Compliant Joints Research Articles

Learning-Based Multifunctional Elbow Exoskeleton Control

We propose a learning-based model for multifunctional elbow exoskeleton control, i.e., assist- and resist-as-needed (AAN and RAN). The model consists of online iterative learning and impedance adaptation mechanisms for predictive and variable compliant joint control. The model was implemented on a lightweight (0.425 kg) and portable elbow exoskeleton (i.e., POW-EXO) worn by three subjects, respectively. The implementation relies only on internal pose (e.g., joint position) feedback, rather than physical compliant mechanisms (e.g., springs) and external sensors (e.g., electromyography (EMG) or force) typically required by conventional exoskeletons and controllers. The proposed model provides a novel technique to achieve multifunctional exoskeleton control with minimal mechatronics and sensing. Interestingly, its RAN control and POW-EXO as a quantification means, may reveal interactive (mechanical) impedance variance and invariance in human motor control.

Nonlinear disturbance observer-based compliance error compensation in robotic milling

Robotic machining is of growing interest around the world, but the joint deflection from the reference trajectory due to the robot’s low rigidity restricts the use of robots only to machining with low cutting force. This paper proposes a new method for compensating the compliance error based on the nonlinear disturbance observer to reduce the deflection of robot joints against cutting forces. The disturbance observer designed in the joint spaces allows estimating the cutting forces online without any transformation between spaces so that the cutting forces could be obtained with high accuracy. The low-pass filter of the observer is optimized to reduce the effect of model uncertainty arising from the identification process. The deviation obtained by multiplying the joint compliances by the estimated cutting torques can be used to modify the reference position of robot joints. The proposed approach has the benefit to correct the robot's deflection in real time without a sensor. The experimental results reveal that the nonlinear disturbance observer can correctly estimate the cutting forces. Also, they show that the tool center point (TCP) deviation from the predefined path has been reduced using the proposed compliance error compensation.

A new resonance-based design approach to reduce motor torque requirements in automated machinery

In the last decades, compliant mechanisms have been widely studied but their application has not been widespread due to their susceptibility to fatigue and the lack of systematic design methodologies. In this paper, the authors propose a new approach to be used in the automated machinery mechanism design (the mechanisms are usually subjected to predominant inertial loads) that exploits the capability of the compliant joints to store and release elastic energy in order to reduce the motor torque requirements. Thanks to the carbon-fiber reinforced 3D printing technologies, the compliant joint stiffness can be properly designed to obtain, for the considered mechanism, a resonant condition during its nominal functioning. Moreover, topology optimization can be successfully employed to reduce the mechanism component inertia (keeping the same overall mechanism stiffness) and thus, further diminish the torque requirements. In order to assess the quality of the proposed approach, a pusher mechanism used in a real automated machine has been considered. A prototype has been manufactured to evaluate the effect of the compliant joint introduction and the topology optimization on the motor torque reduction. To validate the results, an experimental campaign has been conducted. Comparison between the standard design approach and the new one emphasizes the superior contribution of compliant joint introduction on the motor torque reduction: a 97% and 96% reduction on the RMS and peak motor torque, respectively, is achieved resorting to the new design approach. Although a high repeatability is achieved, a slight deviation of the trajectory with respect to the ideal one is however registered.

3D printing non-assembly compliant joints for soft robotics

This paper investigates integrating non-assembly three-dimensional (3D)-printed joints and soft robotic muscles in order to make a tendon-driven robotic finger. A finger-type structure actuated by electro-thermal soft actuator mechanism is introduced, including a bio-inspired 3D-printed compliant joint. As an affordable but high-performance component, twisted and coiled polymer (TCP) is used to drive the system as an actuator. The Euler–Lagrangian method and a transfer function based on an electro-thermo-mechanical model are used to analyze finger joints. The compliant joints are non-assembly 3D-printed spiral springs with high customization capabilities incorporated into the model. The simulation analysis is conducted to elucidate how the electro-thermal muscle and the spiral spring joint properties influence the finger motion. The results reveal further understanding of the 3D-printed spiral spring joints effects on the behavior of the soft robotic limbs. The suggested method can be adapted and employed in a broad variety of medicinal and industrial applications.

