Partially compliant spatial slider-crank (RSSP) mechanism

In this study, a novel compliant mechanism, “partially compliant spatial slider-crank (RSSP)” is proposed. All possible configurations of compliant RSSP mechanisms are classified and discussed. A method is derived to determine deflection of the multiple-axis flexural hinge for all positions of the crank. A design procedure for partially compliant RSSP mechanisms is introduced. In order to prove the feasibility of the proposed mathematical model, a real model is built and it is shown that results are consistent.     

全柔性机构与MEMS

柔性机构是一种新型机构。首先描述了柔性机构和全柔性机构的概念及特点,论述了它们与MEMS之间的关系。然后详细介绍了全柔性机构在MEMS领域内包括微装配、微操作等应用背景下的状况及前景。最后就对全柔性机构研究中的几个关键技术问题如机构的分析、设计及加工,柔性铰链的选择与设计,驱动器的选择及设计等进行了探讨。     

A nonlinear analysis of spatial compliant parallel modules: Multi-beam modules

This paper presents normalized, nonlinear and analytical models of spatial compliant parallel modules—multi-beam modules with a large range of motion. The models address the non-linearity of load-equilibrium equations, applied in the deformed configuration, under small deflection hypothesis. First, spatial nonlinear load-displacement equations of the tip of a beam, conditions of geometry compatibility and load-equilibrium conditions for a spatial three-beam module are derived. The nonlinear and analytical load-displacement equations for the three-beam module are then solved using three methods: approximate analytical method, improved analytical method and numerical method. The nonlinear-analytical solutions, linear solutions and large-deflection FEA solutions are further analyzed and compared. FEA verifies that the accuracy of the proposed nonlinear-analytical model is acceptable. Moreover, a class of multi-beam modules with four or more beams is proposed, and their general nonlinear load-displacement equations are obtained based on the approximate load-displacement equations of the three-beam module. The proposed multi-beam modules and their nonlinear models have potential applications in the compliant mechanism design. Especially, the multi-beam modules can be regarded as building blocks of novel compliant parallel 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.     

Analysis of frequency characteristics of compliant mechanisms

Much work is needed for a further study on the dynamic analysis of compliant mechanisms to improve their performance and operational accuracy. This paper uses the finite element method to develop a dynamic equation of the compliant mechanism. Natural frequencies and modes are derived. Using the differentials of a stiffness matrix to design parameters, a method for calculating the sensitivity of natural frequency is presented. The numerical simulation results indicate that the design parameters have an impact on the frequency characteristics of the compliant mechanisms and the proposed method is more accurate and convenient for analyzing frequency characteristics.     

Mechanical and geometric advantages in compliant mechanism optimization

This paper presents a focused examination of the mechanical and geometric advantages in compliant mechanisms and their ramifications in the design formulations of compliant mechanisms posed as a topology optimization problem. With a linear elastic structural analysis, we quantify mechanical (and geometric) advantage in terms of the stiffness elements of the mechanism’s structure. We then analyze the common formulations of compliant mechanism optimization and the role of the external springs added in the formulations. It is shown that the common formulations using mechanical (or geometric) advantage would directly emulate at best a rigid-body linkage to the true optimum design. As a result, the topology optimization generates point flexures in the resulting optimal mechanisms. A case study is investigated to demonstrate the resulting trends in the current formulations.     

Compliant high-precision E-quintet ratcheting (CHEQR) mechanism for safety and arming devices

Ratchet and pawl mechanisms are used in safety applications to provide mechanical isolation between inputs and an output to insure that extreme environmental conditions do not inadvertently allow an unexpected output. These devices have become smaller and are approaching a size regime where traditional precision components, such as precision bearings and springs, are not available. This paper introduces the compliant high-precision E-quintet ratcheting (CHEQR) mechanism as a means of exploiting the advantages of compliant mechanisms to create safety devices that eliminate the need for bearings and springs. The pseudo-rigid-body model was used to design a mechanism with the desired force-deflection characteristics, and the result is a radical departure from traditional ratchet and pawl mechanisms. Large-scale proof-of-concept prototypes were followed by micro-wire EDM fabrication of precipitation hardened stainless steel devices with flexible segment widths of 50 μm. The device was integrated with a 6 mm ratchet wheel and rotary solenoid actuator.     

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.     

平面双稳态柔性微机构的优化设计

讨论了一种平面双稳态柔性微机构的设计问题。首先给出了机构稳定平衡位置的物理含义 ,建立了两种类型平面双稳态柔性微机构的伪刚体模型。提出了一种允许设计者随意指定稳定平衡位置点的具有较大自由度的优化设计方法 ,建立了优化数学模型及相应的约束准则 ,采用一种改进的遗传进化算法获得了全局最优解。根据所得的最优解对双稳态柔性微机构进行了分析 ,结果表明该设计方法是有效的     

Transmission angle in compliant slider-crank mechanism

The transmission angle is an important parameter for the quality of motion transmission in a mechanism. However, in the literature there is no study available on compliant mechanisms regarding their transmission characteristics. In this paper, the transmission angle of a compliant slider-crank mechanism is introduced. Similarity conditions for the transmission angle of the compliant slider-crank and its rigid body counterpart are devised via two theorems. A real model is manufactured and one of these theorems is verified experimentally. Finally, the effect of eccentric slider on motion transmission quality is discussed. It is believed that newly proposed theorems will find use in the design of compliant slider-crank mechanisms.     

