigate the effects of the muscles’ elements on reducing or increasing the cost of transport of the gait and maximum actuating forces.

Torque Control of a Series Elastic Tendon-Sheath Actuation Mechanism

Tendon-sheath actuation mechanisms can provide compact and lightweight tendon routing. However, torque control of a tendon-sheath actuation system is challenging because of variable friction with respect to the sheath configuration. Model-based feedforward friction compensation algorithms have been developed to accurately deliver desired torque, but it is difficult to apply such algorithms to multi-degrees of freedom (DOFs) systems because of changes in sheath configurations that in turn alter the base tension and friction parameters. In this article, we develop a series elastic tendon-sheath actuation mechanism that allows feedforward torque control in multi-DOFs systems. The mechanism features series elastic elements on the motor side to reduce base tension changes and enable accurate input torque control. Friction is compensated by a feedforward controller with a modeled friction parameter to transmit desired torque to the distal joint under varying sheath configurations. The performance of the proposed series elastic tendon-sheath actuation mechanism is demonstrated in experiments using a control interface for a tele-operation system.

A System for Simple Robotic Walking Assistance With Linear Impulses at the Center of Mass.

Walking can be simplified as an inverted pendulum motion where both legs generate linear impulses to redirect the center of mass (COM) into every step. In this work, we describe a system to assist walking in a simpler way than exoskeletons by providing linear impulses directly at the COM instead of providing torques at the joints. We developed a novel waist end-effector and high-level controller for an existing cable-robot. The controller allows for the application of cyclic horizontal force profiles with desired magnitudes, timings, and durations based on detection of the step timing. By selecting a lightweight rubber series elastic element with optimal stiffness and carefully tuning the gains of the closed-loop proportional-integral-derivative (PID) controller in a number of single-subject experiments, we were able to reduce the within-step root mean square error between desired and actual forces up to 1.21% of body weight. This level of error is similar or lower compared to the performance of other robotic tethers designed to provide variable or constant forces at the COM. The system can produce force profiles with peaks of up to 15 ± 2% of body weight within a root mean square error (RMSE) of 2.5% body weight. This system could be used to assist patient populations that require levels of assistance that are greater than current exoskeletons and in a way that does not make the user rely on vertical support.

Contracting striated muscle has a dynamic I-band spring with an undamped stiffness 100 times larger than the passive stiffness.

Fast sarcomere-level mechanics in contracting intact fibres from frog skeletal muscle reveal an I-band spring with an undamped stiffness 100 times larger than the known static stiffness. This undamped stiffness remains constant in the range of sarcomere length 2.7-3.1µm, showing the ability of the I-band spring to adapt its length to the width of the I-band. The stiffness and tunability of the I-band spring implicate titin as a force contributor that, during contraction, allows weaker half-sarcomeres to equilibrate with in-series stronger half-sarcomeres, preventing the development of sarcomere length inhomogeneity. This work opens new possibilities for the detailed in situ description of the structural-functional basis of muscle dysfunctions related to mutations or site-directed mutagenesis in titin that alter the I-band stiffness. Force and shortening in the muscle sarcomere are due to myosin motors from thick filaments pulling nearby actin filaments toward the sarcomere centre. Thousands of serially linked sarcomeres in muscle make the shortening (and the shortening speed) macroscopic, while the intrinsic instability of in-series force generators is likely prevented by the cytoskeletal protein titin that connects the thick filament with the sarcomere end, working as an I-band spring that accounts for the rise of passive force with sarcomere length (SL). However, current estimates of titin stiffness, deduced from the passive force-SL relation and single molecule mechanics, are much smaller than what is required to avoid the development of large inhomogeneities among sarcomeres. In this work, using 4kHz stiffness measurements on a population of sarcomeres selected along an intact fibre isolated from frog skeletal muscle contracting at different SLs (temperature 4°C), we measure the undamped stiffness of an I-band spring that at SL>2.7µm attains a maximum constant value of ∼6pNnm-1 per half-thick filament, two orders of magnitude larger than expected from titin-related passive force. We conclude that a titin-like dynamic spring in the I-band, made by an undamped elastic element in-series with damped elastic elements, adapts its length to the SL with kinetics that provide force balancing among serially linked sarcomeres during contraction. In this way, the I-band spring plays a fundamental role in preventing the development of SL inhomogeneity.

