Compliant Elements Research Articles

Analysis of planar compliant mechanisms based on non-linear analytical modeling including shear and lateral contraction

Compliant mechanisms are commonly used in precision engineering while analyzing their deflection is particularly challenging. Often, FEM simulations are chosen in an iterative process. Analytical approaches that consider pure bending, shear or other effects are usually limited to the mechanism as a system. However, certain configurations comprise compliant elements with different aspect ratios. The aim of this paper is to integrate the theories of shear and lateral contraction into a unified form with the existing theory of bending for large deflections and make them applicable individually for specific sections of continuous compliant mechanisms. Recommendations are made as to when which theory should be used. Building on that, a comprehensive tool for analyzing compliant mechanisms developed in Python is introduced. The tool offers the possibility to create arbitrary compliant mechanisms including branched links and various boundary conditions. A tool for parametric studies allows to optimize the given geometry for realizing a specific motion task. Further, FEM and measurement results correlate well with the application results. The presented user interface can be beneficial for the accelerated analysis and synthesis of compliant mechanisms.

Physical Human-Robot Interaction Using HandsOn-SEA: An Educational Robotic Platform With Series Elastic Actuation.

For gaining proficiency in physical human-robot interactions, it is crucial for engineering students to be provided with the opportunity to gain hands-on experience with robotic devices that feature kinesthetic feedback. In this article, we propose HandsOn-SEA, a low-cost, single degree-of-freedom, force-controlled educational robot with series elastic actuation and introduce educational modules for the use of the device to allow students to experience the fundamental performance trade-offs inherent in robotic systems. The novelty of the proposed robot is due to the deliberate introduction of a compliant element between the actuator and the handle, whose deflections are measured to perform closed-loop force control. As an admittance-type robot, HandsOn-SEA relies on force feedback to achieve the desired level of safety and transparency and complements the existing impedance-type educational robots. We present the integration of HandsOn-SEA into the robotics curriculum, by providing guidelines for its use in a senior level robotics course, to help students experience the challenges involved in the synergistic design and control of robotic devices. We systematically evaluate the efficacy of the device in a robotics course delivered for five semesters and provide evidence that HandsOn-SEA is effective in instilling fundamental concepts and trade-offs in the design and control of robotic devices.

The Shari’ah Compliance Spa for Wellness and Tourism Context in Malaysia

Spa, Tourism and Wellness are a relatively new trend that has registered an impressive growth rate. The spa market has turned into the fastest growing leisure sector which provide facilities as venue to improve a person’s health and well-being. In Malaysia, Shari’ah compliance spa has increasingly becoming an important marketing strategy which attract customers in the context of wellness industry. This is parallel with the growing demand for products and services that comply with Islamic law with consideration trend nowadays. Thus, there are specific criteria for the spa sector to be complied for a Shari’ah compliance. The Shari’ah compliance elements practiced by Islamic Spa Practices (ISP) include the usages of Halal Products; Gender Segregations in Treatments and Procedures, as well as Physical Construct Elements. The five vital elements of Maqasid Shar’iyyah which were Protection of Religion (Al-Diin); Protection of Life (Al-Hayah); Protection of Mind (Al-‘Aql); Protection of Dignity (Al-Muru’ah); and Protection of Wealth (Al-Mal) considered in delivering the Shari’ah Compliance Spa. To date, there is no much framework that elaborates the Shari’ah compliance spa that includes the ISP practices and Maqasid Shar’iyyah elements. However, an initial framework of Sha’riah compliance spa is developed based on the Muslim-friendly hospital services

A Cable-Driven Three-DOF Wrist Rehabilitation Exoskeleton With Improved Performance.

This paper developed a cable-driven three-degree-of-freedom (DOF) wrist rehabilitation exoskeleton actuated by the distributed active semi-active (DASA) system. Compared with the conventional cable-driven robots, the workspace of this robot is increased greatly by adding the rotating compensation mechanism and by optimizing the distribution of the cable attachment points. In the meanwhile, the efficiency of the cable tension is improved, and the parasitic force (the force acting on the joint along the limb) is reduced. Besides, in order to reduce the effects of compliant elements (e.g., cables or Bowden cables) between the actuators and output, and to improve the force bandwidth, we designed the DASA system composed of one geared DC motor and four magnetorheological (MR) clutches, which has low output inertia. A fast unbinding strategy is presented to ensure safety in abnormal conditions. A passive training algorithm and an assist-as-needed (AAN) algorithm were implemented to control the exoskeleton. Several experiments were conducted on both healthy and impaired subjects to test the performance and effectiveness of the proposed system for rehabilitation. The results show that the system can meet the needs of rehabilitation training for workspace and force-feedback, and provide efficient active and passive training.

