Compliant Parallel Mechanism Research Articles

Design and kinematic analysis of a novel decoupled 3D ultrasonic elliptical vibration assisted cutting mechanism

The 3D elliptical vibration-assisted cutting (EVC) mechanism with arbitrary elliptical locus in space has a wide array of industrial applications for generating micro/nano-structured surface. However, the current 3D EVC mechanism are limited by their motion couplings, resonant frequencies and regulation of arbitrary elliptical locus. In order to improve the output properties, an innovative decoupled 3D ultrasonic EVC mechanism is proposed in the form of compliant parallel mechanism. First, the proposed 3D ultrasonic EVC mechanism is specifically designed to be capable of generating uniformly magnified output displacement in three directions and its 3D elliptical locus is obtained by the designed multi-axis flexure hinge structure with three orthogonal sub chains. Design process of multi-axis flexure hinge structure is respectively described from displacement amplification and decoupling output. The kinematics and amplification ratios of the designed 3D EVC mechanism are analytically modeled and a finite element analysis is performed to validate the designed 3D EVC mechanism. Based on the analysis results, a prototype device is fabricated, and then its vibration characteristics are evaluated by using the established test system. The test experiments show that the performance of the developed 3D ultrasonic EVC mechanism is satisfied.

Design and DOF Analysis of a Novel Compliant Parallel Mechanism for Large Load.

The degree of freedom (DOF) and motion characteristics of a kind of compliant spherical joint were analyzed based on the screw theory, and a new design scheme for force-inversion of the compliant spherical joint was proposed in this paper. A novel type of six DOF compliant parallel mechanism (CPM) was designed based on this scheme to provide a large load capacity and achieve micrometer-level positioning accuracy. The compliance matrix of the new type of CPM was obtained through matrix transformation and was then decomposed into its generalized eigenvalues. Then, the DOF of the mechanism was numerically analyzed based on the symbolic formulation. The finite element analysis model of the compliant parallel mechanism was established. The static load analysis was used to verify the large load capacity of the mobile platform. By comparing the deformation obtained by the compliance matrix numerical method with the deformation obtained by the finite element method, the correctness of the compliance matrix and the number of the DOF of the CPM was verified.

A closed-form nonlinear model for spatial Timoshenko beam flexure hinge with circular cross-section

Beam flexure hinges can achieve accurate motion and force control through the elastic deformation. This paper presents a nonlinear model for uniform and circular cross-section spatial beam flexure hinges which are commonly employed in compliant parallel mechanisms. The proposed beam model takes shear deformations into consideration and hence is applicable to both slender and thick beam flexure hinges. Starting from the first principles, the nonlinear strain measure is derived using beam kinematics and expressed in terms of translational displacements and rotational angles. Second-order approximation is employed in order to make the nonlinear strain within acceptable accuracy. The natural boundary conditions and nonlinear governing equations are derived in terms of rotational Euler angles and subsequently solved for combined end loads. The resulting end load-displacement model, which is compact and closed-form, is proved to be accurate for both slender and thick beam flexure using nonlinear finite element analysis. This beam model can provide designers with more design insight of the spatial beam flexure and thus will benefit the structural design and optimization of compliant manipulators.

On the validity of compliance-based matrix method in output compliance modeling of flexure-hinge mechanism

Compliance-based matrix method (CMM) has been regarded as an efficient technique for output compliance modeling of the flexure hinge-based compliant mechanism, owing to its simplicity and high accuracy. However, this study demonstrates that CMM is not always valid due to the intrinsic ill-condition of the compliance matrix of right circular flexure hinge (RCFH). Inversion of compliance matrix can result in numerical instability in the calculation of its stiffness matrix. It is shown in this study that CMM can be effectively applied to serial compliant mechanism, while its adoption in modeling parallel compliant mechanism needs to be carefully examined due to the matrix inversion involved. The validity of CMM is highly dependent on the spatial configuration, degree of freedom, and singularity of the parallel mechanism. The validity criteria of CMM are discussed in detail with exemplary configurations of 3RRR, 2RR, and bridge-type compliant mechanisms.

Investigation of 2-DOF Compliant Translational Parallel Mechanism and Applied in the Docking Device

Investigation of 2-DOF Compliant Translational Parallel Mechanism and Applied in the Docking Device

Kinematic analysis and optimization of a planar parallel compliant mechanism for self-alignment knee exoskeleton

Abstract. Misalignment between the instantaneous center of rotation (ICR) of human joint and the ICR of wearable robotic exoskeleton widely exists among most of exoskeletons widely used in rehabilitation, which results in discomfort, even endangers human safety. In order to alleviate it, this study focuses on the solution of misalignment in knee joint of lower limb exoskeletons, and proposes a compliant five-bar parallel mechanism, which offers two mobility in sagittal plane, as well as the torsional springs mounted on this mechanism, have the potential to automatically adjust the ICR of output link connected to thigh with respect to the basis link connected to shank. To reach this goal, we build the stiffness model of the mechanism and optimize its variables. And the self-alignment of the compliant five-bar parallel mechanism is verified via experimental investigations.