Landing Attitude Control in 1-DOF Repeated Jumping Robot Using Series Elastic Component

By utilizing series elastic element for the jumping motion, it becomes possible to increase the energy input time and store the kinetic energy as elastic energy. Therefore, a higher jump height can be expected. In the aerial attitude control by exerting the joint torque, repeated jumping with a small number of degree of freedom is possible. In this study, we describe the landing attitude control in a 1-DOF robot using a series elastic component by exerting the joint torque aiming at repeated jumping. we optimize the torque time series, starting from the air and performing a series of movements from landing to jumping.

Do Stretch-Shortening Cycles Really Occur in the Medial Gastrocnemius? A Detailed Bilateral Analysis of the Muscle-Tendon Interaction During Jumping.

The effect of stretch-shortening cycles (SSCs) is often studied in laboratory settings, yet it remains unclear whether highly active muscle SSCs actually occur during in vivo movement. Nine highly trained jumping athletes performed single-leg pre-hop forward jumps at maximal effort. We hypothesized that these jumps would induce a SSC at the level of the muscle in the medial gastrocnemius. Kinematic and kinetic data were collected together with electromyography signals (EMG) and muscle fascicle length and pennation angle changes of the medial gastrocnemius of both legs and combined with a musculoskeletal model to calculate the stretch-shortening behavior of the muscle (fascicles) and tendon (series-elastic element). The length changes of the fascicles, longitudinal muscle displacement, series-elastic element, and whole muscle-tendon unit further allowed for a detailed analysis of the architectural gearing ratio between different phases of the SSC within a single movement. We found a SSC at the level of the joint, muscle-tendon unit and tendon but not at the muscle. We further found that the average architectural gearing ratio was higher during the stretching of the series-elastic element as compared to when the series-elastic element was shortening, yet this was not statistically tested because of low sample size for this parameter. However, we found no correlation when plotting the architectural gearing ratio as a function of the fascicle velocities at each instance in time. Despite the athletes having a clear preferred leg for jumping, we found no differences in any kinematic or kinetic parameter between the preferred and non-preferred leg or any parameter from the muscle-tendon interaction analysis other than a reduced longitudinal muscle shortening in the non-preferred leg (p = 0.008). We conclude that, although common at the level of the joints, MTUs, and tendon (series-elastic element), highly active SSCs very rarely occur in the medial gastrocnemius, even in movements that induce high loading. This has important implications for the translation of ex vivo findings on SSC effects, such as residual force enhancement, in this muscle. We further conclude that there is no precise tuning of the architectural gearing ratio in the medial gastrocnemius throughout the whole movement.

Hurry Up and Get Out of the Way! Exploring the Limits of Muscle-Based Latch Systems for Power Amplification.

Animals can amplify the mechanical power output of their muscles as they jump to escape predators or strike to capture prey. One mechanism for amplification involves muscle-tendon unit (MT) systems in which a spring element (series elastic element [SEE]) is pre-stretched while held in place by a "latch" that prevents immediate transmission of muscle (or contractile element, CE) power to the load. In principle, this storage phase is followed by a triggered release of the latch, and elastic energy released from the SEE enables power amplification (PRATIO=PLOAD/PCE,max >1.0), whereby the peak power delivered from MT to the load exceeds the maximum power limit of the CE in isolation. Latches enable power amplification by increasing the muscle work generated during storage and reducing the duration over which that stored energy is released to power a movement. Previously described biological "latches" include: skeletal levers, anatomical triggers, accessory appendages, and even antagonist muscles. In fact, many species that rely on high-powered movements also have a large number of muscles arranged in antagonist pairs. Here, we examine whether a decaying antagonist force (e.g., from a muscle) could be useful as an active latch to achieve controlled energy transmission and modulate peak output power. We developed a computer model of a frog hindlimb driven by a compliant MT. We simulated MT power generated against an inertial load in the presence of an antagonist force "latch" (AFL) with relaxation time varying from very fast (10ms) to very slow (1000ms) to mirror physiological ranges of antagonist muscle. The fastest AFL produced power amplification (PRATIO=5.0) while the slowest AFL produced power attenuation (PRATIO=0.43). Notably, AFLs with relaxation times shorter than ∼300ms also yielded greater power amplification (PRATIO>1.20) than the system driving the same inertial load using only an agonist MT without any AFL. Thus, animals that utilize a sufficiently fast relaxing AFL ought to be capable of achieving greater power output than systems confined to a single agonist MT tuned for maximum PRATIO against the same load.