Kinematic Modelling and Motion Analysis of a Humanoid Torso Mechanism

This paper introduces a novel kinematic model for a tendon-driven compliant torso mechanism for humanoid robots, which describes the complex behaviour of a system characterised by the interaction of a complex compliant element with rigid bodies and actuation tendons. Inspired by a human spine, the proposed mechanism is based on a flexible backbone whose shape is controlled by two pairs of antagonistic tendons. First, the structure is analysed to identify the main modes of motion. Then, a constant curvature kinematic model is extended to describe the behaviour of the torso mechanism under examination, which includes axial elongation/compression and torsion in addition to the main bending motion. A linearised stiffness model is also formulated to estimate the static response of the backbone. The novel model is used to evaluate the workspace of an example mechanical design, and then it is mapped onto a controller to validate the results with an experimental test on a prototype. By replacing a previous approximated model calibrated on experimental data, this kinematic model improves the accuracy and efficiency of the torso mechanism and enables the performance evaluation of the robot over the reachable workspace, to ensure that the tendon-driven architecture operates within its wrench-closure workspace.

Collective Force Generator Model of Muscle Contraction

Muscle contraction results from cyclic interactions of actin-myosin binding coupled to the catalyzed hydrolysis of ATP. Although the mechanics and kinetics of muscle myosins are well established, it is less evident how these single molecule behaviors scale up to the collective behaviors of many myosin molecules working together. We have developed a computer simulation of collective force generation by myosin molecules based on well-established kinetic and mechanical properties of single myosin molecules and use an in-vitro motility assay to test model predictions. A collective force model predicts that even in in vitro motility assays myosin heads collectively generate force in common compliant elements and at sufficiently high numbers, N, reach a stall force Consistent with our collective force model, we show that ATPase activity in a motility assay increases linearly at low myosin density, saturating with actin sliding velocities, V, at high myosin densities. We show that activation of V upon addition of inorganic phosphate, Pi, results from Pi decreasing the auto-inhibiting collective force, which in turn activates the ATPase activity. Collective force generation by myosin results in unexpected emergent mechanical behaviors that offer new interpretations for how muscle works.

Torque-Sensorless Control of Stepper Motors for Low-Cost Compliant Motion Generation

Actuators that can generate controllable compliant output motion are suitable for robots that need to interact safely with humans or the environment. To obtain the accurate output torque required to control the compliant motion, existing robotic actuators use one or more sensors to measure the deformation of a stiff or compliant element between the actuator and the output. The complexity, reliability, and cost of sensors are the current challenges. Deformation-based sensing also suffers from limited bandwidth and stability range. This paper proposes a torque-sensorless control method of stepper motors to generate compliant motion. Stepper motors are used because of their low cost and reliability. They also have a much higher torque-to-weight ratio and torque-to-rotor-inertia ratio than other DC motors. Torque and impedance controllers based on stepper motor current feedback are developed. Torque-sensorless impedance, and gripping force control experiments are provided to show the advantages of the proposed method. It is expected that the new control method for stepper motors can offer a competitive alternative when cost, stability, or bandwidth of complaint actuators are the major concerns.

A Reconfigurable and Adjustable Compliance System for the Measurement of Interface Orthotic Properties.

A measurement system which provides INterface with Tunable Ergonomic properties using a Reconfigurable Framework with Adjustable Compliant Elements (INTERFACE system) is developed to implement the Rapid Evaluate and Adjust Device (READ) methodology. The geometry and stiffness of the Medial Longitudinal Arch (MLA) support provided by the INTERFACE system can be adjusted via linear actuators and tunable stiffness mechanisms, based on objective interface pressure/load distribution and subjective feedback evaluations. Validation tests were conducted on 13 subjects to measure the plantar pressure/load distribution and record the subjective feedback in different combinations of geometry and stiffness. The interface pressure/load distribution and subjective feedback of the support level indicate the efficacy of the adjustable geometry and stiffness. As the stiffness and geometrical height increased, the plantar loadings increased in the MLA region and decreased in the rear foot. Geometrical fitting can be achieved with the reconfigurable MLA support. The integration of locally adjustable stiffness makes it possible to fine tune the plantar pressure/load and provides the subjects with options of orthotic stiffness. The proposed INTERFACE system can be applied to conduct the measurement of the desired orthotic properties which satisfy the interface pressure/load requirement and the subject's comfort.

