Parallel Elastic Elements Research Articles

Design and verification of a parallel elastic robotic leg

This paper presents the design and experimental verification of a parallel elastic robotic leg mechanism that aims to capture the dynamics of the linear mass-spring-damper model. The mechanism utilizes a wrapping cam mechanism to linearize the non-linear force resulting from the elongation of the parallel elastic element. Firstly, we explain the desired dynamics of the mass-spring-damper model, including the impact transitions, and the design of the wrapping cam mechanism. We then introduce a system identification procedure to estimate the parameters of the leg mechanism corresponding to the dynamic model. The estimated parameters are tested with a cross-validation approach to evaluate the mechanism’s performance in tracking the desired model. The experimental results show that the passive dynamics of the mechanism resemble the linear model as intended. Thus, the robot provides a basis for using parallel elastic actuation while using model-based controllers that benefit the analytic solutions of the linear model.

Crustal heterogeneity effects on coseismic deformation: numerical simulation of the 2008 MW 7.9 Wenchuan earthquake

Coseismic deformation of large earthquakes causes significant property damages and fatalities, which requires quantitative research of multiple disciplines such as geodesy, geological investigation, seismic tomography, and seismic dislocation theory. The finite element method accounts for material heterogeneity and geometric complexity, making it suitable for studying the coseismic deformation of large earthquakes. This paper develops a parallel elastic finite element program that utilizes split nodes and high-performance parallel computing technology on the FELAC software platform to study the coseismic deformation of large earthquakes. We verify the accuracy of the parallel elastic finite element program by comparing its results with the analytical solutions from seismic dislocation theory for four ideal earthquake cases. Finally, we established parallel elastic finite element models to study the coseismic deformation of the 2008 Wenchuan earthquake. The simulation results are consistent with the GPS and InSAR data. Coseismic surface deformation results are significantly influenced by medium regional heterogeneity with different layered structures besides the Longmenshan fault. The finite element program lay the foundation for the inversion of the coseismic fault rupture process based on the heterogeneous medium model and complex geometric model.

Optimization of Mono- and Bi-Articular Parallel Elastic Elements for a Robotic Arm Performing a Pick-and-Place Task

Optimization of Mono- and Bi-Articular Parallel Elastic Elements for a Robotic Arm Performing a Pick-and-Place Task

Actuation system modelling and design optimization for an assistive exoskeleton for disabled and elderly with series and parallel elasticity.

The aim of a robotic exoskeleton is to match the torque and angular profile of a healthy human subject in performing activities of daily living. Power and mass are the main requirements considered in the robotic exoskeletons that need to be reduced so that portable designs to perform independent activities by the elderly users could be adopted. This paper evaluates a systematic approach for the design optimization strategies of elastic elements and implements an actuator design solution for an ideal combination of components of an elastic actuation system while providing the same level of support to the elderly. A multi-factor optimization technique was used to determine the optimum stiffness and engagement angle of the spring within its elastic limits at the hip, knee and ankle joints. An actuator design framework was developed for the elderly users to match the torque-angle characteristics of the healthy human with the best motor and transmission system combined with series or parallel elasticity in an elastic actuator. With the optimized spring stiffness, a parallel elastic element significantly reduced the torque and power requirements up to 90% for some manoeuvres for the users to perform ADL. When compared with the rigid actuation system, the optimized robotic exoskeleton actuation system reduced the power consumption of up to 52% using elastic elements. A lightweight, smaller design of an elastic actuation system consuming less power as compared to a rigid system was realized using this approach. This will help to reduce the battery size and hence the portability of the system could be better adopted to support elderly uses in performing daily living activities. It was established that parallel elastic actuators (PEA) can reduce the torque and power better than series elastic actuators (SEA) in performing everyday tasks for the elderly.

Fitting a model to multiscale data suggests thick filament activation can produce force depression in muscle fibers.

