Compliant Joints Research Articles

Design and optimization of a planar anti-buckling compliant rotational joint with a remote center of motion

Compliant mechanisms (CMs) exhibit some excellent mechanical properties and provide numerous innovative solutions for many existing mechanical applications. Among them, planar compliant rotational joints have made substantial contributions to precision engineering. To achieve high-precision positioning with a compliant rotational joint, it is essential to study characteristics such as anti-buckling and constant stiffness. The remote center of motion (RCM) mechanism, with its compact structure and ease of precise control, is expected to enhance overall rigidity and reduce parasitic displacements. Here, we propose a planar anti-buckling compliant rotational joint with a RCM. Static modeling and model validation are conducted for different geometric configurations, including single and combined structures. A distributed configuration with bidirectional anti-buckling properties is selected for optimization. Using a global parameter optimization model, single-objective optimization studies are conducted for three distinct characteristics. Subsequently, a multi-objective optimization model for constant stiffness and high precision is established. Based on the optimization results, a compliant rotational joint with bidirectional anti-buckling, constant rotational stiffness, and high precision is designed. Finally, the effectiveness of the optimization method is validated through physical experiments.

Through-Window Home Aerial Delivery System with In-Flight Parcel Load and Handover: Design and Validation in Indoor Scenario

Abstract This paper presents the design, development, and validation in indoor scenario of an aerial delivery system intended to conduct the delivery of light parcels directly to the user through the window of his/her home, motivated by the convenience of facilitating the access to medicines to people with reduced mobility.The system consists of a fully-actuated multi-rotor (FAMR) equipped with a front basket where the parcel to be delivered is loaded by a lightweight and compliant anthropomorphic dual arm system (LiCAS) located at the supply point, using one of the arms to drop the parcel in the basket while the other arm holds its base to support the sudden moment exerted at the FAMR. The paper analyses four types of physical interactions raised during the operation on flight: (1) sudden changes in the mass distribution of the FAMR during the load/unload phase, affecting the multi-rotor position-attitude controllers, (2) impact and impulsive forces exerted by the human on the FAMR to demonstrate the reliability and robustness of conventional cascade controllers, (3) passive accommodation of the LiCAS while holding the FAMR during the parcel load, relying on the mechanical joint compliance, and (4) compliant human–FAMR interaction, interpreting the multi-rotor pose control error as a Cartesian/angular deflection to implement an admittance controller that allows the user guiding the platform. Experimental results allow the identification and characterization of these effects for different payload masses. The execution of the complete operation, involving the parcel load with the LiCAS and handover by the user through a window, is validated in a representative indoor scenario. Graphical Abstract

Sonic P-wave attenuation based on fluid pressure differential between joint and matrix

When P-wave compresses in-situ rocks saturated with fluid, there is a fluid pressure differential between compliant joints and stiff matrix. The pressure differential automatically drives a mesoscale squirt between joint wall and matrix interior. This mechanism is likely to dominate sonic P-wave attenuation in the field. A new model of P-wave attenuation based on the mesoscale squirt is established, in which the first porosity is represented by matrix pores while the second porosity is represented by joint. Sonic log of a sandstone reservoir in Saudi Arabia is used to illustrate the model. Both estimated phase velocity and measured quality factor of sonic P-wave are accurately simulated. The results show that for the sandstone reservoir, the relative second porosity is 5%, inter-joint distance is 0.1 m, squirt permeability at very low frequencies is about half of Darcy permeability of the matrix, and joint gap is 800 μm (quadruple grain diameter of 200 μm). Surprisingly, the model of joint-matrix squirt is also capable of reproducing seismic P-wave attenuation measured in the shallow crust of southern California. Therefore, mesoscale squirt across the joint wall is probably the underlying mechanism of attenuation for sonic and seismic P-waves shallower than 10 km.

