Design and fabrication of miniature compliant hinges for multi-material compliant mechanisms

Multi-material molding (MMM) enables the creation of multi-material mechanisms that combine compliant hinges, serving as revolute joints, and rigid links in a single part. There are three important challenges in creating these structures: (1) bonding between the materials used, (2) the ability of the hinge to transfer the required loads in the mechanism while allowing for the prescribed degree(s) of freedom, and (3) incorporating the process-specific requirements in the design stage. This paper presents the approach for design and fabrication of miniature compliant hinges in multi-material compliant mechanisms. The methodology described in this paper allows for the concurrent design of the part and the manufacturing process. For the first challenge, mechanical interlocking strategies are presented. For the second challenge, the development of a simulation-based optimization model of the hinge is presented, involving functional and manufacturing constrains. For the third challenge, the development of hinge positioning features and gate positioning constraints is presented. The developed MMM process is described, along with the main constraints and performance measures. This includes the process sequence, the mold cavity design, gate selection, and runner system development. A case study is presented to demonstrate the feasibility of creating multi-material mechanisms with miniature hinges serving as joints through MMM process. The approach described in this paper was utilized to design a drive mechanism for a flapping wing micro air vehicle. The methods described in this paper are applicable to any lightweight, load-bearing compliant mechanism manufactured using multi-material injection molding.     

集中柔度全柔性机构拓扑优化设计研究

根据集中柔度全柔性机构特点,基于连续体拓扑优化技术,采用SIMP人工材料密度方法.以机构的刚度和柔度要求相结合的功能函数作为优化目标,建立集中柔度全柔性机构拓扑优化设计模型.采用优化准则法进行数值计算,并推导了迭代公式.通过所建立的优化模型设计出的机构拓扑图形具有"集中柔度"特征,为集中柔度全柔性机构的设计提供了基础.数值算例证明了研究方法的有效性.     

Modeling of large-deflection links for compliant mechanisms

The traditional pseudo-rigid-body model (PRBM) has one degree of freedom (DOF) and performs a good simulation to the tip locus of flexible links for compliant mechanisms on the basis of a parametric approximation method. In this study, a new approach of a two-DOF PRBM is proposed to simulate both the tip locus and tip deflection angle of large-deflection links for compliant mechanisms on the basis of the angular deflection approximation technique. A linear regression for the spring stiffness coefficient of the 2R PRBM using the optimization technique is presented. The advantage of the new model is well illustrated through a numerical comparison between the 1R and the 2R PRBM.     

Design of compliant straight-line mechanisms using flexural joints

Straight-line compliant mechanisms are important building blocks to design a linear-motion stage, which is very useful in precision applications. However, only a few configurations of straight-line compliant mechanisms are applicable. To construct more kinds of them, an approach to design large-displacement straight-line flexural mechanisms with rotational flexural joints is proposed, which is based on a viewpoint that the straight-line motion is regarded as a compromise of rigid and compliant parasitic motion of a rotational flexural joint. An analytical design method based on the Taylor series expansion is proposed to quickly obtain an approximate solution. To illustrate and verify the proposed method, two kinds of flexural joints, cross-axis hinge and leaf-type isosceles-trapezoidal flexural（LITF） pivot are used to reconstruct straight-line flexural mechanisms. Their performances are obtained by analytic and FEA method respectively. The comparisons of the results show the accuracy of the approach. Both examples show that the proposed approach can convert a large-deflection flexural joint into approximate straight-line mechanism with a high linearity that is higher than 5 000 within 5 man displacement. This can lead to a new way to design, analyze or optimize straight-line flexure mechanisms.     