Multiscale muscle models aim to connect muscle's molecular and organ-scale function to, e.g., inform the treatment of muscle diseases. Current muscle models have not quantitatively fit data spanning the molecular to cellular scales due, in part, to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single skinned rabbit psoas muscle fibers to ramp shortenings (5% amplitude) and step stretches (0.25%, 0.5%, 0.75% amplitude), performed on the plateau region of the force-length relationship. We isolated myosin from the same muscle source and, under similar conditions, performed single molecule and mini ensemble measurements of event duration and displacement using optical trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of the superrelaxed state, a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force following stretch (residual force enhancement). By optimizing the model fit to fiber measurements, we specified seven unknown parameters. The model then successfully predicted our molecular measurements from the optical trap and in vitro motility at different ATP concentrations. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale modeling efforts. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combined with thick filament activation serve to decrease the number of cycling cross-bridges.

Design and Electromechanical Performance Evaluation of a Powered Parallel-Elastic Ankle Exoskeleton

The widespread adoption of powered lower-limb exoskeletons for augmenting mobility requires energy-efficient actuation to provide meaningful assistance over relevant walking durations. We designed, modeled, and validated an ankle exoskeleton design with a parallel elastic element in the form of a carbon fiber leaf spring that stored and returned energy in parallel to a cable-drive ankle joint during stance phase. We assessed the impact of the parallel elastic element on the performance of the untethered robotic ankle exoskeleton at walking speeds of 0.75–1.25 m/s using a previously validated-controller, and a controller designed specifically to maximize the spring's benefit. The spring selected for our adult cohort had a stiffness of 97.2 Nm/rad, engaged best at 0-degrees ankle dorsiflexion, and produced 10–15 Nm peak assistive torque at all walking speeds. When tracking the previously validated exoskeleton controller, peak motor current was reduced by 14–20% and integrated current was reduced by 16–19% for parallel-elastic design vs. without spring engagement; this translated to 15–26% more assisted steps for the same battery capacity. When utilizing the controller designed to take advantage of the parallel spring torque, the number of assisted steps for the same battery capacity increased 46–76% compared to the no spring configuration depending on walking speed. Seeking to facilitate real-world adoption, this powered parallel elastic ankle exoskeleton design holds potential to significantly extend powered walking duration, and improve battery and motor life of operation by reducing peak and mean motor current requirements.

Design of a bioinspired cable driven actuator with clutched elastic elements for the ankle.

Bioinspiration can be used to improve the efficiency of these assistive biomechatronic devices. In this paper, a cable driven actuator for the human ankle was designed using a bioinspired approach. The torque reduction was achieved by means of force amplifying elements such as cables with pulley, and, to reduce the power requirements for the motor, the actuator mimics a muscle using a clutched parallel elastic element. The simulations to validate the model were performed using real gait data and the results prove the viability of the device to be used in anthropomorphic legs and exoskeletons. Although the losses due to friction were not considered, the simulations showed a reduction of 60% in the force peak and 40% in the power peak.

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.

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.

Modeling of Novel Compound Tendon-Sheath Artificial Muscle Inspired by Hill Muscle Model

Various types of artificial muscles have been developed in recent years. Nevertheless, they are not well suited to robot applications due to the defects of their mechanical properties, such as small output, limited shrinkage, and slow response. Moreover, portable designs are difficult to realize because of the special power-source requirement. For the shortcomings above, the paper presents a motor-driven tendon-sheath artificial muscle inspired by Hill muscle model. The series and parallel elastic elements both made up of linear springs are applied on the tendon-sheath actuation system. Consequently, the tendon-sheath artificial muscle is created with a compliant structure, variable elasticity, and high power transmission capacity. Next, a compound tendon-sheath artificial muscle transmission system similar to the form of antagonist muscles is modeled based on the static Coulomb friction model. The transmission model with a sinusoidal input is simulated and analyzed in detail. And experiments are performed to validate our transmission model. The model shows high accuracy in predicting the system output. At the frequency of 1 Hz, the fidelity of output torque is 92.3% and the output displacement is 94.2%. Moreover, the maximum output force of the tendon-sheath artificial muscle with 0.8 mm tendon (under the safety factor of 4) can reach 80 N.

A modelling approach for exploring muscle dynamics during cyclic contractions.