Proximal Joint Compliance as a Passive Method for Ground Reaction Force Redirection During Legged Locomotion

Abstract Ground reaction forces (GRFs) are a critical component of legged locomotion, and controlling their direction leads to more stable, efficient, and robust performance. The novelty of this work is to studying passive proximal joint (hips/shoulders) compliance for the purpose of redirecting the GRF passively. Previous works have redirected the GRF actively or studied passive proximal joint compliance for purposes such as swing phase efficiency, but passive methods of stance-phase GRF redirection are under-developed. This paper analyzes the relationship between hip compliance and the GRF direction analytically and with simulations of a trotting quadruped. The results show increased GRF redirection, on average, with increased joint stiffness, for a range of cases. An example method of utilizing this relationship to improve locomotion performance is presented by simulating online compliance adaptation. By adapting the compliance parameter during locomotion, the cost of locomotion was reduced toward the known minimum within the parameter space explored. These results support the conclusion that adjusting the hip compliance provides a passive way of redirecting the GRF, which leads to improved locomotion performance. Other systems can utilize this knowledge to passively improve their own performance.

Finding the rhythm: Humans exploit nonlinear intrinsic dynamics of compliant systems in periodic interaction tasks.

Activities like ball bouncing and trampoline jumping showcase the human ability to intuitively tune to system dynamics and excite motions that the system prefers intrinsically. This human sensitivity to resonance has been experimentally supported for interactions with simple linear systems but remains a challenge to validate in more complex scenarios where nonlinear dynamics cannot be predicted analytically. However, it has been found that many nonlinear systems exhibit periodic orbits similar to the eigenmodes of linear systems. These nonlinear normal modes (NNM) are computable with a recently developed numerical mode tool. Using this tool, the present resarch compared the motions that humans excite in nonlinear systems with the predicted NNM of the energy-conservative systems. In a user study consisting of three experiment parts, participants commanded differently configured virtual double pendula with joint compliance through a haptic joystick. The task was to alternately hit two targets, which were either aligned with the NNM (Experiments 1 and 2) or purposefully arranged offset (Experiment 3). In all tested experiment variations, participants intuitively applied a control strategy that excited the resonance and stabilized an orbit close to the ideal NNM of the conservative systems. Even for increased task accuracy (Experiment 2) and targets located away from the NNM (Experiment 3), participants could successfully accomplish the task, likely by adjusting their arm stiffness to alter the system dynamics to better align the resonant motions to the task. Consequently, our experiments extend the existing research on human resonance sensitivity with data-based evidence to nonlinear systems. Our findings emphasize the human capabilities to apply control strategies to excite and exploit resonant motions in dynamic object interactions, including possibly shaping the dynamics through changes in muscle stiffness.

Passive Realization of Object Spatial Compliance by a Hand Having Multiple Four-Joint Hard Fingers

Abstract This paper presents an approach to passively realize any specified object spatial compliance using the grasp of a robotic hand. The kinematically anthropomorphic hands considered have multiple 4-joint fingers making hard point contact with the held object, and the joints of each finger have selectable passive elastic behavior. It is shown that the space of passively realizable compliances is restricted by the kinematic structure of the anthropomorphic hand. To achieve an arbitrary compliant behavior, fingers must be able to adjust their orientation. Synthesis procedures for grasps having 3, 4, and 5 or more fingers are developed. These procedures identify the finger configurations and the individual finger joint compliances needed to passively achieve any specified spatial object compliance matrix in the 20-dimensional subspace of grasp-realizable behaviors.

[formula omitted]adaptive resonance ratio control for series elastic actuator with guaranteed transient performance

Series elastic actuator (SEA) technology is promising for the development of compliant robotic joints. Despite advancements in the realization of precise tracking, challenges persist in controlling the vibration and transient performance. This study enhanced the resonance ratio control (RRC) algorithm by integrating it with the L1 adaptive control (L1AC) method to address overshoot, static error, and vibration in SEA position control. Initially, the resonance between the motor and link sides caused by the elastic transmission structure was analyzed, which can result in overshoots and vibrations that affect the transient performance of the SEA control. Subsequently, a control scheme based on L1AC was introduced to enhance the performance. The stability of the proposed algorithm was demonstrated through a comprehensive exploration of key control parameters. Furthermore, the algorithm was augmented with gravity compensation, effectively reducing the predicted and reference errors. Consequently, the transient performance was improved. The efficacy of this enhanced algorithm was validated through simulations and experimental platforms, and comparisons with the RRC and model reference adaptive control algorithms. In all the experiments, the overshoot did not exceed 1.1%, the maximum jitter amplitude on the link side was within 0.2° , and a larger time constant in the controller could effectively eliminate the overshoot and vibration with a small response time delay. Furthermore, the algorithm exhibited a protective response during link side collisions by moderating link velocity and limiting motor current, to safeguard the contact environment, humans, and the SEA itself, which take advantage of the L1AC’s low-pass filter (LPF) properties in disturbance handling.