Series Elastic Behavior of Biarticular Muscle-Tendon Structure in a Robotic Leg.

We investigate the role of lower leg muscle-tendon structures in providing serial elastic behavior to the hip actuator. We present a leg design with physical elastic elements in leg angle and virtual leg axis direction, and its impact onto energy efficient legged locomotion. By testing and comparing two robotic lower leg spring configurations, we can provide potential explanations of the functionality of similar animal leg morphologies with lower leg muscle-tendon network structures. We investigate the effects of leg angle compliance during locomotion. In a proof of concept, we show that a leg with a gastrocnemius inspired elasticity possesses elastic components that deflect in leg angle directions. The leg design with elastic elements in leg angle direction can store hip actuator energy in the series elastic element. We then show the leg's advantages in mechanical design in a vertical drop experiment. In the drop experiments the biarticular leg requires 46% less power. During drop loading, the leg adapts its posture and stores the energy in its springs. The increased energy storing capacity in leg angle direction reduces energy requirements and cost of transport by 31% during dynamic hopping to a cost of transport of 1.2 at 0.9 kg body weight. The biarticular robot leg design has major advantages, especially compared to more traditional robot designs. Despite its high degree of under-actuation, it is easy to converge into and maintain dynamic hopping locomotion. The presented control is based on a simple-to-implement, feed-forward pattern generator. The biarticular legs lightweight design can be rapidly assembled and is largely made from elements created by rapid prototyping. At the same time it is robust, and passively withstands drops from 200% body height. The biarticular leg shows, to the best of the authors' knowledge, the lowest achieved relative cost of transport documented for all dynamically hopping and running robots of 64% of a comparable natural runner's COT.

Modeling the Determinants of Mechanical Advantage During Jumping: Consequences for Spring- and Muscle-Driven Movement.

Systems powered by elastic recoil need a latch to prevent motion while a spring is loaded but allow motion during spring recoil. Some jumping animals that rely on elastic recoil use the increasing mechanical advantage of limb extensor muscles to accomplish latching. We examined the ways in which limb morphology affects latching and the resulting performance of an elastic-recoil mechanism. Additionally, because increasing mechanical advantage is a consequence of limb extension that may be found in many systems, we examined the mechanical consequences for muscle in the absence of elastic elements. By simulating muscle contractions against a simplified model of an extending limb, we found that increasing mechanical advantage can limit the work done by muscle by accelerating muscle shortening during limb extension. The inclusion of a series elastic element dramatically improves mechanical output by allowing for additional muscle work that is stored and released from the spring. This suggests that elastic recoil may be beneficial for more animals than expected when assuming peak isotonic power output from muscle during jumping. The mechanical output of elastic recoil depends on limb morphology; long limbs moving small loads maximize total work, but it is done at a low power, whereas shorter limbs moving larger loads do less work at a higher power. This work-power trade-off of limb morphology is true with or without an elastic element. Systems with relatively short limbs may have performance that is robust to variable conditions such as body mass or muscle activation, while long-limbed systems risk complete failure with relatively minor perturbations. Finally, a changing mechanical advantage latch allows for muscle work to be done simultaneously with spring recoil, changing the predictions for spring mechanical properties. Overall, the design constraints revealed by considering the mechanics of this particular latch will inform our understanding of the evolution of elastic-recoil mechanisms and our attempts to engineer similar systems.