Optimized Design for Cable-Driven Shoulder-Elbow Exoskeleton Robot

The cable-driven exoskeletons have the advantages of low inertia and simple structure, and they are widely applied for human augmentation and rehabilitation. However, they have limited workspace and tension efficiency because of the unidirectional nature of the cables. The limited performance affects the human-robot interaction and leads to potential danger. The workspace and tension efficiency can be optimized by conventional methods, which are adjusting the cable attachment points and increasing the actuators. But the workspace still cannot cover the human joint space of activities of daily living, and the efficiency is also not high. This paper analyzed the specific application for shoulder and elbow joints rehabilitation and proposed a dynamic adaptive structure. This design can increase the workspace and improve tension efficiency greatly. The dynamic compensation control strategy is designed for the optimized system. Besides, in order to reduce the effects of compliant elements (e.g., cables or Bowden cables) between the actuators and output, and to improve the force bandwidth, we designed the distributed active semi-active system composed of the geared DC motor and magnetorheological clutches, which has low output inertia. The related experiments are carried out based on several healthy subjects. The results verified that the exoskeleton with the dynamic adaptive structure has a large workspace covering the activities of daily living joint space, high tension efficiency, and high force bandwidth, which is beneficial for the safety and comfort of human-robot interaction during rehabilitation training.

Topology Optimization of Linkage Mechanisms Simultaneously Considering Both Kinematic and Compliance Characteristics

Abstract Studies on the topology optimization of linkage mechanisms have thus far focused mainly on mechanism synthesis considering only kinematic characteristics describing a desired path or motion. Here, we propose a new topology optimization method that synthesizes a linkage mechanism considering both kinematic and compliance (K&C) characteristics simultaneously, as compliance characteristics can also significantly affect the linkage mechanism performance; compliance characteristics dictate how elastic components, such as bushings in a vehicle suspension, are deformed by external forces. To achieve our objective, we use the spring-connected rigid block model (SBM) developed earlier for mechanism synthesis considering only kinematic characteristics, but we make it suitable for the simultaneous consideration of K&C characteristics during mechanism synthesis by making its zero-length springs multifunctional. Variable stiffness springs were used to identify the mechanism kinematic configuration only, but now in the proposed approach, they serve to determine not only the mechanism kinematic configuration but also the compliance element distribution. In particular, the ground-anchoring springs used to anchor a linkage mechanism to the ground are functionalized to simulate actual bushings and to identify the desired linkage kinematic chain. After the proposed formulation and numerical implementation are presented, case studies are considered. In particular, the effectiveness of the proposed method is demonstrated with a simplified two-dimensional vehicle suspension design problem.

Building Block Synthesis of Self-Supported Three-Dimensional Compliant Elements for Metallic Additive Manufacturing

Abstract Compliant mechanisms gain motion through the elastic deformation of the monolithic flexible elements. The geometric design freedom of metallic additive manufacturing enables the fabrication of complex and three-dimensional (3D) compliant elements within mechanisms previously too complicated to produce. However, the design of metallic additive manufactured mechanisms faces various challenges of manufacturing restrictions, such as avoiding critical overhanging geometries and minimizing the amount of support structure, which has been reported in a few cases. This paper presents a synthesis approach for translational compliant elements, involving building blocks based on leaf-type springs and covering building orientations between 0 deg and 90 deg. In particular, this range is approached by the synthesis of self-supported 3D building blocks with orientations of 0 deg, 45 deg and 90 deg. The compliant elements are built based on linear and circular plane curves and compared numerically according to their mechanical performance to create preferable building blocks. The applicability of the presented procedure and the manufacturability of the compliant mechanisms are proven by printing individual 3D building blocks and their serial aggregation with laser-based powder bed fusion. Consequently, several prototypes are demonstrated, including a bistable switch mechanism and a large displaceable rotational spring joint. In addition, a small-scale highly maneuverable segment of a surgical instrument with a grasping mechanism at the distal end is proposed.