Increasing displacement range in 3D printed compliant joints via bio-inspired slot patterns: An exploratory study

Compliant joints own their motion performance to three main aspects: base material, geometrical design, and dimensions. When aiming to increase their motion range without affecting the overall assembly of the system in which they are employed, modifying the design or dimensions is not appropriate anymore. To overcome this, the current work presents a novel strategy for increasing the motion range of the split tube flexural pivots joint based on removing material from the complaint joint using two specific bio-inspired patterns. These bio-inspired patterns are based on the shells encountered in Testudines (tortoise) and Dasypodidae (armadillo). Then, these patterns were parametrized, and their effective mechanical properties evaluated on 3D printed samples. Features of the flexible region of the flexural pivot joint were varied to identify the conditions in which the motion range increases. A factorial analysis was made to obtain the angular displacement response based on the determined parameters, which depend on the flexible region features. The use of these patterns successfully demonstrated the reduction in stiffness of the joints, obtaining increments in displacements twice in the stiffest case and 4.25 times in the most flexible one. Secondary displacements were also analyzed. Displacements measured were characterized via computationally analyzed images and recordings. Finally, the mechanical properties measured were compared to computationally predicted properties via Finite Element Models. Predictions resulted in good agreement with the experimental measurements with errors below 10% in most cases and up to 15% in the worst cases. These were attributed to manufacturing defects in the samples.

Impedance Control Using Selected Compliant Prismatic Joint in a Free-Floating Space Manipulator

The success of space missions like capture-and-deorbit or capture-and-service relies on the ability of the capturing satellite to establish a stable mechanical connection by its gripping tool with the object being intercepted. Most of the potential objects of capture missions are not equipped with dedicated docking ports; hence, the satellite robot intercepting them will have to provide the mechanical compliance necessary for the safe establishment of contact between the two structures. Articulated robotic arms with controlled mechanical impedance are one set of promising solutions for this challenge. In this study, the authors discuss how the mechanical impedance realized only along a single axis can be useful for facilitating the contact between the manipulator arm’s end effector of a free-floating robot and an uncooperative object in microgravity. By distinguishing a dominant direction in the final approach and contact establishment maneuver, the need for impedance control of six degrees of freedom may be relaxed, and a single prismatic joint with controlled impedance can be used at the end effector. Such architecture is simulated and compared with the full model-based six-degree-of-freedom Cartesian impedance control of a free-floating manipulator. Authors then discuss the limitations and possibilities of such architecture in a potential practical setting.

A computational design of robotic grasper by intelligence-based topology optimization for microassembly and micromanipulation

In robotic microassembly and micromanipulation, robotic grasper plays a vital role in picking up and releasing the product. However, the design synthesis method for creating a new robotic grasper has not deeply considered yet. Therefore, this article presents an effective computation method for designing a new robotic grasper that can be used for microassembly and micromanipulation. Firstly, a new structural scheme of robotic grasper is made by using the topology procedure. The compliance is the objective with the stress constraint during the topology. Then, a new variant of the grasper is refined where compliant joints are needed to reach the better compliance and the elastic motions of grasping hands. In the second phase, the modeling establishment for predicting the behaviors of the grasper are built via using the intelligent computation, namely GENFIS#1-neuro-fuzzy inference system (ANFIS), GENFIS#2-ANFIS, and GENFIS#3-ANFIS. The numerical data of the grasper are collected via the design of experiment-based finite element method. The results indicated that the GENFIS#3-ANFIS type is the best solver for modeling the hand’s stroke, the resonant frequency, and the strain energy. Meanwhile, the GENFIS#2-ANFIS type was the best procedure for modeling the stress. Subsequently, the optimum geometrical dimensions of the grasper are searched by using the Bonobo optimizer to improve the four mentioned performances of the grasper. In the circumstance #1, the results found that the hand’s displacement is about 0.0922 mm, the resonant frequency is 67.6247 Hz, the elastic energy is 1.4550 mJ, and the stress is 6.7249 MPa. The circumstance #2 determined the resonant frequency of 67.6247 Hz, the hand’s displacement of 0.0883 mm, the elastic energy of 1.9914 mJ, and the stress of 6.7086 MPa. Finally, the circumstance #3 found the elastic energy of 2.0501 mJ, the hand’s displacement of 0.0884 mm, the resonant frequency of 80.0012 Hz, and the stress of 6.7046 MPa. Statistically compared with the other methods, the presented method is the simple and effective procedure for designing 3D printed robotic grasper.