Geometric Approach to the Realization of Planar Elastic Behaviors With Mechanisms Having Four Elastic Components

This paper addresses the passive realization of any selected planar elastic behavior with redundant elastic manipulators. The class of manipulators considered are either serial mechanisms having four compliant joints or parallel mechanisms having four springs. Sets of necessary and sufficient conditions for mechanisms in this class to passively realize an elastic behavior are presented. The conditions are interpreted in terms of mechanism geometry. Similar conditions for nonredundant cases are highly restrictive. Redundancy yields a significantly larger space of realizable elastic behaviors. Construction-based synthesis procedures for planar elastic behaviors are also developed. In each, the selection of the mechanism geometry and the selection of joint/spring stiffnesses are completely decoupled. The procedures require that the geometry of each elastic component be selected from a restricted space of acceptable candidates.

Position-Space-Based Design of a Symmetric Spatial Translational Compliant Mechanism for Micro-/Nano-Manipulation.

Symmetry enables excellent motion performance of compliant mechanisms, such as minimized parasitic motion, reduced cross-axis coupling, mitigated buckling, and decreased thermal sensitivity. However, most existing symmetric compliant mechanisms are heavily over-constrained due to the fact that they are usually obtained by directly adding over-constraints to the associated non-symmetric compliant mechanisms. Therefore, existing symmetric compliant mechanisms usually have relatively complex structures and relatively large actuation stiffness. This paper presents a position-space-based approach to the design of symmetric compliant mechanisms. Using this position-space-based approach, a non-symmetric compliant mechanism can be reconfigured into a symmetric compliant mechanism by rearranging the compliant modules and adding minimal over-constraints. A symmetric spatial translational compliant parallel mechanism (symmetric XYZ compliant parallel mechanism (CPM)) is designed using the position-space-based design approach in this paper. Furthermore, the actuation forces of the symmetric XYZ CPM are nonlinearly and analytically modelled, which are represented by the given primary translations and the geometrical parameters. The maximum difference, between the nonlinear analytical results and the nonlinear finite element analysis (FEA) results, is less than 2.58%. Additionally, a physical prototype of the symmetric XYZ CPM is fabricated, and the desirable motion characteristics such as minimized cross-axis coupling are also verified by FEA simulations and experimental testing.

Systematic Approach to the Design of Spatial Translational Compliant Parallel Mechanisms

Systematic Approach to the Design of Spatial Translational Compliant Parallel Mechanisms

Stiffness Analysis and Optimization for a Compliant-Parallel Mechanism

Stiffness Analysis and Optimization for a Compliant-Parallel Mechanism

A novel 5-DOF high-precision compliant parallel mechanism for large-aperture grating tiling

Abstract. In combination with the advantages of parallel mechanisms and compliant mechanisms, a 5-DOF compliant parallel mechanism is designed to meet the requirements, such as large stroke, large load capacity, high precision and high stability, for a large-aperture grating tiling device. The structure and characteristics of the 5-DOF compliant parallel mechanism are presented. The kinematics of the mechanism are derived based on a pseudo-rigid-body model as well. To increase the tiling position retention stability of the mechanism, a closed-loop control system with capacitive position sensors, which are employed to provide feedback signals, is realized. A position and orientation monitoring algorithm and a single neuron adaptive full closed-loop control algorithm are proposed. Performance testing is implemented to verify the accuracy and the tiling position retention stability of the grating tiling device. The experimental results indicate that the tiling accuracy reaches 0.2 µrad per step and 20 nm per step, and the tiling position retention stability can achieve 1.2 µrad per 30 min and 35 nm per 30 min in the rotational direction and the translational direction, respectively.

Compact compliant parallel XY nano-positioning stage with high dynamic performance, small crosstalk, and small yaw motion

This paper presents a novel XY nano-positioning stage using a compliant parallel mechanism with small crosstalk and yaw motion. A parallel mechanism can implement multi-degree-of-freedom motion with a small footprint. However, this implies crosstalk between the motion axes. In an effort to reduce crosstalk and yaw motion, we proposed a novel flexure guide structure. The proposed stage consists of two flexure displacement amplifiers driven by piezoelectric actuators, two combined double four-bar flexure guides, and two additional parallelogram guides. To prevent the rotational deformation of one amplifier due to the transverse force of the other, we introduce an intermediate leaf spring at the output ends of the amplifiers. This new parallel mechanism is optimally designed based on an analytical model of the stage to assure small crosstalk and yaw motion. The analytical model is verified as being well-described using a finite element analysis. An XY nano-positioning stage of size 150 × 150 × 30 mm3 is fabricated following the optimal design. Experiments are carried out to verify the static and dynamic performances of the proposed XY nano-positioning stage. The proposed stage has an X and Y directional motion range of 120 μm in closed loop. The resolution of the stage is 3 nm in both the X and Y directional motions. The actual crosstalk and yaw were limited to 0.770 μm and 13.5 μrad, while in the optimal design they were estimated at 0.5 μm and 15 μrad, respectively.

