Compliant Link Research Articles

Multistable compliant linkages with multiple kinematic paths separated by energy barriers

Multistable morphing structures can reconfigure between different stable states that are separated by energy barriers, and one-degree-of-freedom (1-DOF) mechanisms have many merits, like simple actuation. This paper combines the two and proposes a new family of reconfigurable compliant linkages with many (2−6) 1-DOF kinematic paths that are separated by energy barriers. This new type of design is an extension of multistable structures, where each stable state corresponds to not just one configuration but a 1-DOF configuration space, i.e., a kinematic path. Components of the linkages are made elastically compliant, therefore enabling the switch between two isolated compatible paths with multi-stability. A generation-selection hybrid design algorithm to follow prescribed reconfigurable paths is proposed, and a minimum energy path (MEP) finding method to guide actuation to switch between different kinematic paths is developed. Four design examples with 2–3 reconfigurable paths and their experiments are presented, and the effectiveness of this method is verified. This work provides a fresh perspective to design the single-DOF reconfigurable mechanisms with larger design space, more reconfigurable kinematic paths, and easier reconfiguration actuation.

Design of a Flexure-Jointed Linkage in a Quadruped Walking Robot

Flexure-jointed linkages (FJLs) have distinct advantages, such as ease of manufacturing and assembly, no backlash, and light weight designs, over their rigid counterparts. However, the synthesis and analysis of FJLs are more complicated, especially when the compliant flexures have large deflections. This article addresses the optimal design of a large-deflection FJL, which is used as the leg of a compliant quadruped robot. The proposed FJL originates from a rigid six-bar linkage to mimic the foot path of walking mammals by replacing the passive revolute joints with two-segment combined flexible beams. Its kinematic and strain energy models are derived and verified by numerical simulations. Subjecting to material failures and geometrical constraints, the optimization of the FJL is carried out by minimizing the path deviation and strain energy to reduce needed input power, leading to the development of a quadruped walking robot. Experimental tests on the output path of the FJL and the motion capability of the robot are implemented. The results demonstrate the effectiveness of the derived models in predicting the deflections of the FJL and the feasibility of applying compliant linkages for legged robots.

Parametric joint compliance analysis of a 3-UPU parallel robot

Sufficiently low compliance is required for robot end-effectors to perform various tasks with high static and dynamic accuracy. The joint compliance and link compliance of robots are the two major factors for the determination of overall end-effector compliance. Unlike serial robots that can allow larger joint sizes to improve the joint compliance, the joints of parallel robots are usually closely located and hence the joint size cannot be easily increased. Compared with the link compliance, the joint compliance of a parallel robot contributes more to the end-effector compliance, but its importance is often overlooked. To reduce the computational intensity of robot compliance design, analytical joint compliance models are proposed for the class of 3-UPU parallel robots. These joint compliance models can be used to quickly evaluate the compliance contribution of each revolute joint at various parallel robot configurations. Numerical and experimental verifications are provided to demonstrate these models. We expect that the parametric analysis of 3-UPU parallel robot compliance can be facilitated by using the proposed joint compliance models.

Signal integrity analysis and Peripheral Component Interconnect Express backplane link compliance assessment

AbstractThis article presents research conducted on the backplane high‐speed Peripheral Component Interconnect Express version 4 (PCIe gen4) link between central processor root complex and the end‐point device in order to confirm its compliance. Signal integrity analysis was performed using a method that included channel segmentation, development of corner models for channel segments, full‐wave electromagnetic simulation utilizing the finite element method (FEM) and the creation of cascaded channel models, as well as determination of the worst‐case models for the channel. The results of this analysis were then used to modify the channel design in order to decrease insertion loss. Changes in the design included utilizing a very low loss dielectric for the backplane board, correcting the sizes of differential pairs and decreasing the via stubs. Frequency domain simulation of the modified channel design has shown a 25% decrease in insertion loss. The calculation of eye diagrams for the modified design has confirmed that the channel parameters meet the requirements for the PCIe gen4 standard.