Manufacturing of multi-material compliant mechanisms using multi-material molding

Multi-material compliant mechanisms enable many new design possibilities. Significant progress has been made in the area of design and analysis of multi-material compliant mechanisms. What is now needed is a method to mass-produce such mechanisms economically. A feasible and practical way of producing such mechanisms is through multi-material molding. Devices based on compliant mechanisms usually consist of compliant joints. Compliant joints in turn are created by carefully engineering interfaces between a compliant and a rigid material. This paper presents an overview of multi-material molding technology and describes feasible mold designs for creating different types of compliant joints found in multi-material compliant mechanisms. It also describes guidelines essential to successfully utilizing the multi-material molding process for creating compliant mechanisms. Finally, practical applications for the use of multi-material molding to create compliant mechanisms are demonstrated.     

Output decoupling modeling of a XY flexure-based compliant manipulator

Journal of Mechanical Science and Technology - This paper presents the coupling stiffness modeling of an XY flexure-based manipulator. Stiffness/compliance equations for compliant mechanisms are...     

Analysis of frequency characteristics and sensitivity of compliant mechanisms

Based on a modified pseudo-rigid-body model, the frequency characteristics and sensitivity of the large-deformation compliant mechanism are studied. Firstly, the pseudo-rigid-body model under the static and kinetic conditions is modified to enable the modified pseudo-rigid-body model to be more suitable for the dynamic analysis of the compliant mechanism. Subsequently, based on the modified pseudo-rigid-body model, the dynamic equations of the ordinary compliant four-bar mechanism are established using the analytical mechanics. Finally, in combination with the finite element analysis software ANSYS, the frequency characteristics and sensitivity of the compliant mechanism are analyzed by taking the compliant parallel-guiding mechanism and the compliant bistable mechanism as examples. From the simulation results, the dynamic characteristics of compliant mechanism are relatively sensitive to the structure size, section parameter, and characteristic parameter of material on mechanisms. The results could provide great theoretical significance and application values for the structural optimization of compliant mechanisms, the improvement of their dynamic properties and the expansion of their application range.     

全柔性微位移放大机构的设计与分析

微机械放大器中常采用全柔性微位移放大机构来实现输出位移的放大,且大多采用短臂柔性铰链连接各构件。设计了一种对称的长柔性杆微位移放大机构,结合弹性力学和Bernoulli-Eu-ler假设,推导出该放大机构的力位移计算公式及放大比公式。对影响该机构放大比的关键因素进行了分析,通过实例分析得到该机构中的长柔性杆角度与输出位移之间的关系。同时用有限元方法对该实例进行了仿真分析,并对两种方法所得结果进行了分析比较。     

Conceptual design of compliant mechanisms using level set method

We propose a level set method-based framework for the conceptual design of compliant mechanisms. In this method, the compliant mechanism design problem is recast as an infinite dimensional optimization problem, where the design variable is the geometric shape of the compliant mechanism and the goal is to find a suitable shape in the admissible design space so that the objective functional can reach a minimum. The geometric shape of the compliant mechanism is represented as the zero level set of a one-higher dimensional level set function, and the dynamic variations of the shape are governed by the Hamilton-Jacobi partial differential equation. The application of level set methods endows the optimization process with the particular quality that topological changes of the boundary, such as merging or splitting, can be handled in a natural fashion. By making a connection between the velocity field in the Hamilton-Jacobi partial differential equation with the shape gradient of the objective functional, we go further to transform the optimization problem into that of finding a steady-state solution of the partial differential equation. Besides the above-mentioned methodological issues, some numerical examples together with prototypes are presented to validate the performance of the method.     

A novel analytical model for flexure-based proportion compliant mechanisms

This paper proposes a novel analytical model for flexure-based proportion compliant mechanisms. The displacement and stiffness calculations of such flexure-based compliant mechanisms are formulated based on the principle of virtual work and pseudo rigid body model (PRBM). According to the theory and method, a set of closed-form equations are deduced in this paper, which incorporate the stiffness characteristics of each flexure hinge, together with the other geometric and material properties of the compliant mechanism. The rotation center point for a corner-filleted flexure hinge is investigated based on the finite element analysis (FEA) and PRBM. An empirical equation for the rotational angle is fitted in this paper in order to calculate accurately the position of the end-point of the flexure hinge. The displacement proportion equation for such mechanisms is derived according to the new approach. Combining the new proposed design equation and the existed stiffness equation, a new proportion compliant mechanism with corner-filleted flexure hinges is designed by means of the least squares optimization. The designed models are verified by finite element analysis.     