Design and analysis of a lightweight lower extremity exoskeleton with novel compliant ankle joints.

The exoskeleton for lower limb rehabilitation is an uprising field of robot technology. However, since it is difficult to achieve all the optimal design values at the same time, each lower extremity exoskeleton has its own focus. This study aims to develop a modular lightweight lower extremity exoskeleton (MOLLEE) with novel compliant ankle joints, and evaluate the movement performance through kinematics analysis. The overall structure of the exoskeleton was proposed and the adjustable frames, active joint modules, and compliant ankle joints were designed. The forward and inverse kinematics models were established based on the geometric method. The theoretical models were validated by numerical simulations in ADAMS, and the kinematic performance was demonstrated through walking experiments. The proposed lower extremity offers six degrees of freedom (DoF). The exoskeleton frame was designed adjustable to fit wearers with a height between 1.55m and 1.80m, and waist width from 37cm to 45cm. The joint modules can provide maximum torque at 107Nm for adequate knee and hip joint motion forces. The compliant ankle can bear large flexible deformation, and the relationship between its angular deformation and the contact force can be fitted with a quadratic polynomial function. The kinematics models were established and verified through numerical simulations, and the walking experiments in different action states have shown the expected kinematic characteristics of the designed exoskeleton. The proposed MOLLEE exoskeleton is adjustable, modular, and compliant. The designed adjustable frame and compliant ankle can ensure comfort and safety for different wearers. In addition, the kinematics characteristics of the exoskeleton can meet the needs of daily rehabilitation activities.

Finite Element Modeling of Internally Actuated Triangular Lattice and Its Variants for Modular Active Cell Robots (MACROs)

Modular Active Cell Robots (MACROs) is an approach for modular robot hardware that leverages simple components such as actuators and compliant joints to make large deformable robotic structures. In this letter, we consider the planar triangular lattice and its sparser variants as the candidate mesh topologies for MACROs. Through Finite Element (FE) simulations, we quantify the deformations obtained for different choices of edges being actuated in the MACRO mesh. Further, we use this data to identify optimal actuation strategies for a target deformation. We demonstrate a trade-off between passive stiffness and actuation energy and thereafter, we refine the triangular lattice by removing edges to reduce the actuation energy without a significant reduction in stiffness. We also identify the refined meshes optimal for desired specifications.

Compliant Cross-Axis Joints: A Tailoring Displacement Range Approach via Lattice Flexures and Machine Learning

Compliant joints are flexible elements that allow displacement due to the elastic deformations they experience under the action of external loading. The flexible parts responsible for these displacements are known as flexure hinges. Displacement, or motion range, in compliant joints depends on the stiffness of the flexure hinges and can be tailored through various parameters, including the overall dimensions, the base material, and the distribution within the hinge. Considering the distribution, we propose the stiffness modification of a compliant cross-axis joint via the use of lattice mechanical metamaterials. Due to the wide range of parameters that influence the stiffness of a lattice, different machine learning algorithms (artificial neural networks, support vector machine, and Gaussian progress regression) were proposed to forecast these parameters. Here, the machine learning algorithm with the best forecasting was the Gaussian progress regression; this algorithm has the advantage of well-tuning even with small regression databases, allowing these functions to more easily adjust to suit specific data, even if the dataset is small. Hexagonal, re-entrant, and square lattices were studied as flexure hinges. For each, the effect of the unit cell size and its orientation with respect to the principal axis on the effective stiffness were studied via computational and laboratory experiments on additively manufactured samples. Finite element predictions resulted in good agreement with the experimentally obtained data. As a result, using lattice-flexure hinges led to increments in displacement ranging from double to ten times those obtained with solid hinges. The most suitable machine learning algorithm was the Gaussian progress regression, with a maximum error of 0.12% when compared to the finite element analysis results.