Jacobian-Based Topology Optimization Method Using an Improved Stiffness Evaluation

A Jacobian-based topology optimization method is recently proposed for compliant parallel mechanisms (CPMs), in which the CPMs' Jacobian matrix and characteristic stiffness are optimized simultaneously to achieve kinematic and stiffness requirement, respectively. Lately, it is found that the characteristic stiffness fails to ensure a valid topology result in some particular cases. To solve this problem, an improved stiffness evaluation based on the definition of stiffness is adopted in this paper. This new stiffness evaluation is verified and compared with the characteristic stiffness by using several design examples. In addition, several typical benchmark problems (e.g., displacement inverter, amplifier, and redirector) are solved by using the Jacobian-based topology optimization method to show its general applicability.

A 3-D Printed Ti-6Al-4V 3-DOF Compliant Parallel Mechanism for High Precision Manipulation

This paper presents the synthesis and evaluation of a 3-D printed three degrees-of-freedom (DOF) spatial-motion compliant parallel mechanism (CPM). The CPM was synthesized by the beam-based structural optimization method and a prototype was fabricated by the electron beam melting (EBM) technology with Ti6Al4V material. The mechanical characteristics of 3-D printed compliant mechanism for precision applications, i.e., stiffness property, dynamic response, and large elastic deformation, were experimentally evaluated. Most importantly, a coefficient factor of 1.27 was proposed to determine the effective thickness for 3-D printed compliant mechanisms with 0.5 mm thick flexures. Using the effective thickness, the characteristics of the 3-D printed CPM have shown to agree with the prediction, with a maximum deviation of 10.5%. The Ti6Al4V CPM is able to achieve the large work range up to 4 mm of linear displacement, 6 degrees of angular displacements, fast dynamic response of 119 Hz, good decoupled motions, and high non-actuating stiffness. A 3-DOF manipulator was built based on the 3-D printed CPM and actuated by three voice-coil motors. Experimental results have shown that the 3-DOF manipulator could achieve repeatable motions with resolution of 20 nm for the translation along the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -axis, 0.14 arcsecond for the rotation about the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -axis, and 0.12 arcsecond for the rotation about the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> -axis. In conclusion, EBM technology is suitable for fabricating compliant mechanisms in precision manipulator systems; the mechanical characteristics of 3-D printed compliant mechanisms are predictable when an effective thickness is used.

Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints

This paper focuses on a new type of configuration design of a compliant parallel mechanism (CPM) planar continuum structure and its characteristic analysis of vibration-inherent frequency for planar motion, which can suppress the impact of random vibration in ultra-precision positioning and manufacturing equipment and improve the inherent frequency response of the mechanism. Firstly, a vector-mapping isomorphism between the fully CPM and conventional isomorphic parallel mechanism was constructed with a kinematic differential Jacobian matrix. Then, the mathematical model of topology optimization was put forward considering the compromise programming on the static stiffness and mean vibration-inherent frequency of the mechanism as the design variable and the minimization of compliance as the objective function. A constraint of volume fraction was considered and multi-objective micro displacement mechanism topology optimization based on a prismatic-revolute-revolute (3-PRR) planar nano-positioning continuum structure was performed using the solid isotropic material with penalization (SIMP) technique, which combines the criteria of the optimization algorithm and the vector isomorphic mapping method. Multi-objective topology optimization of the continuum structure micro displacement mechanism was investigated and presented by optimizations with different initial rejection rates. The simulation results show that the stiffness and vibration suppression performance of the continuum structure were improved, whereas the positioning of differential kinematics characteristics of the 3-PRR micro displacement planar fully CPM and isomorphic prototype mechanism retain the same. The modal analysis also provides a rational configuration for the micro displacement mechanism dimensional design and its optimal modal parameters. The crossover oscillation in frequency response of the continuum structure was reduced and quickly converged in the optimization iterations. The performance of the optimized mechanism was verified by the experiments on a planar fully compliant micro displacement continuum structure based on Lead Zirconate Titanate (PZT) actuator.