Spring-joint method for topology optimization of planar passive compliant mechanisms

There is seldom approach developed for the initial topology design of flexure-based compliant mechanisms. The most commonly-used approaches, which start with an existing rigid-body mechanism, do not consider the performances between different topologies. Moreover, they rely heavily on the rigid-body topology, therefore limit the diversity of compliant mechanisms topology. To obtain the optimal initial topology of such mechanisms directly from problem specifications without referencing to the existing mechanism topologies, a spring-joint method is presented for a restricted class of the serial passive flexure-based compliant mechanisms, which are the building blocks of parallel compliant mechanisms. The topology of the compliant mechanisms is represented by a serial spring-joint mechanism（SSJM） that is a traditional rigid-body mechanism with a torsional spring acting on each joint, and is described by position vectors of the spring-joints. A simplified compliance matrix, determined by the position vectors, is used to characterize the tip of the SSJM kinematically, and is optimized to ensure the desired freedoms of the compliant mechanisms during optimization. The topology optimization problem is formulated as finding out the optimal position of the spring-joints in a blank design domain with an objective function derived from the simplified compliance matrix. In design examples, syntheses of the compliant mechanisms with both single freedom and two decoupled freedoms are presented to illustrate the proposed method. The proposed method provides a new way for the initial design of flexure-based compliant mechanisms.     

Pseudo-rigid-body model for corrugated cantilever beam used in compliant mechanisms

Common compliant joints generally have limited range of motion, reduced fatigue life and high stress concentration. To overcome these shortcomings, periodically corrugated cantilever beam is applied to design compliant joints. Basic corrugated beam unit is modeled by using pseudo-rigid-body method. The trajectory and deformation behavior of periodically corrugated cantilever beam are estimated by the transformation of coordinate and superposition of the deformation of corrugated beam units. Finite element analysis（FEA） is carried out on corrugated cantilever beam to estimate the accuracy of the pseudo-rigid-body model. Results show that the kinetostatic behaviors obtained by this method, which has a relative error less than 6%, has good applicability and corrugated cantilever beam has the characteristics of a large range of motion and high mechanical strength. The corrugated cantilever beam is then applied to design a flexible rotational joint to obtain a larger angle output. The paper proposes a pseudo-rigid-body model for corrugated cantilever beam and designed a flexible rotational joint with large angle output.     

Dynamic contact stress analysis using a compliant sensor array

A flexible sensor array has been developed for the measurement of contact stress distribution between flexible bodies. The array incorporates 960 contact geometry modulation resistive (CGMR) transducers to provide a spatial resolution of 10 mm × 10 mm. The high flexibility of the array and its special structure enable it to comply with the very large displacements of the interface between the human body and a flexible cushion. In addition, a method and instrument have been developed to measure, digitize and record dynamic contact stress distributions with a sampling rate of up to 300 frames per second (960 sensors/frame). Measurements performed using this system under static and dynamic conditions are consistent with those performed through the contact pressure display (CPD) method. The new method has been used by the authers and their associates to obtain basic data required for the new field of cushioning mechanics.     

Design and forward kinematics of the compliant micro-manipulator with lever mechanisms

This paper presents the forward kinematics of a five-bar compliant micro-manipulator. To overcome the limited displacement of such a flexure-based mechanism driven by piezoelectric actuators, lever mechanisms are utilized to enlarge the working range. The mechanical design of the micro-manipulator is firstly described. Mathematical formulations for the five-bar mechanism are described and the solutions are developed to decide the end-effector position in Cartesian space. The amplification factor of the lever mechanism is also derived based on the analytical solution of the four-bar linkages. The velocity of the end-effector is obtained by differentiating the forward position kinematic equation, and the local mobility index of the five-bar compliant mechanism is determined and analysed. Based on linearization of trigonometric functions and constant Jacobian matrix, numerical simulations are carried out to investigate the performance of the five-bar compliant manipulator and to determine the optimal geometric parameters for the configuration. The comparisons between the exact solution and simplified methodologies are conducted. Experiments are carried out to validate the established model and the performance of the developed micro-manipulator.     

