Variable Stiffness Joint Research Articles

Design and Validation of a Novel Leaf Spring-Based Variable Stiffness Joint With Reconfigurability

Compliant joints can provide safer physical human–robot interaction. To effectively balance the response bandwidth and output impedance, variable stiffness joints have been studied by many researchers. Leaf spring-based variable stiffness joint (LSVSJ) has the advantages of easy construction and large stiffness range. This article presents the design and validation of a novel LSVSJ with reconfigurability (LSJR). Compared with most of the existing LSVSJ, this novel LSJR ensures the contact performance between the roller and the leaf spring, uses a novel effective length adjustment mechanism, and provides multiple stiffness ranges. The compliance of the LSJR is generated by leaf springs. The spring is bent by two rows of rollers integrated on an adjustable slider, where the distance between the rollers can be changed so as to achieve a tighter contact between the roller and the spring. The effective length of the spring can be adjusted by changing the position of the slider locating at the intersection between a straight rail and an arcuate rail. A reconfigurable number of leaf springs provide six different stiffness ranges (e.g., 138.55–396.08 N·m/rad for single leaf spring, and 384.56–1222.60 N·m/rad for a combination of three leaf springs). By integrating a high-resolution angle sensor, the LSJR can also measure the joint torque. Moreover, the hollow shaft structure of the joint is beneficial for passing cables through it. Experiments were performed to measure the stiffness of the LSJR under different configurations, validate its efficacy in unexpected collisions, and investigate its potential to be a one-degree-of-freedom torque sensor.

Influence of magnetic field, magnetic particle percentages, and particle diameters on the stiffness of magnetorheological fluids

Generally, variable stiffness joints of soft robots are generally fabricated using thermoplastics and elastomers due to their ability to change state from rigid to flexible and vice versa. However, these materials require a considerable amount of time to change states and are associated with other technical drawbacks. We demonstrate the instantaneous physical transformation of a Ga-based magnetorheological fluid called Gallistan from a liquid to a viscoelastic solid, and precisely controlled within milliseconds under an applied magnetic field. We studied the magnetic properties of a magnetorheological fluid by dispersing Fe particles in a Ga–In–Sn eutectic alloy. Theoretical analysis of the movement of two particles under magnetic field and typical defects in dipolar chains is studied. The experimental results showed a reversible change in Young’s modulus depending not only on the magnetic field intensity but also the percentage of magnetic particles. Thus, we confirm that the arrangement of magnetic particles transition from random distribution to stable chain structures in the magnetic field. Based on the bi-material nested cantilever beam, the variable stiffness joints can also be precisely adjusted under a magnetic field. In future, this property of the magnetorheological fluid will help develop a variable stiffness joint for soft robotics.

Analysis of Stiffness and Energy Consumption of Nonlinear Elastic Joint Legged Robot.

In order to reduce the energy consumption of the legged robot in walking, this paper designs a kind of nonlinear elastic joint from the flexible variable-stiffness joint based on the mammal walking on the limb and optimizes the leg structure of the legged robot. The motor is rigidly connected to the articulated lever. When the lever is accelerated or decelerated, the elastic unit is introduced. The system can be considered as a special variable-rate elastic system. This paper will study it from theory and simulation experiments. Based on the dynamic analysis, a functional relationship between the output torque and the torsion spring stiffness and between the energy consumption and the torsion spring stiffness was established. By finding the extremum, the two optimum torsional spring stiffness that can minimize the required output average torque and the energy consumed during one cycle of motion were deduced. The results show that using this design in a reasonable position can effectively reduce the energy consumption of the system and can achieve up to a 50% reduction in energy consumption.

Conceptual mechanical design of antagonistic variable stiffness joint based on equivalent quadratic torsion spring.

The variable stiffness joint is a kind of flexible actuator with variable stiffness characteristics suitable for physical human-robot interaction applications. In the existing variable stiffness joints, the antagonistic variable stiffness joint has the advantages of simple implementation of variable stiffness mechanism and easy modular design of the nonlinear elastic element. The variable stiffness characteristics of antagonistic variable stiffness joints are realized by the antagonistic actuation of two nonlinear springs. A novel design scheme of the equivalent nonlinear torsion spring with compact structure, large angular displacement range, and desired stiffness characteristics is presented in this article. The design calculation for the equivalent quadratic torsion spring is given as an example, and the actuation characteristics of the antagonistic variable stiffness joint based on the equivalent quadratic torsion spring are illustrated. Based on the design idea of constructing the antagonistic variable stiffness joint with compact structure and high compliance, as well as the different design requirements of the joints at different positions of the multi-degrees of freedom robot arm, nine types of mechanical schemes of antagonistic variable stiffness joint with the open design concept are proposed in this article. Finally, the conceptual joint configuration schemes of the robot arm based on the antagonistic variable stiffness joint show the application scheme of the designed antagonistic variable stiffness joint in the multi-degrees of freedom robot.