Reverse-twisting of helicoidal shells to obtain neutrally stable linkage mechanisms

Mechanisms that consist of many elements and are potentially small sized, benefit from kinematic elementary units like revolute joints that are compliant and monolithic, and therefore could be produced without need for assembly. We present a novel concept of a compliant revolute joint that features low axis drift, high support stiffness and a large range of motion. The concept is based on a helicoidal shell of which a portion reverses its twist direction upon application of a rotation. The reversed region increases gradually, resulting in a constant reaction moment. Analytical, numerical, and experimental analyses are presented to reveal and quantify the constant-moment behaviour. Prototypes of the concept are employed in exemplary linkages to demonstrate the ability to create a large variety of neutrally stable compliant linkages, which require extremely low actuation forces and exhibit large ranges of motion.

Design, Modeling, and Manufacturing of a Variable Lateral Stiffness Arm Via Shape Morphing Mechanisms

Abstract In this article, we present a continuously tunable stiffness arm for safe physical human–robot interactions. Compliant joints and compliant links are two typical solutions to address safety issues for physical human–robot interactions via introducing mechanical compliance to robotic systems. While extensive studies explore variable stiffness joints/actuators, variable stiffness links for safe physical human–robot interactions are much less studied. This article details the design and modeling of a compliant robotic arm whose stiffness can be continuously tuned via cable-driven mechanisms actuated by a single servo motor. Specifically, a 3D-printed compliant robotic arm is prototyped and tested by static experiments, and an analytical model of the variable stiffness arm is derived and validated by testing. The results show that the lateral stiffness of the robot arm can achieve a variety of 221.26% given a morphing angle of 90 deg. The variable stiffness arm design developed in this study could be a promising approach to address safety concerns for safe physical human–robot interactions.

Self-Compliant Track-Type Wall-Climbing Robot for Variable Curvature Facade

The paper presents a wall-climbing robot featuring self-compliance for variable curvature façades. The high payload and maneuverability make it highly potential in heavy-duty operation of industrial applications. The robot consists of two traction modules and one link module. Each traction module is equipped with magnetic adhesion and crawler traction submodules. The two traction modules are connected by the link module with 4 degrees of freedom (DoF) of passive compliance. Variable curvature façade self-compliance is achieved by the passive compliant link module, which results in the attitude change decoupling of the two traction modules. The attitude can be adjusted under the effect of magnetic adhesion force to comply with the curvature variations. High payloads are achieved by the large contact area between the crawler and the surface. Omni-directional high maneuverability is enabled by the speed difference between the motors of two traction modules. The robot can maneuver in any direction on the surface with a minimum radius of 1 m and carry 36 kg payload on vertical surfaces.

Static Balancing of Four-Bar Compliant Mechanisms With Torsion Springs by Exerting Negative Stiffness Using Linear Spring At the Instant Center of Rotation

Abstract A design approach for the quasi-static balancing of four-bar linkages with torsion springs is proposed. Such an approach is useful in the design of quasi-statically balanced fully compliant mechanisms by tuning the stiffness of the pseudo-rigid-body-model. Here, the positive stiffness exhibited by torsion springs at the R-joints is compensated by a negative stiffness function. The negative stiffness is created by a non-zero-free-length linear spring connected between the coupler link and the ground, and where both connecting points trace a line directed to the coupler link’s instant center of rotation. A full example of the static balancing of two compliant linkages for approximate straight path generation is developed, where actuation energy of the compliant designs is reduced in 66% and 54%, respectively.