DeltaFlex—An Additively Manufactured Delta Robot With Compliant Joints: Virtual Prototyping and Experimental Evaluation

Abstract The current study presents the development and validation of a compliant Delta robot with a monolithic structure, which has been fabricated using additive manufacturing (AM). The monolithic design and the use of AM accelerate the robot development cycle by enabling rapid prototyping and deployment while also facilitating experimentation with novel or different robot kinematics. The use of flexible joints for robots presents a challenge in achieving sufficient workspaces. However, parallel architectures are well suited for incorporating compliant joints, as they require lower ranges of motion for individual joints compared to serial architectures. Therefore, the Delta configuration has been chosen for this study. Multibody flexible dynamics (MfBD) simulations have been used as a means to guide design choices and simulate the structural behaviour of the robot. A design for additive manufacturing (DfAM) technique has been adopted to minimize the need for support structures and maximize mechanical strength. The quantitative evaluation of the Delta’s overall performance has been conducted in terms of stiffness and precision. The stiffness test aimed to gauge the robot’s ability to withstand applied loads, whereas the repeatability test assessed its precision and accuracy. This approach offers a promising path for robot design with significant potential for future advancements and practical applications while highlighting the trade-offs that designers should consider when adopting this methodology.

Ground Adaptability of Crawler Mobile Robots with Sub-Crawler Rotary Joint Compliance

Remote-controlled mobile robots are expected to be used in difficult- or impossible-to-access environments for inspection workers and responders, such as in investigations and search activities at accident/disaster sites and inspection/investigation work at plants/infrastructure. Among ground mobile robots, crawler mobile robots with sub-crawlers (also known as ground-adaptive crawler robots) excel at in-ground adaptability and stack escape; however, their operators require advanced remote-control technology and experience. Therefore, the introduction of semi-autonomous control to assist the operator is required. In this study, the principle of the pushing-up sequence and the possibility of mobiligence emerging from interaction with obstacles caused by the robot movement were described. In addition, the sub-crawler rotary joint’s compliance, which significantly contributes to ground adaptability, was hypothesized, and a compliance control system design method that uses the sub-crawler constraint angle as a design condition was proposed. It was confirmed that the model robot for the evaluation, which used the proposed method, could adapt to unknown obstacles without measuring their height and shape and traverse them based on experimental results. In addition, based on the numerical calculation results, it was determined that the optimum solution for the restriction angle of the sub-crawler was approximately 35°–50° from the perspective of propulsive force and tumble stability.

Design of High-Performance Triple-axis Cross Pivots

Abstract Cross-axis flexural pivots are increasingly implemented in mechanical systems due to their high precision and wide range of motion. However, designing high-performance pivots in terms of low axis drift, low rotational stiffness, and low values of maximum stress remains a challenging task. In fact, these features often behave antagonistically to each other. In this paper, the design of a novel family of high-performance cross-axis pivots is presented. The compliant joints are obtained by the composition of two crossing flexible elements with initially curved axis, and of one auxiliary flexure with straight axis. Two different arrangements, that depend on the constraints layout, are proposed. Chained beam constraint model and non-linear finite element analysis are implemented for the analysis of the kinetostatic response of the pivots. The effects of initial curvature and orientation of the flexures on axis drift, stiffness, and maximum stress, are investigated and reported in the form of design maps. A global performance index, that embodies the above-mentioned features and captures the overall kinetostatic behavior of the pivot is introduced. The design maps and the global index serve as key tools for the design procedure, giving insight into the antagonistic issue and leading to the determination of the best trade-off solutions that meet the application requirements. An experimental campaign is conducted to compare the performance improvement of triple-axis pivots with respect to a benchmark double-axis joint, and to validate the design method.