Design, Dynamics Analysis, and Real-Time Stiffness Control of a Variable Stiffness Joint

This paper proposes a variable stiffness joint based on a symmetrical crank slider mechanism (SCM-VSJ). Firstly, the mechanical design and the working principle of the variable stiffness joint is described, and its stiffness regulation characteristics are studied. Secondly, the dynamical model of variable stiffness joint including joint motor, harmonic reducer and stiffness adjustment motor is established, in addition, the transmission mechanism of the crank slider mechanism and the elastic deformation of the spring bar are considered in the dynamic modeling. Finally, in order to control the dynamic stiffness of the variable stiffness joint in real time, a kind of improved PID (proportional-integral-derivative) control algorithm based on feed-forward and feedback closed-loop is proposed on the basis of the existing dynamical model, and the simulation analysis of real-time tracking control of dynamic stiffness for sinusoidal wave expected stiffness signal and random expected stiffness signal is carried out respectively. The research shows that the real-time stiffness control of SCM-VSJ can be realized effectively, and during the stiffness adjustment process, the output torque of the stiffness adjustment motor will be affected by the elastic deformation of the spring bar.

Development of a Rigidity Tunable Flexible Joint Using Magneto-Rheological Compounds-Toward a Multijoint Manipulator for Laparoscopic Surgery.

Laparoscopic surgery is a representative operative method of minimally invasive surgery. However, most laparoscopic hand instruments consist of rigid and straight structures, which have serious limitations such as interference by the instruments and limited field of view of the endoscope. To improve the flexibility and dexterity of these instruments, we propose a new concept of a multijoint manipulator using a variable stiffness mechanism. The manipulator uses a magneto-rheological compound (MRC) whose rheological properties can be tuned by an external magnetic field. In this study, we changed the shape of the electromagnet and MRC to improve the performance of the variable stiffness joint we previously fabricated; further, we fabricated a prototype and performed basic evaluation of the joint using this prototype. The MRC was fabricated by mixing carbonyl iron particles and glycerol. The prototype single joint was assembled by combining MRC and electromagnets. The configuration of the joint indicates that it has a closed magnetic circuit. To examine the basic properties of the joint, we conducted preliminary experiments such as elastic modulus measurement and rigidity evaluation. We confirmed that the elastic modulus increased when a magnetic field was applied. The rigidity of the joint was also verified under bending conditions. Our results confirmed that the stiffness of the new joint changed significantly compared with the old joint depending on the presence or absence of a magnetic field, and the performance of the new joint also improved.

A Comparative Study on the Effect of Mechanical Compliance for a Safe Physical Human–Robot Interaction

Abstract In this paper, we study the effects of mechanical compliance on safety in physical human–robot interaction (pHRI). More specifically, we compare the effect of joint compliance and link compliance on the impact force assuming a contact occurred between a robot and a human head. We first establish pHRI system models that are composed of robot dynamics, an impact contact model, and head dynamics. These models are validated by Simscape simulation. By comparing impact results with a robotic arm made of a compliant link (CL) and compliant joint (CJ), we conclude that the CL design produces a smaller maximum impact force given the same lateral stiffness as well as other physical and geometric parameters. Furthermore, we compare the variable stiffness joint (VSJ) with the variable stiffness link (VSL) for various actuation parameters and design parameters. While decreasing stiffness of CJs cannot effectively reduce the maximum impact force, CL design is more effective in reducing impact force by varying the link stiffness. We conclude that the CL design potentially outperforms the CJ design in addressing safety in pHRI and can be used as a promising alternative solution to address the safety constraints in pHRI.