Hill-type muscle models are widely used within the field of biomechanics to predict and understand muscle behaviour, and are often essential where muscle forces cannot be directly measured. However, these models have limited accuracy, particularly during cyclic contractions at the submaximal levels of activation that typically occur during locomotion. To address this issue, recent studies have incorporated effects into Hill-type models that are oftentimes neglected, such as size-dependent, history-dependent, and activation-dependent effects. However, the contribution of these effects on muscle performance has yet to be evaluated under common contractile conditions that reflect the range of activations, strains, and strain rates that occur in vivo. The purpose of this study was to develop a modelling framework to evaluate modifications to Hill-type muscle models when they contract in cyclic loops that are typical of locomotor muscle function. Here we present a modelling framework composed of a damped harmonic oscillator in series with a Hill-type muscle actuator that consists of a contractile element and parallel elastic element. The intrinsic force-length and force-velocity properties are described using Bézier curves where we present a system to relate physiological parameters to the control points for these curves. The muscle-oscillator system can be geometrically scaled while preserving dynamic and kinematic similarity to investigate the muscle size effects while controlling for the dynamics of the harmonic oscillator. The model is driven by time-varying muscle activations that cause the muscle to cyclically contract and drive the dynamics of the harmonic oscillator. Thus, this framework provides a platform to test current and future Hill-type model formulations and explore factors affecting muscle performance in muscles of different sizes under a range of cyclic contractile conditions.

MATHEMATICAL MODEL OF DPKR-2 DYZEL TRAIN CAR

Purpose. In order to study the dynamic phenomena arising when rolling stock moves along a rail track both in the straight and curved track sections, the article is aimed to construct a mathematical model of DPKr-2 diesel train car. It will be constructed on the basis of mechanical model of this car of Kryukiv Railway Car Building Works. Methodology. To construct a mathematical model a system of 38 differential equations of the diesel train movement is formed. When it is used a pneumatic spring in the core stage of spring suspension, its equivalent mechanical mo-del is presented as Kelvin-Voigt knot. It includes a parallel elastic element and an element of viscous friction. Rail track flexibility is taken into account by elastic and dissipative elements. During simulation it was assumed that the wheel pair and the track weight interacting with it were moving intact. Geometric inequalities of the left and right rails were accepted as disturbances when studying the forced vertical and horizontal oscillations. Findings. On the basis of the adopted mechanical model of the diesel train car we constructed the mathematical model consisting of 38 differential equations of motion . Originality. For the first time, for the DPKr-2 diesel train car we developed its spatial mathematical model taking into account the features of the interaction of individual elements of its construction and the possibilities of the rail track depression. When constructing the mathematical model, it was proposed to take into account the flexibility of the rail track by elastic and dissipative elements. Originality. The mathematical model of the diesel train car will be used for studying the dynamic phenomena and determining the dynamic loads of structural elements during operation. The study of these phenomena is necessary for optimal choice of the scheme and parameters of rolling stock equipment, in particular antivibration devices (spring suspension, horizontal, longitudinal and transverse joints of wheel pairs with the bogie frame, bogie with the body), as well as for reduction of dynamic forces acting on the elements of rolling stock construction and rail track.

Optimizing the power and energy consumption of powered prosthetic ankles with series and parallel elasticity

Several works have shown that series and parallel elasticity can reduce peak power and energy consumption in prosthetic ankles. Setting the right stiffness of the elastic elements is essential to unlock this potential. In this work, we perform a thorough optimization of series and parallel elastic elements for a prosthetic ankle driven by a geared DC motor. Through simulation, we study the effect of drivetrain limitations and compare different mechanical and electrical optimization objectives. The results highlight the importance of selecting a motor and gearbox in an early stage of the design process. Drivetrain inertia causes peaks in electrical power in the swing phase, which would go unnoticed in an optimization based solely on mechanical power. Furthermore, limitations of the drivetrain and controller reduce the range of applicable springs. This has a direct influence on the optimized spring stiffness values, which, as a result, are different from other works. Overall, the results suggest that, by integrating motor selection into the early stages of the design process, designs can be made lighter, more compact and more efficient.