A Parametric Study of Compliant Link Design for Safe Physical Human–Robot Interaction

SUMMARYRobots of next-generation physically interact with the world rather than be caged in a controlled area, and they need to make contact with the open-ended environment to perform their task. Compliant robot links offer intrinsic mechanical compliance for addressing the safety issue for physical human–robot interactions (pHRI). However, many important research questions are yet to be answered. For instance, how do system parameters, for example, mechanical compliance, motor torque, impact velocities, and so on, affect the impact force? how to formulate system impact dynamics of compliant robots, and how to size their geometric dimensions to maximize impact force reduction. In this paper, we present a parametric study of compliant link (CL) design for safe pHRI. We first present a theoretical model of the pHRI system that is comprised of robot dynamics, an impact contact model, and dummy head dynamics. After experimentally validating the theoretical model, we then systematically study the effects of CL parameters on the impact force in more detail. Specifically, we explore how the design and actuation parameters affect the impact force of pHRI system. Based on the parametric studies of the CL design, we propose a step-by-step process and a list of concrete guidelines for designing CL with safety constraints in pHRI. We further conduct a simulation case study to validate this design process and design guidelines.

Finger Clamping Unit: A Clamping Device with a Large Clamping Range

Finger Clamping Unit (FCU) is a small-sized single-point clamp developed to clamp thin object of various thicknesses. It has a six-bar linkage with one compliant link, uses an electric motor as an actuator and induces toggle-lock motion by singular configuration. The main purpose of the FCU is to clamp car bodies in car assembly lines, while adapting to various thicknesses of car body. Unlike other clamping devices in the industry, it has a large clamping range (defined as the thickness range that the FCU can clamp). In this paper, the overall process of FCU development is presented. The six-bar linkage was chosen in type synthesis, and compliance was added for toggle-lock motion. Static analysis of the compliant FCU was completed, and results were plotted in a three-dimensional (3D) plot which expresses the behavior of the FCU. The lengths of each link were optimized in dimension synthesis. An FCU was constructed to reinforce the simulated results. The unique design of both the six-bar linkage FCU and the compliant link were presented. Simulated and experimental 3D plots were compared and analyzed. An appropriate friction model that best fits the experiment data was found. The advantage of the FCU—its clamping range—was proved by experiment.

Dynamic analysis of a hybrid compliant mechanism with flexible central chain and cantilever beam

Membrane peeling in retinal and cataractous surgery is a challenging task due to physiological hand tremors and delicate tissue. To relieve this problem, we proposed a hybrid compliant mechanism with a flexible central chain and a cantilever beam to suppress hand tremors and vibrate along peeling direction since the vibration can reduce peeling force. The particularly designed mass block makes the axial deformation of central chain and cantilever beam negligible in dynamic modeling. We then studied the dynamic response of the proposed hybrid compliant mechanism. The pseudo-rigid-body model (PRBM) of compliant links, central chain and cantilever beam is given. The relationship between the moving platform and parallel kinematic chains is derived. Next, the full dynamic model is established using the Lagrange equation. Furthermore, the dimension of the full dynamic model is reduced by the proper orthogonal decomposition (POD) method. Simulation results show that the reduced-order model is about 9.0 times faster than the full dynamic model. Experimental results show that the average relative errors of the full dynamic model and the reduced-order model are 2.12% and 1.93%, respectively.

Stiffness modeling of a variable stiffness compliant link

Recently, a variable stiffness robotic link based on the rotating beam concept has been developed for applications in physical human robot interaction. A substantial challenge for design of such links is the modeling of stiffness behavior to permit stiffness control. In this paper we present a general 3D model of the link stiffness using screw theory and compliance matrices as well as a planar model for the lateral and torsional stiffness. Since axial buckling is a major failure mode, we also derive an analytical model for predicting axial buckling behavior. The analytical models are compared to the finite element method and experimental results. One of the challenges involved in design and analysis of variable stiffness links is the parasitic compliance of the mechanical elements that support and drive the active portion of the mechanism. For the design analyzed in this paper, we use the models we derive to identify the major sources of parasitic compliance and suggest optimizations to minimize their effects. These results can be used as guidelines for designing variable stiffness links.