Adaptive joints with variable stiffness: strategically arranged materials with transduction properties

The environment around buildings keeps changing, while the static design solutions of buildings cannot perform well during the whole service life. In order to improve structural performances including strength (i.e. avoid collapse) and serviceability, adaptive structures are likely to establish as one of future trends in both research and application for the built environment. This project aims to synthesize a type of structural joints with variable stiffness capabilities. Stiffness variation is achieved by strategically arranged materials with transduction properties. Shape memory polymers (SMPs) feature large variation of stiffness between a glassy and a rubbery state, which makes them good candidates for application in shape control of adaptive structures. The structures will change themselves into optimal shapes corresponding to different load conditions. However, large shape changes require significant flexibility of the joints because their fixity can affect load-path and shape control. To address this problem, a variable stiffness joint is proposed. During shape/load-path control, the joint reduces its stiffness so that required deformation patterns can be achieved with low actuation energy. After shape control the joint recovers rigidity. Experimental studies showed the potential for application of joints with variable stiffness in adaptive structures.

Spring Effects on Workspace and Stiffness of a Symmetrical Cable-Driven Hybrid Joint

This paper aims to investigate how to determine the basic parameters of the helical compression spring which supports a symmetrical cable-driven hybrid joint (CDHJ) towards the elbow joint of wheelchair-mounted robotic manipulator. The joint design of wheelchair-mounted robotic manipulator needs to consider lightweight but robust, workspace requirements, and variable stiffness elements, so we propose a CDHJ which becomes a variable stiffness joint due the spring under bending and compression provides nonlinear stiffness characteristics. Intuitively, different springs will make the workspace and stiffness of CDHJ different, so we focus on studying the spring effects on workspace and stiffness of CDHJ for its preliminary design. The key to workspace and stiffness analysis of CDHJ is the cable tension, the key to calculate the cable tension is the lateral bending and compression spring model. The spring model is based on Castigliano’s theorem to obtain the relationship between spring force and displacement. The simulation results verify the correctness of the proposed spring model, and show that the spring, with properly chosen parameters, can increase the workspace of CDHJ whose stiffness also can be adjusted to meet the specified design requirements. Then, the modelling method can be extended to other cable-driven mechanism with a flexible compression spring.

Robust Tracking Control of Variable Stiffness Joint Based on Feedback Linearization and Disturbance Observer With Estimation Error Compensation

The variable stiffness joint (VSJ) has the characteristics of independent and controllable position and stiffness. The variable stiffness characteristics and inherent flexibility make the VSJ suitable to be used as the actuation joint of the physical human-robot interaction application robot, so as to improve the task adaptability of the robot and physical human-robot interaction safety. The VSJ based on equivalent lever mechanism has the advantages of low energy consumption in stiffness adjustment, so there are many researches on this type of VSJ. The tracking control of output link angular position and joint output stiffness are two basic control targets of the VSJ. For the system dynamic model of the VSJ based on equivalent lever mechanism, considering the unknown parametric perturbations, the unknown friction torques acting on the drive units, the unknown external disturbance acting on the output link and the control input saturation constraints, a robust tracking controller based on feedback linearization, disturbance observer with anti-windup measures, sliding mode control and estimation error compensator is designed to improve the tracking control accuracy of the position and stiffness of the VSJ. The simultaneous tracking control of position and stiffness of the VSJ can be achieved by the designed controller, and the simulation results show the effectiveness and robustness of the proposed controller. Moreover, the simulation results show that the proposed estimation error compensator for the disturbance observer with fixed preset observation gain can effectively reduce the system output tracking error and improve the anti-disturbance characteristics of the controller.

A novel design of shape-memory alloy-based soft robotic gripper with variable stiffness

Soft robotic grippers with compliance have great superiority in grabbing objects with irregular shape or fragility compared with traditional rigid grippers. The main limitations of such systems are small grasping force resulted from properties of soft actuators and lacking variable stiffness of soft robotic grippers, which prevent them from a larger wide range of applications. This article proposes a shape-memory alloy (SMA)-based soft gripper with variable stiffness composed of three robotic fingers for grasping compliantly at low stiffness and holding robustly at high stiffness. Each robotic finger mainly consisted of stiff parts and two variable stiffness joints is installed on the base with a specific angle. The paraffin as a variable stiffness material in the joint can be heated or cooled to change the stiffness of the robotic fingers. Results of experiments have shown that a single robotic finger can approximately achieve 18-fold stiffness enhancement. Each finger with two joints can actively achieve multiple postures by both changing the corresponding stiffness of joints and actuating the SMA wire. Based on these principles, the gripper can be applied to grasp objects with different shapes and a large range of weights, and the maximum grasping force of the gripper is increased to about 10 times using the variable stiffness joints. The final experiment is conducted to validate variable stiffness of the proposed soft grippers grasping an object.