Mechanical Characterization of Compliant Cellular Robots. Part I: Passive Stiffness

Abstract Modular active cell robots (MACROs) are a design paradigm for modular robotic hardware that uses only two components, namely actuators and passive compliant joints. Under the MACRO approach, a large number of actuators and joints are connected to create mesh-like cellular robotic structures that can be actuated to achieve large deformation and shape change. In this two-part paper, we study the importance of different possible mesh topologies within the MACRO framework. Regular and semi-regular tilings of the plane are used as the candidate mesh topologies and simulated using finite element analysis (FEA). In Part 1, we use FEA to evaluate their passive stiffness characteristics. Using a strain-energy method, the homogenized material properties (Young's modulus, shear modulus, and Poisson's ratio) of the different mesh topologies are computed and compared. The results show that the stiffnesses increase with increasing nodal connectivity and that stretching-dominated topologies have higher stiffness compared to bending-dominated ones. We also investigate the role of relative actuator-node stiffness on the overall mesh characteristics. This analysis shows that the stiffness of stretching-dominated topologies scales directly with their cross-section area whereas bending-dominated ones do not have such a direct relationship.

Mechanical Characterization of Compliant Cellular Robots. Part II: Active Strain

Abstract Modular active cell robots (MACROs) is a design approach in which a large number of linear actuators and passive compliant joints are assembled to create an active structure with a repeating unit cell. Such a mesh-like robotic structure can be actuated to achieve large deformation and shape-change. In this two-part paper, we use finite element analysis (FEA) to model the deformation behavior of different MACRO mesh topologies and evaluate their passive and active mechanical characteristics. In Part I, we presented the passive stiffness characteristics of different MACRO meshes. In this Part II of the paper, we investigate the active strain characteristics of planar MACRO meshes. Using FEA, we quantify and compare the strains generated for the specific choice of MACRO mesh topology and further for the specific choice of actuators actuated in that particular mesh. We simulate a series of actuation modes that are based on the angular orientation of the actuators within the mesh and show that such actuation modes result in deformation that is independent of the size of the mesh. We also show that there exists a subset of such actuation modes that spans the range of deformation behavior. Finally, we compare the actuation effort required to actuate different MACRO meshes and show that the actuation effort is related to the nodal connectivity of the mesh.

An Approach for Predicting Stiffness of a 5-DOF Hybrid Robot for Friction Stir Welding

This paper presents an approach for stiffness identification of a 5-DOF hybrid robot named TriMule for friction stir welding. The novelty of this approach is to visualize the realistic robotic system that considers the elastic deflections of all joints and links as a fictitious robotic system that only considers the elastic deflections of joints along their axes. Thus the number of parameters to be identified is reduced significantly. The stiffness identification is essentially implemented by the following four steps: (1) formulating the Cartesian stiffness model that maps the joint compliances of the fictitious system to the deflection twist of the end-effector, (2) parameterizing the joint compliances by a set of polynomial functions in terms of nominal actuated joint variables, (3) constructing the multiple linear regression equations by projecting the measured elastic deflections from the operational space onto the joint space, and (4) estimating the polynomial coefficients by robust biased estimation. The stiffness identification experiment and offline compensation experiment for the tool path deviations are carried out on a prototype machine to demonstrate the effectiveness of the proposed approach.

Compliant Joints with Remote Centre of Compliance for the Improvement of the Motion Accuracy of a Gantry Stage

Compliant Joints with Remote Centre of Compliance for the Improvement of the Motion Accuracy of a Gantry Stage

Novel Adaptive Extended State Observer for Dynamic Parameter Identification with Asymptotic Convergence

In this paper, a novel method of parameter identification of linear in parameter dynamic systems is presented. The proposed scheme employs an Extended State Observer to online estimate a state of the plant and momentary value of total disturbance present in the system. A notion is made that for properly redefined dynamics of the system, this estimate can be interpreted as a measure of modeling error caused by the parameter uncertainty. Under this notion, a disturbance estimate is used as a basis for classic gradient identification. A global convergence of both state and parameter estimates to their true values is proved using the Lyapunov approach under an assumption of a persistent excitation. Finally, results of simulation and experiments are presented to support the theoretical analysis. The experiments were conducted using a compliant manipulator joint and obtained results show the usefulness of the proposed method in drive control systems and robotics.

