On the influence of local and global stress constraint and filtering radius on the design of hinge-free compliant mechanisms

Distributed compliant mechanisms are components that use elastic strain to obtain a desired kinematic behavior. Compliant mechanisms obtained via topology optimization using the standard approach of minimizing/maximizing the output displacement with a spring at the output port, representing the stiffness of the external medium, usually contain one-node connected hinges. Those hinges are undesired since an ideal compliant mechanism should be a continuous part. This work compares the use of two strategies for stress constrained problems: local and global stress constraints, and analyses their influence in eliminating the one-node connected hinges. Also, the influence of spatial filtering in eliminating the hinges is studied. An Augmented Lagrangian formulation is used to couple the objective function and constraints, and the resulting optimization problem is solved by using an algorithm based on the classical optimality criteria approach. Two compliant mechanisms problems are studied by varying the stress limit and filtering radius. It is observed that a proper combination of filtering radius and stress limit can eliminate one-node connected hinges.     

A novel design and fabrication of a micro-gripper for manipulation of micro-scale parts actuated by a bending piezoelectric

In this study, a novel micro-gripper using a piezoelectric actuator was designed and improved by the design of experiments (DOE) approach. Using a bending PZT actuator connected to the micro-gripper by a rigid wedge can be considered as a novel approach in this field. Almost all of the similar grippers in this category were former actuated by a piezo-stack which has some limitations and difficulties like fabrication in MEMS proportions. The basic design was borrowed from compliant mechanisms that are suitable for MEMS application and easy to manufacture in micro-scale because of the intrinsic integration characteristic. Since stress concentration is common in flexure hinge compliant mechanisms, our focus was to consider strength as an important factor in our design. Finite element analysis tools were used to implement the DOE based on two criteria; minimizing stress concentration and maximizing the output displacement in the micro-gripper structure as much as possible with the consideration of the total size of the gripper. The experiment was performed to validate the simulation results and experiment results agreed well with the simulation one. The slight geometrical discrepancy in significant portions of structure like flexure hinges partially contributes to the accumulated error between the simulation and the experiments.

     

Optimal design of a micro-positioning Scott-Russell mechanism by Taguchi method

In this paper, main features in kinematics of a micro-positioning Scott-Russell (SR) mechanism associated with two flexure hinges are its displacement amplification and straight-line motion, which are widely needed in practical industries. Without increasing the radial displacement, the SR mechanism is optimally designed by Taguchi method to obtain a maximum amplification of a small displacement driven by a lead zirconate titanate (PZT) actuator. According to kinematic characteristics of the SR mechanism the control factors include the direction, radius, width and offset of flexure hinges. It is found that the directions and offsets of flexure hinges have obvious effects on the amplifying factor and linearity ratio. The software ANSYS is utilized to obtain the numerical simulations, which are compared with the experimental results for the SR mechanism with and without offset of flexible hinges. Finally, some conclusions about the effects of control factors on the performance of the SR mechanism are drawn.     

Design of high-bandwidth high-precision flexure-based nanopositioning modules

This paper presents the design of a single degree-of-freedom high-bandwidth high-precision nanopositioning module for high-throughput nanomanufacturing applications. Compared with widely used lumped-compliance mechanisms (using notch-flexure hinges) and distributed-compliance mechanisms (using compliant flexure beams), this nanopositioning module adopts a hybrid compliant-notch-flexure-based structure. This flexure design decouples the performance requirements for the structural bandwidth and parasitic accuracy that are correlated in the lumped-compliance mechanisms and distributed-compliance mechanisms. The parallelogram hybrid compliant-notch-flexure-based structure enables simultaneous achievement of a higher structural bandwidth and a smaller parasitic motion. The behavior of the nanopositioning module is analyzed theoretically with respect to its design parameters and performance objectives. Finite element analysis is adapted to study the dynamic responses and parasitic displacement of the designed nanopositioning module. The results from the theoretical and FEA analysis demonstrate the effectiveness of the hybrid compliant-notch-flexure design over commonly used lumped-compliance mechanisms and distributed-compliance mechanisms, especially when a high structural bandwidth is required for high-throughput nanomanufacturing applications.     