Topology design and analysis of compliant mechanisms with composite laminated plates

To improve the small deformation and high stress level in hinge zones of compliant mechanisms with isotropic material, a topology optimization method of compliant mechanisms with composite laminated plates was proposed. Based on the anisotropy and designability of composite laminated plates, a topology optimization model of compliant mechanisms with composite laminated plates was built to maximize the deformable capability. Numerical examples of designing compliant inverters and grippers were investigated to demonstrate the effectiveness of the proposed method. The influence mechanism of layer sequences on topologic shapes, deformation and loading capability were also discussed. The results showed that the deformable capability and stress levels of compliant mechanisms with composite laminated plates were further improved by a reasonable configuration of layer sequences.

     

圆柱螺旋压缩弹簧参数化建模

针对复杂零件三维模型的更新过程非常繁琐的问题,研究了在SolidWorks环境下圆柱螺旋压缩弹簧参数化建模的方法.首先建立了圆柱螺旋压缩弹簧三维模型,将控制弹簧模型结构的特征尺寸定义为变量参数,选用Visual Basic 6.0作为编程工具,与Access 2003数据库技术相结合,开发出VB应用程序.在VB界面中通...     

Analytical modeling, optimization and testing of a compound bridge-type compliant displacement amplifier

This paper investigates a flexure-based compound bridge-type (CBT) displacement amplifier for piezoelectric drives. In addition to the advantages of large amplification ratio and compact size, the CBT amplifier has a larger lateral stiffness and is more suitable for actuator isolation and protection than the ordinary bridge-type amplifier. An analytical model for amplification ratio calculation is established based on the Euler-Bernoulli beam theory because other simple theoretical approaches cannot predict the ratio properly. The reason why those approaches fail is discovered by resorting to the elastic model. The input stiffness and resonance frequency of the amplifier are also analytically modeled and verified by finite-element analysis (FEA). The derived models are utilized to optimize the amplifier structure through particle swarm optimization (PSO) to obtain a large resonance frequency subject to other performance constraints. The performances of the fabricated amplifier with optimized parameters are confirmed by both FEA simulation and experimental studies. Because an output displacement over 1 mm is achieved by the designed amplifier, it is employable to develop micro/nanopositioning stages with a cubic millimeter sized workspace.     

Motion and stress analysis of direct-driven compliant mechanisms with general-purpose finite element software

Compliant mechanisms with embedded direct-driven actuators are gaining a wide interest in manufacturing systems as well as structural systems. In this paper, we present a procedure for motion analysis of a compliant mechanism which is driven by three embedded piezoelectric actuators with a general-purpose finite element system, in particular, ANSYS. This includes finite element modeling of the piezoelectric actuator and finite element modeling of the compliant mechanism. An experimental validation was conducted, which shows that the model is highly accurate. The contribution of this paper is a novel application of finite element methods with multidisciplinary elements to motion and stress analysis of compliant mechanisms with embedded piezoelectric actuators. In the current literature, for a complaint mechanism, either the piezoelectric actuator is modeled with absence of piezoelectric effects or a pseudo rigid body approach is applied with poor accuracy. Another contribution lies in the use of a general-purpose finite element software system, which will greatly increase the generalization of finite element modeling applications.     

基于伪刚体动力学模型的柔顺机构驱动特性研究

基于柔顺机构的等效伪刚体动力学模型,对柔顺曲柄滑块机构的驱动问题进行了研究.当给定从动件的运动规律时或者当从动件产生预期变形时候,分析了求解原动件驱动问题的一般方法,并与有限元分析方法进行了比较,结果表明该方法有效.