Mechanically Robust Lubricating Hydrogels Beyond the Natural Cartilage as Compliant Artificial Joint Coating.

Natural cartilage exhibits superior lubricity as well as an ultra-long service lifetime, which is related to its surface hydration, load-bearing, and deformation recovery feature. Until now, it is of great challenge to develop reliable cartilage lubricating materials or coatings with persistent robustness. Inspired by the unique biochemical structure and mechanics of natural cartilage, the study reports a novel cartilage-hydrogel composed of top composite lubrication layer and bottom mechanical load-bearing layer, by covalently manufacturing thick polyelectrolyte brush phase through sub-surface of tough hydrogel matrix with multi-level crystallization phase. Due to multiple network dissipation mechanisms of matrix, this hydrogel can achieve a high compression modulus of 11.8MPa, a reversible creep recovery (creep strain: ≈2%), along with excellent anti-swelling feature in physiological medium (v/v0 < 5%). Using low-viscosity PBS as lubricant, this hydrogel demonstrates persistent lubricity (average COF: ≈0.027) under a high contact pressure of 2.06MPa with encountering 100k reciprocating sliding cycles, negligible wear and a deformation recovery of collapse pit in testing area. The extraordinary lubrication performance of this hydrogel is comparable to but beyond the natural animal cartilage, and can be used as compliant coating for implantable articular material of UHMWPE to present, offering more robust lubricity than current commercial system.

Response Surface Optimization for Compliant Joint of Humanoid Robot Using ANSYS - Design of Experiment

Objective: A Compliant Joint of humanoid robot is a spring-loaded assembly, which is used to interact safely with the environment, and it helps to stabilized sudden shock and vibration in the robotic system. At the moment, compliant joints are required to optimize their size and dimensions which result into optimized weight and factor of safety of humanoid robot. Methods: Analysis is carried out using Response Surface Methodology (RSM) and Multi-Objective Genetic Algorithm (MOGA) using ANSYS. The current study employed goal-driven optimisation using ANSYS Workbench to minimise weight and achieve the required factor of safety range for the compliant joint. To find out range of variables such as rim thickness, shaft diameter, base thickness, module thickness and spoke thickness affecting on responses such as factor of safety and geometrical mass of compliant joint single factor single response parametric analysis is carried out. Findings: Based on trend of preliminary analysis variable range and combinations are selected to study interaction effect of parameters to obtain favorable factor of safety and low geometrical mass. The optimized compliant joint is compared with various design and validated through the developed actual module. Novelty: Eventually, the geometry mass of the compliant joint was reduced from 0.8604 kg to 0.6449 kg, resulting in a lighter weight (24.06% reduction) with a 1.7533 factor of safety and more compact in size (outer diameter is shrink from 142 to 126 mm). Keywords: Compliant joint, Goal driven optimization, Response surface optimization, Design of experiment, Humanoid robot

Shape Sensing and Kinematic Control of a Cable-Driven Continuum Robot Based on Stretchable Capacitive Sensors.