全柔性机器人机构的结构构型研究

本文对全柔性机器人机构的结构构型问题进行了系统的讨论：首先从应用层面上对 全柔性机器人机构进行了分类，着重讨论了并联机构与全柔性机器人机构之间存在的有机联 系．通过对并联机构的结构及柔性铰链的几何模型进行系统的总结，为全柔性机器人机构“ 型”的选择与构筑提供了丰富的素材．此外，还重点讨论了对全柔性机器人机构的性能产生 较为显著影响的结构布局问题．     

Precision positioning using a novel six axes compliant nano-manipulator

In this paper, a novel micro-scale nano-manipulator capable of positioning in six degrees of freedom (DOF) is introduced. Undesired deflections, while operating in a specific DOF, are restricted by the aid of distinctive design of flexure hinges and actuators’ arrangements. The compliant mechanism is actuated by thermo-electro-mechanical actuators, as they could be integrated and exert large forces in a nanometer resolution. The actuators are bidirectional capable of applying force in both transverse and longitudinal directions. Performance of the two degrees of freedom actuator is thoroughly explored via numerical and analytical analyses, showing a good agreement. The workspace and performance of the precision positioner is studied using finite element methods. Finally, identification of forward and inverse kinematic of the nano-manipulator is performed utilizing neural network concept. A well-trained and appropriate neural network can efficiently replace the time-consuming and complex analytical and experimental methods.

     

Study of the hinge thickness deviation for a 316L parallelogram flexure mechanism fabricated via selective laser melting

3D printing offers great potential for developing complex flexure mechanisms. Recently, thickness-correction factors (TCFs) were introduced to correct the thickness and stiffness deviations of powder-based metal 3D printed flexure hinges during design and analysis. However, the reasons for the different TCFs obtained in each study are not clear, resulting in a limited value of these TCFs for future design and fabrication. Herein, the influence of the porous layer of 3D printed flexure hinges on the hinge thickness is investigated. Samples of parallelogram flexure mechanisms (PFMs) were 3D printed using selective laser melting (SLM) and 316L stainless steel powder. A 3D manufacturing error analysis was completed for each PFM sample via 3D scanning, surface roughness measurement and morphological observation. The thickness of the porous layer of the flexure hinge was independent of the designed hinge thickness and remained close to the average powder particle diameter. The effective hinge thickness could be estimated by subtracting twice the value of the porous layer thickness from the designed value. Guidelines based on finite element analysis and stiffness experiments are proposed. The limitations of the presented method for evaluating the effective hinge thickness of flexure hinges 3D printed via SLM are also discussed.

     

Compliant mechanism design using multi-objective topology optimization scheme of continuum structures

Topology optimization problems for compliant mechanisms using a density interpolation scheme, the rational approximation of material properties (RAMP) method, and a globally convergent version of the method of moving asymptotes (GCMMA) are primarily discussed. First, a new multi-objective formulation is proposed for topology optimization of compliant mechanisms, in which the maximization of mutual energy (flexibility) and the minimization of mean compliance (stiffness) are considered simultaneously. The formulation of one-node connected hinges, as well as checkerboards and mesh-dependency, is typically encountered in the design of compliant mechanisms. A new hybrid-filtering scheme is proposed to solve numerical instabilities, which can not only eliminate checkerboards and mesh-dependency efficiently, but also prevent one-node connected hinges from occurring in the resulting mechanisms to some extent. Several numerical applications are performed to demonstrate the validity of the methods presented in this paper.     

Two-axis flexure hinges with axially-collocated and symmetric notches

The paper introduces a new class of two-axis flexure hinges with axially-collocated and symmetric notches as an alternative to the existing flexure designs with serially-disposed notches. A generic formulation is developed in terms of the geometric curves defining the two notches which includes assessing the capacity of rotation, precision of rotation, sensitivity to parasitic effects, stress values, motion efficiency and shearing effects by means of compliance factors. Closed-form compliance equations are derived for a two-axis flexure hinge that is defined by two non-identical parabolic profiles. The analytical model predictions are confirmed by finite element data. A numerical comparison is made of the parabolic flexure with a constant rectangular cross-section flexure hinge in terms of several performance criteria.     

Design,fabrication and testing of a novel symmetrical 3-DOF large-stroke parallel micro/nano-positioning stage

Limited travel stroke constrains the application of existing XYZ parallel micro/nano-positioning stages. In this paper, a novel parallel-kinematic symmetrical micro/nano-positioning stage is proposed to enlarge the travel range with a compact physical size. For a large-stroke parallel stage, the cross-axis motion increases the difficulty of closed-loop control process. The motions of the parallel stage on different axes are decoupled by employing I-shaped flexure hinges in this work. In order to obtain a large input displacement for actuating the stage, three voice coil motors (VCM) are adopted. In view of the lower output force of the VCM, the guiding flexure mechanism is designed with an optimized cross-sectional dimension. To verify the performance of the stage, analytical modeling and simulation study are carried out. A prototype stage is fabricated for experimental studies. Results show that the designed parallel micro/nano-positioning stage owns a three-degree-of-freedom motion workspace of 2.22 mm × 2.22 mm × 1.81 mm with an overall size of 176 mm × 176 mm × 198 mm, which is more compact than existing symmetrical designs containing the actuators. Moreover, the symmetrical design enables a low crosstalk of 1.7% among the three working axes.     