Integrated Design and Fabrication of a Conductive PDMS Sensor and Polypyrrole Actuator Composite

Polypyrrole (PPy) has been widely used as an electro active polymer actuator owing to its high energy density, and the applicability in low voltage (i.e. less than 3 V) driven systems. Its scalable fabrication process also enables a PPy actuator to be used in mesoscale (a few millimeter to centimeter) robotic mechanisms. Although many PPy actuator driven mechanisms have been studied previously, its in-situ measurement of the motion of a PPy actuator was rarely investigated. To further expand the potential applications of a PPy actuator in automation and control of mesoscale robots, it is essential to develop a highly integrated sensor-actuator structure. In this work, we proposed a new fabrication process to make one kind by electrochemically synthesize a PPy layer on the opposite side of a carbon doped polydimethylsiloxane (CPDMS) based resistive sensor where a polyvinylidene fluoride (PVDF) membrane was used as a common substrate. A simple way to make a CPDMS sensor was proposed, and its electric and mechanical properties were studied using various material combinations. In addition, the characteristics of a CPDMS-PPy composite was studied using cyclic voltammetry, and the integrated sensor response analysis with and without applied load during the electrochemically induced PPy actuation. The proposed structure was not only able to sense its bending motion, but it could also roughly distinguish the stiffness of an object in contact. To demonstrate a simple application, a compliant linkage structure, which simultaneously actuated and sensed by the proposed composite, was built.

A comprehensive performance comparison of linear quadratic regulator (LQR) controller, model predictive controller (MPC), $$H_{\infty }$$ loop shaping and $$\mu $$-synthesis on spatial compliant link-manipulators

Position control and mechanical vibration suppression are still open problems in compliant link mechanisms. Operation and accuracy improvements of manipulators can be made by finding solutions for these problems. This paper presents a comprehensive performance comparison between controllers (two of them robust controllers) to control position and reduce mechanical vibration over a compliant link-manipulator in a three-dimensional environment: (i) linear quadratic regulator, (ii) model predictive controller, (iii) $$H_{\infty }$$ loop shaping, and (iv) $$\mu $$ -synthesis. The comparisons of controllers are made based on position tracking, vibration damping and control effort in the simulation environment by taking the gravity effect into account. Finally, the paper makes a conclusion by providing some information about main purpose, advantages and disadvantages of each controller in compliant link-manipulator applications.

Adaptive Integral Inverse Kinematics Control for Lightweight Compliant Manipulators

In this letter, an adaptive to unknown stiffness algorithm for controlling low-cost lightweight compliant manipulators is presented. The proposed strategy is based on the well-known transpose inverse kinematics approach, that has been enhanced with an integral action and an update law for the unknown stiffness of the compliant links, making it valid for soft materials. Moreover, the algorithm is proven to guarantee global task-space regulation of the end effector. This approach has been implemented on a very low-cost robotic manipulator setup (comprised of 4 actuated and 3 flexible links) equipped with a simple Arduino board running at 27 Hz. Notwithstanding, the strategy is capable of achieving a first-order-like response when undisturbed, and recover from overshoots provided by unforeseen impacts, smoothly returning to its nominal behaviour. Moreover, the adaptive capabilities are also used to perform contact tasks, achieving zero steady-state error. The tracking performance and disturbance rejection capabilities are demonstrated with both theoretical and experimental results.

A class of biaxial micro/meso-scale structures for isotropic in-plane inertial sensing and actuation: design, fabrication and experiments