A Cable-Driven Continuum Robot (CDCR) that consists of a set of identical Cable-Driven Continuum Joint Modules (CDCJMs) is proposed in this paper. The CDCJMs merely produce 2-DOF bending motions by controlling driving cable lengths. In each CDCJM, a pattern-based flexible backbone is employed as a passive compliant joint to generate 2-DOF bending deflections, which can be characterized by two joint variables, i.e., the bending direction angle and the bending angle. However, as the bending deflection is determined by not only the lengths of the driving cables but also the gravity and payload, it will be inaccurate to compute the two joint variables with its kinematic model. In this work, two stretchable capacitive sensors are employed to measure the bending shape of the flexible backbone so as to accurately determine the two joint variables. Compared with FBG-based and vision-based shape-sensing methods, the proposed method with stretchable capacitive sensors has the advantages of high sensitivity to the bending deflection of the backbone, ease of implementation, and cost effectiveness. The initial location of a stretchable sensor is generally defined by its two endpoint positions on the surface of the backbone without bending. A generic shape-sensing model, i.e., the relationship between the sensor reading and the two joint variables, is formulated based on the 2-DOF bending deflection of the backbone. To further improve the accuracy of the shape-sensing model, a calibration method is proposed to compensate for the location errors of stretchable sensors. Based on the calibrated shape-sensing model, a sliding-mode-based closed-loop control method is implemented for the CDCR. In order to verify the effectiveness of the proposed closed-loop control method, the trajectory tracking accuracy experiments of the CDCR are conducted based on a circle trajectory, in which the radius of the circle is 55mm. The average tracking errors of the CDCR measured by the Qualisys motion capture system under the open-loop and the closed-loop control are 49.23 and 8.40mm, respectively, which is reduced by 82.94%.

Analytical Modeling and Validation of New Prismatic Compliant Joints Based on Zero Poisson’s Ratio Lattice Structures

Abstract The design and analysis of prismatic compliant joints have received less attention compared to that given to revolute compliant joints, thus limiting their implementation in compliant mechanisms beyond translational stages. Lattice structures have been used effectively to increase flexibility and stiffness ratios in compliant joints. Considering these, new prismatic compliant joints based on zero Poisson’s ratio lattice structures (ZP-PCJ) are proposed. Lattices with three different cell arrangements are considered: single cells, 2×2, and 3×3 lattices. Additionally, unit cells with three different geometries are studied: triangular, chamfer, and cosine. The compliance matrices of the ZP-PCJs are assembled analytically using Castigliano’s second theorem and compliance series–parallel simplification. The compliance ratios along the three orthogonal axes of the ZP-PCJs are computed varying their geometric parameters. Finite element models are constructed to validate the analytical results. Experimental tests are performed on additively manufactured ZP-PCJs to corroborate the compliance coefficients. Results showed that analytical models can predict the ZP-PCJ’s elastic properties accurately, differences less than 3% and 12% were obtained when compared to computational and experiments, respectively. Based on the compliance ratios obtained, the ZP-PCJs are suitable for two-dimensional applications. Finally, the ZP-PCJs are implemented in a compliant mechanism to evaluate their behavior, analytically and computationally. The ZP-PCJs have advantages such as eliminating axis drift and high flexibility in motion-direction while maintaining stiffness in other directions. The differences observed when comparing the analytically obtained estimations with simulations and experimental data suggest that ZP-PCJ analytical models are reliable for estimating their performance in compliant systems.

Stress field evolution on rebar coupling connection at uniaxial tension

Rebar coupling connections are widely used for joints, and it is necessary to get information about the stress field distribution on the coupling surface at uniaxial tension to characterize operation of such joints.Purpose: The aim of the work is to study the stress-strain state of rebar connections under tension, full-scale junctions of the type A500 rods, and the deformation influence on the steel microstructure of grade С1020.Methodology: Non-contact three-dimensional imaging system VIC-3D and digital image correlation and tracking for studying stress-strain state of rebar connection; transmission electron microscopy for studying the steel microstructure.Research findings: Load-displacement curves are suggested for the valve coupling, and three deformation stages are identified: 1) elastic deformation of the coupling connection, 2) parabolic hardening, 3) preceding the coupling connection destruction. The analysis of the strain field distribution on the coupling connection shows that at any time, plastic strain localizes in certain zones of the sample. The stress field evolution on the coupling connection correlates with the indicated deformation stages. The compliance of the rebar joint made of seamless hot-deformed tube with an outer and inner diameters 51 and 32 mm, respectively, made of С1020 steel grade, induces 500 MPa stress in the normal section of rebar under the tensile axial load.Value: It is shown that during uniaxial tension of 0 to 5 %, perlite fractures, which is accompanied by further polarization of the dislocation structure. The internal stress amplitude increases and at 5% tension, far-range stresses grow as compared with those induced forest dislocations. The main contribution to far-range stresses and their change at 5 % tension is made by the elastic component, that promotes to the microcrack formation.