Distinct mechanical properties in homologous spectrin-like repeats of utrophin

Patients with Duchenne muscular dystrophy (DMD) lack the protein dystrophin, which is a critical molecular component of the dystrophin-glycoprotein complex (DGC). Dystrophin is hypothesized to function as a molecular shock absorber that mechanically stabilizes the sarcolemma of striated muscle through interaction with the cortical actin cytoskeleton via its N-terminal half and with the transmembrane protein β-dystroglycan via its C-terminal region. Utrophin is a fetal homologue of dystrophin that can subserve many dystrophin functions and is therefore under active investigation as a dystrophin replacement therapy for DMD. Here, we report the first mechanical characterization of utrophin using atomic force microscopy (AFM). Our data indicate that the mechanical properties of spectrin-like repeats in utrophin are more in line with the PEVK and Ig-like repeats of titin rather than those reported for repeats in spectrin or dystrophin. Moreover, we measured markedly different unfolding characteristics for spectrin repeats within the N-terminal actin-binding half of utrophin compared to those in the C-terminal dystroglycan-binding half, even though they exhibit identical thermal denaturation profiles. Our results demonstrate dramatic differences in the mechanical properties of structurally homologous utrophin constructs and suggest that utrophin may function as a stiff elastic element in series with titin at the myotendinous junction.

Effect of habitual foot-strike pattern on the gastrocnemius medialis muscle-tendon interaction and muscle force production during running.

The interaction between gastrocnemius medialis (GM) muscle and Achilles tendon, i.e., muscle-tendon unit (MTU) interaction, plays an important role in minimizing the metabolic cost of running. Foot-strike pattern (FSP) has been suggested to alter MTU interaction and subsequently the metabolic cost of running. However, metabolic data from experimental studies on FSP are inconsistent, and a comparison of MTU interaction between FSP is still lacking. We, therefore, investigated the effect of habitual rearfoot and mid-/forefoot striking on MTU interaction, ankle joint work, and plantar flexor muscle force production while running at 10 and 14 km/h. GM muscle fascicles of 9 rearfoot and 10 mid-/forefoot strikers were tracked using dynamic ultrasonography during treadmill running. We collected kinetic and kinematic data and used musculoskeletal models to determine joint angles and calculate MTU lengths. In addition, we used dynamic optimization to assess plantar flexor muscle forces. During ground contact, GM fascicle shortening ( P = 0.02) and average contraction velocity ( P = 0.01) were 40-45% greater in rearfoot strikers than mid-/forefoot strikers. Differences in contraction velocity were especially prominent during early ground contact. Moreover, GM ( P = 0.02) muscle force was greater during early ground contact in mid-/forefoot strikers than rearfoot strikers. Interestingly, we did not find differences in stretch or recoil of the series elastic element between FSP. Our results suggest that, for the GM, the reduced muscle energy cost associated with lower fascicle contraction velocity in mid-/forefoot strikers may be counteracted by greater muscle forces during early ground contact. NEW & NOTEWORTHY Kinetic and kinematic differences between foot-strike patterns during running imply (not previously reported) altered muscle-tendon interaction. Here, we studied muscle-tendon interaction using ultrasonography. We found greater fascicle contraction velocities and lower muscle forces in rearfoot compared with mid-/forefoot strikers. Our results suggest that the higher metabolic energy demand due to greater fascicle contraction velocities might offset the lower metabolic energy demand due to lower muscle forces in rearfoot compared with mid-/forefoot strikers.

Closed-loop positive real optimal control of variable stiffness actuators

Series elastic actuators decouple stiff motors and gear trains from the load by an mechanic elastic element. This elastic element can be used as torque sensor, acts as an energy storage, decouples the actuator from exogenous high frequency excitation and contributes towards shock resistance and safety in human–robot interaction scenarios. A series elastic element, however, fundamentally limits the achievable actuator bandwidth. Variable stiffness actuators (VSA) were introduced to overcome bandwidth limitations in series elastic actuators and to provide the flexibility necessary for energy efficient operation. The variable elastic element, however, complicates the design of torque and impedance controllers, which have to be synthesised by employing contradicting design objectives, such as minimisation of the output impedance, robust stability and performance. To overcome these synthesis problems, we present a new controller design procedure that imposes a positive real constraint on the load output port function to guarantee a stable interaction with respect to a passive, yet otherwise unknown environment. Additional design requirements are subsequently cast into a generalised plant. A H∞ design procedure is employed to design a gain-scheduled torque controller, which adapts to the varying mechanical stiffness of the actuator. It is then extended with a new procedure for the parametrisation of a superimposed impedance control-loop. The space of parameters for the impedance controller is determined in such way that it guarantees a positive real actuator output port function. The control strategy is tested in an in silico environment and in experiments on a test-bench with the Mechanical-Rotary Impedance Actuator (MeRIA).