A micro/meso-scale monolithic architecture was designed, fabricated and tested for in-plane inertial sensing and actuation with isotropic stiffness in the sensitive plane and high frequency-ratios between the insensitive and sensitive directions. The architecture was designed to accommodate any regular polygonal shape with a proof-mass suspension made of a serial array of compliant parallelogram linkages. Structural optimization and finite element analysis were conducted to achieve high frequency ratios and a high degree of compliance in the sensitive directions, for low-g applications and in-plane sensing. Then, the elastically isotropic structure for any regular polygonal shape was modeled in the sensitive plane and validated numerically. Lame curves were introduced in the fillets to relax the stress concentration, while air-damping analysis was introduced to provide prediction of the high resistance in the insensitive out-of-plane motion. Next, the microfabrication process was devised and conducted for triangular and square structures based on the biaxial architecture. Special techniques were studied on the wafer bonding with large cavities and the adhesive influence during deep reactive-ion etching (DRIE). Finally, techniques were studied on the reflectivity adjustment of the sample surface and the in-plane biaxial motion detection of the fundamental frequencies using a uniaxial laser-sensing system. Vibration tests conducted in the micro/meso prototypes validated the isotropic biaxial sensitivity and the size effect of the high squeezed-film air damping in the insensitive direction.

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.

Design, Analysis, Experimentation, and Control of a Partially Compliant Bistable Mechanism

Abstract This study presents the design analysis and development of a novel partially compliant bistable mechanism. Motion behavior dependence on links and relative angles are analyzed, lumped parameter model is derived, mechanism parts including the compliant members are three-dimensional (3D) printed and a state feedback controller is implemented so that the slider follows a well-defined trajectory if designed as an actuator. The proposed mechanism consists of initially straight, large deflecting fixed-pinned compliant links, rigid links, and a sliding mass. Dynamic response of the mechanism is studied using elliptic integral solutions, pseudo rigid body model (PRBM), vector closure loop equations and Elliptic integrals. Nonlinear model is simulated in matlab simulink using fourth‐order Runge‐Kutta algorithms. The research emphasizes on the realization and dynamic response of the mechanism and the trajectory control of the slider so that the slider can be kept constant at specified distances resulting a dwell motion if designed as a linear actuator.

Effect of compliant linkages on suspension under load

Abstract. A numerical investigation is performed into the effects of rigid and compliant suspension linkages, respectively, on: the kinematics and handling performance of a lightweight electric vehicle (EV). CAE models of the front and rear suspension systems are first established based on the measured parameters of the target vehicle. The validity of the CAE models is confirmed by comparing the results obtained for the camber angle and kingpin inclination angle with those obtained mathematically using the vector loop method. CAE models are then performed using half-vehicle and whole-vehicle models. Quarter-vehicle simulations are then performed to compare the solutions obtained from the compliance and rigid-body models for the forces acting on the hardpoints of the two suspension systems under pothole impact conditions. Finally, whole-vehicle simulations are conducted using both the rigid-body model and the compliance model to evaluate the handling performance of the EV in impulse steering tests conducted at vehicle speeds of 40, 60 and 80 km h−1, respectively. In general, the results show that the choice of a rigid-body model or a compliance model has a significant effect on the forces computed at some of the hardpoints in the front and rear suspension systems. Furthermore, the rigid-body model predicts a better vehicle body stability following high-speed turns than the compliance model.

Design and Modeling of a Continuously Tunable Stiffness Arm for Safe Physical Human–Robot Interaction

Abstract To reduce injury in physical human–robot interactions (pHRIs), a common practice is to introduce compliance to joints or arm of a robotic manipulator. In this paper, we present a robotic arm made of parallel guided beams whose stiffness can be continuously tuned by morphing the shape of the cross section through two four-bar linkages actuated by servo motors. An analytical lateral stiffness model is derived based on the pseudo-rigid-body model and validated by experiments. A physical prototype of a three-armed manipulator is built. Extensive stiffness and impact tests are conducted, and the results show that the stiffness of the robotic arm can be changed up to 3.6 times at a morphing angle of 37 deg. At an impact velocity of 2.2 m/s, the peak acceleration has a decrease of 19.4% and a 28.57% reduction of head injury criteria (HIC) when the arm is tuned from the high stiffness mode to the low stiffness mode. These preliminary results demonstrate the feasibility to reduce impact injury by introducing compliance into the robotic link and that the compliant link solution could be an alternative approach for addressing safety concerns of physical human–robot interactions.