Controlling flat-foot limit cycle walkers with compliant joints based on local stability variation.

This study investigates local stability of a four-link limit cycle walking biped with flat feet and compliant ankle joints. Local stability represents the behavior along the solution trajectory between Poincare sections, which can provide detailed information about the evolution of disturbances. The effects of ankle stiffness and foot structure on local stability are studied. In addition, we apply a control strategy based on local stability analysis to the limit cycle walker. Control is applied only in the phases with poor local stability. Simulation results show that the energy consumption is reduced without sacrificing disturbance rejection ability. This study may be helpful in motion control of limit cycle bipedal walking robots with flat feet and ankle stiffness and understanding of human walking principles.

Kinematic and Joint Compliance Modeling Method to Improve Position Accuracy of a Robotic Vision System.

In the field of robotic automation, achieving high position accuracy in robotic vision systems (RVSs) is a pivotal challenge that directly impacts the efficiency and effectiveness of industrial applications. This study introduces a comprehensive modeling approach that integrates kinematic and joint compliance factors to significantly enhance the position accuracy of a system. In the first place, we develop a unified kinematic model that effectively reduces the complexity and error accumulation associated with the calibration of robotic systems. At the heart of our approach is the formulation of a joint compliance model that meticulously accounts for the intricacies of the joint connector, the external load, and the self-weight of robotic links. By employing a novel 3D rotary laser sensor for precise error measurement and model calibration, our method offers a streamlined and efficient solution for the accurate integration of vision systems into robotic operations. The efficacy of our proposed models is validated through experiments conducted on a FANUC LR Mate 200iD robot, showcasing notable improvements in the position accuracy of robotic vision system. Our findings contribute a framework for the calibration and error compensation of RVS, holding significant potential for advancements in automated tasks requiring high precision.

Bioinspired compliant joints for passive-automatic adaptability

Modern engineering requires structural components that adapt to continuously changing conditions. Adaptability leads to multi-functionality, enhanced durability, and functional efficiency of mechanical systems. That is why adaptive structures have received increasing attention, especially in robotics, aerospace, automotive, and biomedical engineering. Current adaptive structures require significant active actuations and controls, factors that add to their complexity, weight, and production costs. In contrast, most biological adaptive systems respond to external stimuli in a passive-automatic way. Here, inspired by a striking biological example, i.e. insect wings and specifically their vein-joints, we develop structures in which adaptability is determined by the presence of a network of bioinspired compliant joints. By systematically changing the key geometric parameters of the bioinspired joints, we show that they can be designed in a variety of patterns to passively control the adaptability of the structures under loading. We further test the performance of the bioinspired joints in practice. The simplicity, scalability, and adjustability are the features that facilitate the widespread community uptake of our designs.

Dynamic compliance of energy-saving legged elastic parallel joints for quadruped robots: design and realization

Dynamic compliance of energy-saving legged elastic parallel joints for quadruped robots: design and realization

Design and position-tracking control of a flexible joint based on the tendon-sheath mechanism

In this study, a flexible joint comprising active and passive driving modes was designed based on the tendon-sheath mechanism. Further, angle sensors and series elastomers (SE) were integrated inside the joint to produce a compact and flexible structure. First, a model of the flexible joint was established based on the involved stiffness relation, and this model was validated using the dSPACE system. Next, to respond to the low control accuracy and poor anti-interference ability of the flexible joints, a sliding-mode controller (SMC) was designed to facilitate the precise position control, as well as achieve improved robustness. However, the flexible joint was prone to considerable tremors when the overall system was subjected to a large load mass. Therefore, a fuzzy-modified adaptive SMC (FMASMC), which adaptively adjusts the SMC parameters, was designed based on the historical-state data of the system. This control method could suppress the trembling phenomenon of the system while improving its control accuracy. Finally, it was experimentally verified that the compliant joint could achieve the expected functions. Compared with the proportional–integral–derivative (PID) and SMC control algorithms, the FMASMC algorithm could effectively overcome the tremors of the compliant actuation system and improve its control accuracy; moreover, it is also suitable for controlling other compliant joints.