Analysis and design of parallel mechanisms with flexure joints

Flexure joints are frequently used in precision-motion stages and microrobotic mechanisms due to their monolithic construction. The joint compliance, however, can affect the static and dynamic performance of the overall mechanism. In this paper, we consider the analysis and design of general platform-type parallel mechanisms containing flexure joints. Based on static performance measures such as task-space stiffness and manipulability, and constraints such as joint stress, mechanism size, and workspace volume, we pose the design problem as a multiobjective optimization. We first calculate the Pareto frontier, which can then be used to select the desired design parameters based on secondary criteria, such as performance sensitivity and dynamic characteristics. To facilitate design iteration, we apply the pseudo rigid-body approach with a lumped approximation of the flexure joints. A planar mechanism is used to illustrate the analysis and design techniques.     

Design of an auto-focusing actuator with a flexure-based compliant mechanism for mobile imaging devices

There is increasing consumer’s demand for high-quality and high-performance mobile imaging devices. In this paper, an auto-focusing (AF) actuator with a flexure hinge that uses the electromagnetic (EM) circuit of a voice coil motor was designed and evaluated. The flexure hinge was designed by using finite element analysis. The EM circuit was designed based on the structural stiffness of the device. The EM circuit was analyzed using the design of experiments procedure. Based on the results, the effective design parameters were selected, and improvements were made to the design. Finally, a prototype of the AF actuator was manufactured, and the feasibility and performance of the actuator with the flexure hinge were verified experimentally. The experimental results indicated that the proposed actuator performed adequately and satisfied the design requirements.     

Optimal design of compliant mechanisms using functionally graded materials

This research applies topology optimization to create feasible functionally graded compliant mechanism designs with the aim of improving structural performance compared to traditional homogeneous compliant mechanism designs. Converged functionally graded designs will also be compared with two-material compliant mechanism designs. Structural performance is assessed with respect to mechanical/geometric advantage and stress distributions. Two design problems are presented – a gripper and a mechanical inverter. A novel modified solid isotropic material with penalization (SIMP) method is introduced for representing local element material properties in functionally graded structures. The method of moving asymptotes (MMA) is used in conjunction with adjoint sensitivity analysis to find the optimal distribution of material properties. Geometric non-linear analysis is used to solve the mechanics problem based on the Neo-Hookean model for hyperelastic materials. Functionally graded materials (FGMs) have material properties that vary based on spatial position. Here, FGMs are implemented using two different resource constraints – one on the mechanism’s volume and the other on the integral of the Young’s modulus distribution throughout the design domain. Tensile tests are performed to obtain the material properties used in the analysis. Results suggest that FGMs can achieve the desired improvements in mechanical/geometric advantage when compared to both homogeneous and two-material mechanisms.     

Design and Optimization of an XYZ Parallel Micromanipulator with Flexure Hinges

In this paper, a nearly decoupled XYZ translational compliant parallel micromanipulator (CPM) is designed for micro/nano scale manipulation with features of piezo-driven actuators and flexure hinges. The CPM structure improvement is made to enlarge the workspace and eliminate or reduce the stress stiffening, buckling phenomenon, and parasitic motions of the original XYZ CPM, which leads to a new CPM with a more compact structure. The CPM kinematics, parasitic motions, and workspace are determined analytically, and the mathematical models describing statics and dynamics of the CPM are established to evaluate its related performances, which are verified by the finite element analysis (FEA) undertaken in ANSYS environment. Based on the analytic models, the CPM dimensions have been optimized by resorting to the particle swarm optimization (PSO) approach, which produces a CPM having minimum parasitic motions and satisfying other performance specifications as validated by the FEA simulations.     