A Hybrid, Wearable Exoskeleton Glove Equipped With Variable Stiffness Joints, Abduction Capabilities, and a Telescopic Thumb

Robotic hand exoskeletons have become a popular and efficient technological solution for assisting people that suffer from neurological conditions and for enhancing the capabilities of healthy individuals. This class of devices ranges from rigid and complex structures to soft, lightweight, wearable gloves. In this work, we propose a hybrid (tendon-driven and pneumatic), lightweight, affordable, easy-to-operate exoskeleton glove equipped with variable stiffness, laminar jamming structures, abduction/adduction capabilities, and a pneumatic telescopic extra thumb that increases grasp stability. The efficiency of the proposed device is experimentally validated through five different types of experiments: i) abduction/adduction tests, ii) force exertion experiments that capture the forces that can be exerted by the proposed device under different conditions, iii) bending profile experiments that evaluate the effect of the laminar jamming structures on the way the fingers bend, iv) grasp quality assessment experiments that focus on the effect of the inflatable thumb on enhancing grasp stability, and v) grasping experiments involving everyday objects and seven subjects. The hybrid assistive, exoskeleton glove considerably improves the grasping capabilities of the user, being able to exert the forces required to execute a plethora of activities of daily living. All files that allow the replication of the device are distributed in an open-source manner.

Design and Analysis of a Novel Truss-Shaped Variable-Stiffness Deployable Robotic Grasper

This paper presents a novel truss-shaped variable-stiffness deployable robotic grasper to grasp large unknown objects, the grasper comprises a series of basic modules and has the advantages of a large workspace, adjustable stiffness, and a high deploy/fold ratio. First, detailed mechanism designs of the grasper and variable-stiffness joint are introduced, and a mobility analysis and variable stiffness analysis are conducted. Second, the structural analysis of the basic module is carried out, by which several major indices, including deploy/fold ratio, grasping angle, deployment angle, grasping torque, and deployment torque, can be calculated. Third, kinematic analysis is presented to provide the workspace and kinematic simulation, and then the joint trajectory planning based on fifth-order polynomial is also conducted. Fourth, the condition of stable grasp is analyzed and a mathematical model of grasping motion is established. Adam optimization algorithm is then applied to optimization of the mathematical model and a grasping simulation is performed with objects of various sizes and for various working states of the variable-stiffness joint. Finally, a simple physical prototype is fabricated, and variable-stiffness experiments and grasping experiments confirm that the proposed grasper shows excellent grasping performance.

Design of a Variable Stiffness Joint Module to Quickly Change the Stiffness and to Reduce the Power Consumption

Variable stiffness actuators (VSA) are finding wide applications in robotics to enhance safety during interactions with stiff environments. Researchers have proposed various design architectures like antagonistic actuation, which requires both the motors to be powered simultaneously for varying the stiffness or equilibrium position. In this paper, the design of a novel joint module, named as variable stiffness joint module (VSJM), is proposed, which consists of a lead-screw arrangement for varying the stiffness range and a cam based mechanism to change the stiffness within the set range quickly. The cam profile has been synthesized to maximize the stiffness variation as well as to maintain the cam and cam follower in static equilibrium when the output link is in the equilibrium position. This was achieved by properly positioning and orienting the friction cones at the contact points. By mechanically compensating the moment due to unbalanced forces at the contact points, the continuous usage of stiffness motor has been eliminated, leading to reduced power consumption. Details of the proposed mechanism are presented along with the mathematical model for cam profile synthesis and static analysis. A simplified prototype of the proposed design has been fabricated to perform the experiments. A hammering-a-nail experiment has been conducted to show the capability of the mechanism, and the results are presented.

Development of a Variable Stiffness Joint by Series Nonlinear Elastic Antagonistic Drives using Polymer Material

Development of a Variable Stiffness Joint by Series Nonlinear Elastic Antagonistic Drives using Polymer Material

Research on Angle and Stiffness Cooperative Tracking Control of VSJ of Space Manipulator Based on LESO and NSFAR Control