Minimization of the Energy Consumption in Industrial Robots through Regenerative Drives and Optimally Designed Compliant Elements

This paper describes a method for reducing the energy consumption of industrial robots and electrically actuated mechanisms performing cyclic tasks. The energy required by the system is reduced by outfitting it with additional devices able to store and recuperate energy, namely, compliant elements coupled in parallel with axles and regenerative motor drives. Starting from the electromechanical model of the modified system moving following a predefined periodic path, the relationship between the electrical energy and the stiffness and preload of the compliant elements is analyzed. The conditions for the compliant elements to be optimal are analytically derived. It is demonstrated that under these conditions the compliant elements are always beneficial for reducing the energy consumption. The effectiveness of the design method is verified by applying it to two test cases: a five-bar mechanism and a SCARA robot. The numerical validations show that the system energy consumption can be reduced up to the 77.8% while performing a high-speed, standard, not-optimized trajectory.

Off-axis frequency response in a dual diaphragm, uniphase moving coil microphone

When the rear port in a uniphase, unidirectional condenser microphone is modified to include a series compliance element (dual diaphragm) the low frequency performance can be improved. The benefit is most notable in the off-axis response as it relates to source/receiverproximity (proximity effect). Due to the significant operational differences between uniphase moving coil and condenser microphones, incorporating a dual diaphragm element into the rear port of a moving coil microphone requires careful attention to the design. Simplified network models of the uniphase system, proximity effect, and dual diaphragm moving coil design are presented. Measured results of a dual diaphragm, uniphase moving coil microphone are presented with off-axis response comparisons to a single diaphragm, uniphase moving coil microphone.

Control Architecture for Human-Like Motion With Applications to Articulated Soft Robots.

Human beings can achieve a high level of motor performance that is still unmatched in robotic systems. These capabilities can be ascribed to two main enabling factors: (i) the physical proprieties of human musculoskeletal system, and (ii) the effectiveness of the control operated by the central nervous system. Regarding point (i), the introduction of compliant elements in the robotic structure can be regarded as an attempt to bridge the gap between the animal body and the robot one. Soft articulated robots aim at replicating the musculoskeletal characteristics of vertebrates. Yet, substantial advancements are still needed under a control point of view, to fully exploit the new possibilities provided by soft robotic bodies. This paper introduces a control framework that ensures natural movements in articulated soft robots, implementing specific functionalities of the human central nervous system, i.e., learning by repetition, after-effect on known and unknown trajectories, anticipatory behavior, its reactive re-planning, and state covariation in precise task execution. The control architecture we propose has a hierarchical structure composed of two levels. The low level deals with dynamic inversion and focuses on trajectory tracking problems. The high level manages the degree of freedom redundancy, and it allows to control the system through a reduced set of variables. The building blocks of this novel control architecture are well-rooted in the control theory, which can furnish an established vocabulary to describe the functional mechanisms underlying the motor control system. The proposed control architecture is validated through simulations and experiments on a bio-mimetic articulated soft robot.

Nonlinear and linearized gray box models of direct-write printing dynamics

PurposeThe purpose of this study is to develop nonlinear and linearized models of DW printing dynamics that capture the complexity of DW while remaining integrable into control schemes. Control of material metering in extrusion-based additive manufacturing modalities, such as positive displacement direct-write (DW), is critical for manufacturing accuracy. However, in DW, transient flows are poorly controlled due to capacitive pressure dynamics – pressure is stored and slowly released over time from the build material and other compliant system elements, adversely impacting flow rate start-ups and stops. Thus far, modeling of these dynamics has ranged from simplistic, potentially omitting key contributors to the observed phenomena, to highly complex, making usage in control schemes difficult.Design/methodology/approachThe authors present nonlinear and linearized models that seek to both capture the capacitive and nonlinear resistive fluid elements of DW systems and to pose them as ordinary differential equations for integration into control schemes. The authors validate the theoretical study with experimental flow rate and material measurements across a range of extrusion nozzle sizes and materials. The authors explore the contribution of the system and build material bulk modulus to these dynamics.FindingsThe authors show that all tested models accurately describe the measured dynamics, facilitating ease of integration into future control systems. Additionally, the authors show that system bulk modulus may be substantially reduced through appropriate system design. However, the remaining build material bulk modulus is sufficient to require feedback control for accurate material delivery.Originality/valueThis study presents new nonlinear and linear models for DW printing dynamics. The authors show that linear models are sufficient to describe the dynamics, with small errors between nonlinear and linear models. The authors demonstrate control is necessary for accurate material delivery in DW.