Parallel Elastic Elements Improve Energy Efficiency on the STEPPR Bipedal Walking Robot

This paper describes how parallel elastic elements can be used to reduce energy consumption in the electric-motor-driven, fully actuated, Sandia Transmission-Efficient Prototype Promoting Research (STEPPR) bipedal walking robot without compromising or significantly limiting locomotive behaviors. A physically motivated approach is used to illustrate how selectively engaging springs for hip adduction and ankle flexion predict benefits for three different flat-ground walking gaits: human walking, human-like robot walking, and crouched robot walking. Based on locomotion data, springs are designed and substantial reductions in power consumption are demonstrated using a bench dynamometer. These lessons are then applied to STEPPR, a fully actuated bipedal robot designed to explore the impact of tailored joint mechanisms on walking efficiency. Featuring high-torque brushless DC motors, efficient low-ratio transmissions, and high-fidelity torque control, STEPPR provides the ability to incorporate novel joint-level mechanisms without dramatically altering high-level control. Unique parallel elastic designs are incorporated into STEPPR, and walking data show that hip adduction and ankle flexion springs significantly reduce the required actuator energy at those joints for several gaits. These results suggest that parallel joint springs offer a promising means of supporting quasi-static joint torques due to body mass during walking, relieving motors of the need to support these torques and substantially improving locomotive energy efficiency.

Stabilization of the vertical reactions of the road on the wheel when driving automobile on periodic profile

For various reasons roads could be in not very good condition. In particular, at the roads could appear the areas with clearly defined periodic profile. The traffic on such road sections may be accompanied by resonance oscillations of the wheels with their separation from the road. This causes a decrease in stability of the vehicle. To combat this phenomenon the new system of active safety of the cat could be applied - stabilization system of the vertical reactions of the road on the wheel when driving on a periodic profile. Such a system to control the vertical reaction uses an execution unit called the actuator. This is the engine in the form of a hydraulic cylinder or linear motor that is included in suspension in the parallel elastic element and shock absorber. The actuator is controlled by a signal generated by the control unit, which receives a signal from the sensor of vertical force that is perceived by a bus or a signal to replace it. The article shows that the linear control system copes with the elimination of separation of wheel from the road, reducing fluctuations in the value of the vertical reaction to 10% of the static load. In the hydraulic control system vertical reaction of road on the wheel may cause the nonlinear relationship of the values of vertical reaction and the force generated by a hydraulic cylinder. The calculations showed the feasibility of stabilizing the vertical reactions in this case. However, this nonlinearity can cause some instability of vibrations of a vertical reaction. Another promising solution to the design of the hydraulic system of stabilization of the vertical reaction to the preservation of its sufficient efficiency is the use of hydraulic cylinders of unilateral action, which simplifies the system and makes it more available for use, even on compact automobiles.

Series and Parallel Elastic Actuation: Impact of natural dynamics on power and energy consumption

This paper provides a detailed analysis of the power and mechanical/electrical energy consumption of Series Elastic Actuators (SEAs) and Parallel Elastic Actuators (PEAs). The study is done by imposing a sinusoidal motion to a pendulum load, such that the natural dynamics automatically present itself in the power and energy consumption. This allows to link the actuators' dynamics to their loss mechanisms, revealing interesting characteristics of series and parallel elastic elements in actuator designs. Simulations demonstrate that the SEA and PEA allow to decrease both peak power and energy consumption, provided that the stiffness of their elastic element is tuned properly. For the SEA, both are minimized by tuning the elastic element to the antiresonance frequency of the actuator. For the PEA, peak power is minimal at the link's resonance frequency, but the optimal stiffness for minimal electrical energy consumption cannot be determined by a theoretical resonance and needs to be calculated using a complete system model. If these guidelines are followed, both types of elastic actuators can provide significant energetic benefits at high frequencies. This was confirmed by experiments, which demonstrated energy reductions of up to 78% (SEA) and 20% (PEA) compared to rigid actuators.

A comparison among different Hill-type contraction dynamics formulations for muscle force estimation

Abstract. Muscle is a type of tissue able to contract and, thus, shorten, producing a pulling force able to generate movement. The analysis of its activity is essential to understand how the force is generated to perform a movement and how that force can be estimated from direct or indirect measurements. Hill-type muscle model is one of the most used models to describe the mechanism of force production. It is composed by different elements that describe the behaviour of the muscle (contractile, series elastic and parallel elastic element) and tendon. In this work we analyze the differences between different formulations found in the literature for these elements. To evaluate the differences, a flexo-extension movement of the arm was performed, using as input to the different models the surface electromyography signal recorded and the muscle-tendon lengths and contraction velocities obtained by means of inverse dynamic analysis. The results show that the force predicted by the different models is similar and the main differences in muscle force prediction were observed at full-flexion. The results are expected to contribute in the selection of the different formulations of Hill-type muscle model to solve a specific problem.