Flexible multibody modelling for exact constraint design of compliant mechanisms

In high precision equipment, the use of compliant mechanisms is favourable as elastic joints offer the advantages of low friction and no backlash. If the constraints in a compliant mechanism are not carefully dealt with, even small misalignments can lead to changes in natural frequencies and stiffnesses. Such unwanted behaviour can be avoided by applying exact constraint design, which implies that the mechanism should have exactly the required degrees of freedom and non-redundant constraints so that the system is kinematically and statically determinate. For this purpose, we propose a kinematic analysis using a finite element based multibody modelling approach. In compliant mechanisms, the system’s degrees of freedom are presented clearly from the analysis of a system in which the deformation modes with a low stiffness are free to deform while the deformation modes with a high stiffness are considered rigid. If the Jacobian matrix associated with the dependent coordinates is not full column or row rank, the system is under-constrained or over-constrained. The rank of this matrix is calculated from a singular value decomposition. For an under-constrained system, any motion in the mechanism that is not accounted for by the current set of degrees of freedom is visualised using data from the right singular matrix. For an over-constrained system, a statically indeterminate stress distribution is derived from the left singular matrix and is used to visualise the over-constraints. The analysis is exemplified for the design of a straight guiding mechanism, where under-constrained and over-constrained conditions are visualised clearly.     

Optimal displacement amplification ratio of bridge-type compliant mechanism flexure hinge using the Taguchi method with grey relational analysis

Microsystem Technologies - The compliant mechanism flexure hinge has been frequently utilized in precision enginering in recent years, such as the bridge-type and rhombus-type compliant mechanisms....     

Topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method

A method for topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method is presented in this paper. The focus of this paper is on how to prevent generating the flexible hinges during the process of topology optimization of compliant mechanisms. In the proposed method, two types of mean compliances are introduced and built in the proposed multi-objective function for topology optimization of hinge-free compliant mechanisms with multiple outputs, therefore, the spring model widely used for topology optimization of compliant mechanisms is no longer needed. Some numerical examples are presented to illustrate the validity of the proposed method.     

Feedforward operational stiffness modulation and external force estimation of planar robots equipped with variable stiffness actuators

A variable stiffness actuator (VSA) is considered a promising mechanism-based approach for realizing compliant robotic manipulators. By changing the stiffness of each joint, the robot can modulate the stiffness of the entire system to enhance safety and efficiency during physical interaction with other systems. This paper presents a feedforward method to modulate the operational stiffness of a parallel planar robot with multiple VSAs. A VSA utilizing a lever mechanism was developed, clearly presenting its mechanical design and kinematic model details. A computational model of joint-restoring torque was developed based on deformation measurements and hysteresis loop geometry to estimate the applied torque of each joint in real-time. An algorithm was proposed to compute the joint stiffness solution using the robot's kinematic model for modulating the operational stiffness of the parallel robot. Experiments were performed to evaluate the proposed method by comparing the performances of two DOF serial and parallel robot systems. The results demonstrated the capability of the VSA in both feedforward stiffness modulation and external force estimation.

     

Decoupling and control of micromotion stage based on hysteresis of piezoelectric actuation

This paper presents the mechanism and control design of a micro-motion stage, which employs the right-angle flexure hinges and piezoelectric actuators (PZT). Aiming at the mechanism with the characteristics of a large stroke and three degrees of freedom, analytical models of statics and dynamics are established; especially the coupling motions of stage are investigated, which are verified by finite element analysis simulation. Via open-loop experiment, the decoupling property is well certified. Owing to the hysteresis of PZT, the dynamic equation of system with Bouc–Wen hysteresis model is proposed, which is identified through the Least squares. Moreover, a closed-loop controller of proportion integral derivative combined with the inverse hysteresis model-based feedforward is developed to reduce the nonlinearity and uncertainty, which can improve the positioning accuracy. Besides, the single-axis and multi-axis motions are tested. Experimental results reveal that the stage has a well-decoupling performance, and the effectiveness of proposed Bouc–Wen model is validated under open-loop control. Furthermore, the micro-motion performance in single- and multi-axis motions can be achieved as well.

     

A novel variable stiffness scotch yoke series elastic actuator for enhanced functional stiffness

This paper presents a new design and modeling of a novel variable stiffness scotch yoke series elastic actuator (VSY-SEA) mechanism that can achieve variable stiffness values with a linear relationship between torque and displacement. The main goal of this study was to design the yoke’s shape in the scotch yoke mechanism for a system with the desired stiffness. The word “variable” in VSY-SEA does not simply mean that the system has different random stiffness, but rather that the system has the stiffness of the functional form desired by the designer. Yoke shapes in the scotch-yoke mechanism were designed by calculating the relationship between external torque and rotation angle of VSY-SEA, and the simulations were performed using CAD models with various yoke designs. A prototype of the model was built and the calculations were verified through experiments.