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.

Granular Jamming Feet Enable Improved Foot-Ground Interactions for Robot Mobility on Deformable Ground

Recent studies on dynamic legged locomotion have focused on incorporating passive compliant elements into robot legs which can help with energy efficiency and stability, enabling them to work in wide range of environments. In this work, we present the design and testing of a soft robotic foot capable of active stiffness control using granular jamming. This foot is designed and tested to be used on soft, flowable ground such as sand. Granular jamming feet enable passive foot shape change when in contact with the ground for adaptability to uneven surfaces, and can also actively change stiffness for the ability to apply sufficient propulsion forces. We seek to study the role of shape change and stiffness change in foot-ground interactions during foot-fall impact and shear. We have measured the acceleration during impact, surface traction force, and the force to pull the foot out of the medium for different states of the foot. We have demonstrated that the control of foot stiffness and shape using the proposed foot design leads to improved locomotion, specifically a 52% reduced foot deceleration at the joints after impact, 63% reduced depth of penetration in the sand on impact, higher shear force capabilities for a constant depth above the ground, and 98% reduced pullout force compared to a rigid foot.

Virtual and physical prototyping of a beam-based variable stiffness actuator for safe human-machine interaction

Abstract This paper reports about the virtual and physical prototyping of an antagonistic Variable Stiffness Actuator (VSA) to be used on robotic arms specifically realized for physical human-robot interaction. Such antagonistic actuation system, which comprises purposely conceived Compliant Transmission Elements (CTEs) characterized by a nonlinear relation between the deflection and the applied torque, allows to simultaneously control both the joint’s position and stiffness. The CTE’s beams geometry, namely slender spline beams, has been defined by means of an automatic routine leveraging on Matlab and ANSYS and allowing for the shape optimization of complex flexures. The synthesized springs are characterized by a predefined quadratic torque-deflection characteristic, which is shown to guarantee a precise stiffness modulation while avoiding the need for a joint’s position sensor. After shape optimization, the CTE is fabricated via additive manufacturing and subsequently tested. The acquired data show a very good consistency with the numerical results, although highlighting a non-negligible hysteresis due to material damping. Therefore, in order to cope with such unavoidable effect along with other parameter uncertainties and unmodeled effects (e.g. static friction), a robust feedback controller is proposed, allowing for the simultaneous and decoupled regulation of joint position and stiffness. Finally, a VSA prototype is produced and tested. Experimental results confirm that the VSA behaves as expected.

Time-Optimal Trajectory Planning for Flexible Joint Robots

In this letter, a new approach is proposed to optimally plan the motion along a parametrized path for flexible joint robots, i.e., robots whose structure is purposefully provided with compliant elements. State-of-the-art methods efficiently solve the problem in case of torque-controlled rigid robots via a translation of the optimal control problem into a convex optimization problem. Recently, we showed that, for jerk-controlled rigid robots, the problem could be recast into a non-convex optimization problem. The non-convexity is given by bilinear constraints that can be efficiently handled through McCormick relaxations and spatial Branch-and-Bound techniques. In this letter, we show that, even in case of robots with flexible joints, the time-optimal trajectory planning problem can be recast into a non-convex problem in which the non-convexity is still given by bilinear constraints. We performed experimental tests on a planar 2R elastic manipulator to validate the benefits of the proposed approach. The scalability of the method for robots with multiple degrees of freedom is also discussed.

Biped Robots With Compliant Joints for Walking and Running Performance Growing

This paper deals with the problem of compliance in biped robots locomotion. After a first literature review, we designed and simulated a 3D virtual model of a biped robot conceived with the same link dimensions (and weights) of a standard man. In all simulation, the same input to the robot actuators is proposed, modifying only the compliance. We first validated the model and then compared results increasing and reducing compliance on hip, knee and ankle joints. The very good results underline how the robot performances may be increased including the compliant element in the knee. In particular, we noted how including a proper value of the compliance in the knee, power and torque of the actuators may be reduced increasing robot speed.