Contraction dynamics and function of the muscle-tendon complex depend on the muscle fibre-tendon length ratio: a simulation study.

Experimental studies show different muscle-tendon complex (MTC) functions (e.g. motor or spring) depending on the muscle fibre-tendon length ratio. Comparing different MTC of different animals examined experimentally, the extracted MTC functions are biased by, for example, MTC-specific pennation angle and fibre-type distribution or divergent experimental protocols (e.g. influence of temperature or stimulation on MTC force). Thus, a thorough understanding of variation of these inner muscle fibre-tendon length ratios on MTC function is difficult. In this study, we used a hill-type muscle model to simulate MTC. The model consists of a contractile element (CE) simulating muscle fibres, a serial element (SE) as a model for tendon, and a parallel elastic element (PEE) modelling tissue in parallel to the muscle fibres. The simulation examines the impact of length variations of these components on contraction dynamics and MTC function. Ensuring a constant overall length of the MTC by L(MTC) = L(SE) + L(CE), the SE rest length was varied over a broad physiological range from 0.1 to 0.9 MTC length. Five different MTC functions were investigated by simulating typical physiological experiments: the stabilising function with isometric contractions, the motor function with contractions against a weight, the capability of acceleration with contractions against a small inertial mass, the braking function by decelerating a mass, and the spring function with stretch-shortening cycles. The ratio of SE and CE mainly determines the MTC function. MTC with comparably short tendon generates high force and maximal shortening velocity and is able to produce maximal work and power. MTC with long tendon is suitable to store and release a maximum amount of energy. Variation of muscle fibre-tendon ratio yielded two peaks for MTC's force response for short and long SE lengths. Further, maximum work storage capacity of the SE is at long relL(SE,0). Impact of fibre-tendon length ratio on MTC functions will be discussed. Considering a constant set of MTC parameters, quantitative changes in MTC performance (work, stiffness, force, energy storage, dissipation) depending on varying muscle fibre-tendon length ratio were provided, which enables classification and grading of different MTC designs.

Variable Recruitment of Parallel Elastic Elements: Series–Parallel Elastic Actuators (SPEA) With Dephased Mutilated Gears

The development and control of variable stiffness actuators (VSAs) led to the capability of embodying physical principles of safety and energy-efficiency compared to traditional stiff servomotors. However, the output torque range and efficiency of servomotors and VSAs are still insufficient which hinders the development of machines with performances comparable to a human. We have developed a novel compliant actuation concept, series-parallel elastic actuation (SPEA), that addresses these problems. The novelty being the variable recruitment of parallel elastic elements and adaptive load cancellation. In this paper, we propose the use of multiple dephased mutilated gears with locking ring and plate, as intermittent mechanisms, linked in parallel to the motor. As a result, the motor torque requirements can be lowered, as such the motor can be downscaled and the efficiency can be drastically increased. After an abstract description of the SPEA concept and an outline of the biological basis, we present the first unidirectional SPEA proof of concept (PoC) setup. Experiments on this PoC setup endorse the feasibility of the SPEA concept. The results match the modeled trend of a lowered motor torque and increased energy efficiency.

Design of an exoskeleton with minimized energy consumption based on using elastic and dissipative elements

This study proposes the design of an exoskeleton featuring minimized energy consumption during stand-to-sit and sit-to-stand (STS) motion and walking while carrying a load through the utilization of elastic and dissipative elements. In order to determine which phase and joint can utilize elastic and dissipative elements, we analyzed a human’s walk and STS motions. With this human motion data, we propose an elastic element for hip adduction and abduction (Ad/Ab), series dissipative actuation (SDA) using a semi-active hydraulic system for hip flexion and extension (Fl/Ex) and parallel elastic and series dissipative actuation (PESDA) for the knee Fl/Ex, which is combined with the SDA and the parallel elastic element. The effect of the developed exoskeleton (EXO) with a hip Ad/Ab spring, hip SDA and knee PESDA was evaluated by measuring the user’s ground reaction force (GRF). When wearing the EXO with a hip Ad/Ab spring, hip SDA and knee PESDA, the subject’s GRF was smaller as compared to when the subject was not wearing the EXO while walking and performing the STS motion under a 20-kg load condition, except during the heel strike of the walk motion.