Systematic Design Method and Experimental Validation of a 2-DOF Compliant Parallel Mechanism with Excellent Input and Output Decoupling Performances

The output and input coupling characteristics of the compliant parallel mechanism (CPM) bring difficulty in the motion control and challenge its high performance and operational safety. This paper presents a systematic design method for a 2-degrees-of-freedom (DOFs) CPM with excellent decoupling performance. A symmetric kinematic structure can guarantee a CPM with a complete output decoupling characteristic; input coupling is reduced by resorting to a flexure-based decoupler. This work discusses the stiffness design requirement of the decoupler and proposes a compound flexure hinge as its basic structure. Analytical methods have been derived to assess the mechanical performances of the CPM in terms of input and output stiffness, motion stroke, input coupling degree, and natural frequency. The CPM’s geometric parameters were optimized to minimize the input coupling while ensuring key performance indicators at the same time. The optimized CPM’s performances were then evaluated by using a finite element analysis. Finally, a prototype was constructed and experimental validations were carried out to test the performance of the CPM and verify the effectiveness of the design method. The design procedure proposed in this paper is systematic and can be extended to design the CPMs with other types of motion.

Analytical Compliance Modeling of Serial Flexure-Based Compliant Mechanism Under Arbitrary Applied Load

Analytical compliance model is vital to the flexure- based compliant mechanism in its mechanical design and motion control. The matrix is a common and effective approach in the compliance modeling while it is not well developed for the closed-loop serial and parallel compliant mechanisms and is not applicable to the situation when the external loads are applied on the flexure members. Concise and explicit analytical compliance models of the serial flexure-based compliant mechanisms under arbitrary loads are derived by using the matrix method. An equivalent method is proposed to deal with the situation when the external loads are applied on the flexure members. The external loads are transformed to concentrated forces applied on the rigid links, which satisfy the equations of static equilibrium and also guarantee that the deformations at the displacement output point remain unchanged. Then the matrix method can be still adopted for the compliance analysis of the compliant mechanism. Finally, several specific examples and an experimental test are given to verify the effectiveness of the compliance models and the force equivalent method. The research enriches the matrix method and provides concise analytical compliance models for the serial compliant mechanism.

Design, Development, and Application of a Compact Flexure-Based Decoupler With High Motion Transmission Efficiency and Excellent Input Decoupling Performance

Here, we present the design, development, and application of a compact flexure-based decoupler, which is commonly utilized in compliant parallel mechanisms (CPMs) to transmit the motion of an actuator and protect the actuator from suffering transverse loads. The kinematic structure selection of the decoupler is first introduced. Then, several specific design requirements are proposed to guarantee its key performances. On this basis, the detailed structures of each part of the decoupler are discussed and the geometric parameters are optimized to obtain an ideal decoupler. The performances of the optimized decoupler are verified with finite element analysis (FEA). According to the optimized results, a prototype is fabricated and experimental tests on the input axial stiffness and natural frequency are presented. Both FEA and the experimental results demonstrate the excellent performance of the decoupler. Finally, the proposed decoupler is applied in the development of a 2-DOF CPM. The definition and calculation expression for the input coupling degree (ICD) of the CPM are given, and its geometric parameters are optimized to reduce the ICD. A prototype of the CPM is fabricated for the performance evaluation. A new method is proposed to test the ICD of the CPM by detecting the variations of axial forces along the two axes. Contouring properties of 2-D trajectories are also provided. The experimental results not only demonstrate the excellent decoupling performance of the CPM but also verify the effectiveness of the adoption of the decoupler.

柔軟パラレルメカニズムの剛性最適化

In this study, we proposed a spring joint’s structure with non-linear rigidity and a 2-DOF compliant parallel mechanism including the spring’s structures. First we conducted a FEM analysis of the spring’s structure. The analysis is revealed that the spring’s structure has a characteristic that the structure is increased rigidity with a 1-DOF rotation of the structure. Finally, we reveal that the spring’s structure compensated a decreasing a rigidity of the compliant mechanism with depending own posture.

Design, modeling, analysis and testing of a novel piezo-actuated XY compliant mechanism for large workspace nano-positioning

In this paper, a new piezo-actuated XY parallel compliant mechanism for large workspace nano-positioning with decoupled motions is developed by incorporating a novel Z-shaped flexure hinge (ZFH)-based mechanism into the mirror-symmetrically distributed structure. The bridge-type mechanism and two-stage leverage mechanisms serve as preliminary displacement amplifiers, while further amplification with motion transfer and decoupled output motions are achieved by means of the ZFH mechanism. Based on finite element theory, a high-precision analytical model of the XY compliant mechanism is established by considering all the connecting linkages as flexible components. Through the improved differential evolution algorithm, the optimized compliant mechanism is capable of performing millimeter-scale workspace nano-positioning with decoupled motions. In addition, the input displacement unbalance, resulting from the lateral force which has potential to damage the piezoelectric actuators, is markedly lowered to a negligible value. The performance of the fabricated compliant mechanism with optimized parameters is investigated to well agree with both the analytical model and ANSYS simulation. In addition, based on the inverse kinematics derived from the model and experimental results, different elliptical vibration trajectories are accurately acquired.