A Novel Design of Torsion Spring-Connected Nonlinear Stiffness Actuator Based on Cam Mechanism

Abstract The nonlinear stiffness actuator (NSA) is a type of compliant joint with variable stiffness that is necessary for human–machine collaboration and has been the focus of extensive research attention. This academic work presents the principle of a torsion spring-connected nonlinear stiffness actuator (TSNSA), a NSA suitable for implementing revolute motions, which contrasts with existing NSAs that often have bulky mechanisms and are affected by a limited range of movement. It has a split sleeve, disc springs, and cam mechanisms (CMs) that when correctly configured, can passively and actively adjust stiffness, where the speed of stiffness regulation can be effectively improved. The mathematical model of a split sleeve inserted into a torsion spring is designed to analyze the behavior of mechanical components. Furthermore, a detailed CM profile has been designed to obtain the desired nonlinear stiffness. Its theoretical analysis includes numerical simulations with results consistent with the desired deflection–torque profile.

Fatigue damage and life evaluation of thick bi‐material double strap joints for use in marine applications

AbstractThe present‐day interest in the use of composite‐steel joints in primary marine structures requires an in‐depth knowledge of the fatigue performance of thick adhesive joints. This paper reports on experimental tests performed on compliant (i.e., thick and ductile) adhesive joints based on a two‐component methyl‐methacrylate adhesive in unaged and aged conditions. Bi‐material double strap joint with thick adhesive bondlines is subjected to quasi‐static and fatigue loading, during which the specimens are monitored by digital mage correlation and infrared thermography techniques to evaluate the types and extent of damage that occur in the joint during fatigue loading. The S‐N curve of the aged joint is evaluated along with its fatigue limit. It is found that the unaged specimens fail due to cohesive damage, hackles, and disbond at the adhesive‐adherend interface and the aged specimens fail due to delamination within the composite. The specimens that survived fatigue loading showed similar residual strength as specimens that were not fatigue loaded.

Optimization of Stress Distribution in Tendon-Driven Continuum Robots Using Fish-Tail-Inspired Method

Tendon-driven continuum robots are widely used in different engineering disciplines due to their simple structure and high flexibility. The typical structure of a tendon-driven continuum robot usually contains a series of identical compliant joints in its backbone to achieve large-deflection bending movements. However, with compliant joints of the same geometry, the real bending shape of the robot backbone is an arc with variable curvature, which results in uneven stress distribution along the robot backbone. In the long term, higher stresses in the compliant joints near the fixation base could lead to fatigue or fracture of the entire robot structure. To cope with this problem, we propose a fish-tail-inspired method in this letter to optimize the stress distribution along the serial compliant joints. Several optimization examples were presented to show the performance of the proposed method. Simulation and experimental results have demonstrated that the developed method can effectively reduce the stress differences in serial compliant joints during large-deflection bending movements.

3D printed deployable origami patterns at intermediate folding configurations for wave guiding applications

Origami-based engineering employs the use of complex reconfigurable structures for a variety of applications in science and engineering. Most origami-inspired structures are designed to be fully deployed, yet wave guiding arrays require deployment to stable intermediate folding configurations to focus waves. Furthermore, current research for origami-inspired wave guiding does not study kinetic and kinematic behavior during compaction and deployment. In this study, the force required to compact the Miura-ori unit cell with compliant joints is investigated for intermediate folding configurations. By starting at intermediate folding angles, the maximum force to reach a fully compact shape can be reduced by over an order of magnitude compared to starting at a flat state.

Identification of elasto-static parameters of an industrial robot using monocular camera

This article discusses the identification of elasto-static parameters of an industrial robot using measurements from a monocular camera. The method of identification involved a parametric method for estimation and the experimental strategy involved joint wise actuation about a particular pose, inspired by the geometric method of parameter identification. The measurements were made using a monocular camera utilizing fiducial markers. The joint compliance values were obtained using a two-stage approach which made it easy to analyze the observability of parameters to be identified. Coupled with the proposed strategy of experiments, it was possible to check the observability of parameters throughout the whole workspace. It was found that most of the workspace regions of the robot where the experiments were feasible, had high values of observability which simplified the experiments. During experimental validation on the Fanuc 165F robot, the kinematic parameters were initially estimated and the results were found to be superior compared to a recently proposed approach while considering the errors in positioning. Later the end-effector of the robot was subjected to an external load. Deflection due to loading on the end-effector, calculated using pose measurements from an industrial camera was found comparable to that from a laser tracker. Measured values for position repeatability of the robot were close to the robot specifications as well. The end-effector errors could be reduced by 45% after compensating errors due to kinematic and elasto-static parameters while using the proposed method wherein measurements from a monocular camera were used.