With the increase in on-orbit maintenance and support requirements, the application of space manipulator is becoming more promising. However, how to control the vibration generated by the space manipulator has been a difficult problem to be solved. The advent of variable stiffness joint (VSJ) has brought about a dawn in solving this problem. But how to achieve coordinated control of joint angle and stiffness is still a problem to be solved, especially when considering system model parameter uncertainty, unknown disturbance and control input saturation. In order to realize the controllable attenuation of the vibration of the space flexible manipulator based on the variable stiffness joint, the dynamic model of the variable stiffness joint was constructed. Then the linear transformation and feedback linearization method are used to transform its complex nonlinear dynamic model system into a pseudo-linear system containing aggregate disturbance and input saturation constraints. This paper constructs a linear extended state observer (LESO) for estimating the state of unknown systems in pseudo-linear systems. Based on the idea of state feedback control, a Neural State Feedback Adaptive Robust (NSFAR) control is constructed by using Radial Basis Function Neural Network. The adaptive input saturation compensation control law is also designed by using Radial Basis Function Neural Network to deal with the input saturation compensation problem. The ultimate uniform bounded stability of the constructed system is proved by the stability analysis based on Lyapunov function. Finally, the effectiveness and superiority of the constructed tracking algorithm are verified by compared simulation and semi-physical experiment.

Realizing Controllable Physical Interaction Based on an Electromagnetic Variable Stiffness Joint

This paper puts forward a linear variable stiffness joint (VSJ) based on the electromagnetic principle. The VSJ is constituted by an annular permanent magnet (PM) and coaxial cylindrical coil. The output force and stiffness are linearly proportional to the coil current. In consequence, the stiffness adjustment motor and mechanisms required by many common designs of VSJs are eliminated. A physical prototype of the electromagnetic VSJ is manufactured and tested. The results indicate that the prototype can achieve linear force-deflection characteristics and rapid stiffness variation response. Using an Arduino and H-bridge driver board, the electromagnetic compliance control system is developed in order to realize the precise control of the interaction force. The static force control error is no more than ±0.5 N, and the settling time can be controlled within only 40 ms. At last, an experiment of squeezing the raw egg is conducted. The experiment intuitively exhibits the performance of electromagnetic compliance in stable force control and keeping safe robot-environment interaction.

Directional Stiffness Modulation of Parallel Robots With Kinematic Redundancy and Variable Stiffness Joints

Parallel robots have been primarily investigated as potential mechanisms with stiffness modulation capabilities through the use of actuation redundancy to change internal preload. This paper investigates real-time stiffness modulation through the combined use of kinematic redundancy and variable stiffness actuators. A known notion of directional stiffness is used to guide the real-time geometric reconfiguration of a parallel robot and command changes in joint-level stiffness. A weighted gradient-projection redundancy resolution approach is demonstrated for resolving kinematic redundancy while satisfying the desired directional stiffness and avoiding singularity and collision between the legs of a Gough/Stewart parallel robot with movable anchor points at its base and with variable stiffness actuators. A simulation study is carried out to delineate the effects of using kinematic redundancy with or without the use of variable stiffness actuators. In addition, modulation of the entire stiffness matrix is demonstrated as an extension of the approach for modulating directional stiffness.

A Novel Wire-Driven Variable-Stiffness Joint Based on a Permanent Magnetic Mechanism

The variable-stiffness joint (VSJ) plays an important role in creating compliant and powerful motions. This paper presents a novel wire-driven VSJ based on a permanent magnetic mechanism (PMM). The proposed joint regulates the joint stiffness with lower energy consumption through a wide range via the permanent magnetic mechanism. This effect possibly depends on the novel nonlinear combination of a permanent magnet-spring and wire-driven system that achieves the same stiffness with lower wire tension. A trapezoidal layout of the joint is proposed. Because of the relationship among the stiffness, the position of the joint and the stiffness of the PMM, the stiffness model is also been established. Based on this model, the decoupling controller is built to independently control the position and stiffness of the joint. Experiments show that the VSJPMM achieves position and stiffness independently and also reduces energy and power required to regulate the stiffness compared with the traditional approach. In addition, the proposed mechanism displays a powerful motion and short stiffness adjustment time.

A Novel Underactuated Robotic Finger with Variable Stiffness Joints.

Existing robotic hands mostly consist of rigid finger mechanism with constant joint stiffness, leading to poor handling performance and even unexpected safety issues. This paper proposed a novel underactuated robotic finger with variable stiffness joints based on human finger anatomy and electrostatic adhesion(ESA) principle. The proposed finger is unique in the 3D printable one-piece body structure consisting of three similar joints, actuated by only one linear actuator to mimic the flexion/extension movement of the human finger. It is characterized by simple actuation, light weight, low cost and compliant grasp. We constructed a portable finger prototype to investigate the variable stiffness performance. It turns out that the joint stiffness shows a growing trend as the applied voltage increases, which verifies the effectiveness of this design. The proposed novel finger indicates potential applications in service robots and prosthetic hands.