具有空间复合变形构件的机械系统分析方法

用李群李代数的理论方法探讨了具有空间变形构件的机械系统的分析问题。根据弹性力学的基本原理,建立了考虑弯曲、拉伸和扭转的空间变形杆件的弹性方程。将杆件作为基本元素,将其理论扩展应用于具有空间柔性变形杆件的串联机器人系统,分析了系统空间弹性性能与运动学问题。进而,研究了其在柔性并联机构振动平台分析中的应用。最后,应用该理论很好地解决了螺旋弹簧的空间弹性性能分析问题。将李群李代数理论成功地拓展应用于空间柔性机构系统的分析,验证了该方法的有效性。     

Lamina Emergent Torsional (LET) Joint

Part of the challenge in designing compliant mechanisms is finding suitable joints that provide the needed motion and force–deflection characteristics. The Lamina Emergent Torsional (LET) Joint is presented as a compliant joint suited for applications where large angular rotation is desired, but high off-axis stiffness is not as critical. The joint is introduced and the equations necessary for determining the force–deflection characteristics are presented. Since the LET Joint can be fabricated from a single planar layer, it is well suited for macro and micro applications. Illustrative examples are provided with devices fabricated from materials as diverse as steel, polypropylene, and polycrystalline silicon.     

A parameter optimization framework for determining the pseudo-rigid-body model of cantilever-beams

This paper focuses on developing a framework for determining the optimal pseudo-rigid-body (PRB) model of 2D cantilever beams. PRB models are commonly used in design and analysis of compliant mechanisms since they significantly reduce the number of degrees of freedom compared with the finite element approach. Although a number of PRB models are available in literature, there is not a unified method to determine the most suitable pseudo-rigid-body model for a specific application. In this work, we first study a modified Timoshenko beam equation which accommodates shear forces and axial deformation. The numerical solution to the Timoshenko beam equation provides a baseline for comparing various models. A novel concept of “PRB matrix” is proposed for representing topologies of all PRB models in a uniform way. The optimal set of kinematic parameters (characteristic lengths and spring constants) of PRB models are determined by minimizing the error of tip deflection and comparing with the solution of the Timoshenko beam equation. To validate this formulation, we compare the results with existing PRB models and obtained equivalent if not a more accurate set of PRB parameters. At last, a case study of a compliant slider mechanism is provided to demonstrate the accuracy of two PRB models in this particular application.     

Analytical modeling and FEM Simulations of single-stage microleverage mechanism

Microleverage mechanisms have potentially wide applications in micro-electro-mechanical systems (MEMS) for transferring an input force/displacement to an output to achieve mechanical or geometrical advantages. Constrained by micro-fabrication technology, a microleverage mechanism is made of planar flexures, achieving mechanical transformation through elastic deformation. This kind of mechanism is referred to as a compliant mechanism. In this paper, the analysis and optimization of a single-stage microleverage mechanism is presented with a double-ended tuning fork as the output system in a resonant accelerometer to address the design issues. A very good agreement is obtained between the results of analytical modeling and those of FEM simulation with a SUGAR software package. Although the SUGAR data are more accurate, the analytical equations give clearer insights as to how to design a microleverage mechanism. While high axial spring constants and low rotational spring constants are desirable, the axial and rotational spring constants at pivot need to match those at the output system to achieve the maximum force amplification factor. This compliance-match concept is very important for the design of both single-stage and multiple-stage leverage mechanisms.     

Structural synthesis of a class of 2R2T hybrid mechanisms

Conventional overconstrained parallel manipulators have been widely studied both in industry and academia, however the structural synthesis of hybrid mechanisms with additional constraints is seldom studied, especially for the four degrees of freedom(DOF) hybrid mechanisms. In order to develop a manipulator with additional constraints, a class of important spatial mechanisms with coupling chains(CCs) whose motion type is two rotations and two translations(2R2T) is presented. Based on screw theory, the combination of different types of limbs which are used to construct parallel mechanisms and coupling chains is proposed. The basic types of the general parallel mechanisms and geometric conditions of the kinematic chains are given using constraint synthesis method. Moreover, the 2R2T motion pattern hybrid mechanisms which are derived by adding coupling chains between different serial kinematic chains(SKCs) of the corresponding parallel mechanisms are presented. According to the constraint analysis of the mechanisms, the movement relationship of the moving platform and the kinematic chains is derived by disassembling the coupling chains. At last, fourteen novel hybrid mechanisms with two or three serial kinematic chains are presented. The proposed novel hybrid mechanisms and construction method enrich the family of the spatial mechanisms and provide an instruction to design more complex hybrid mechanisms.     

Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis

This paper presents the dimensionless empirical equations and graph expressions of three flexure hinges for compliant mechanism designs. The in-plane and out-of-plane stiffnesses of the flexure hinges are developed. The rotational precision, denoted by the midpoint stiffness, is derived for the purpose of optimized geometric design. Based on the developed methodologies, the influences of the geometric parameters on the performance of the flexure hinges are investigated, and the performance comparisons among the flexure hinges are conducted to further understand the characteristics of these kinds of compliant mechanisms.     

基于最大应力约束的柔顺机构拓扑优化设计

采用拓扑优化方法获得柔顺机构构型容易出现类铰链结构,导致应力集中、疲劳可靠性差。为了抑制类铰链结构,提出了一种基于最大应力约束的柔顺机构拓扑优化设计方法。采用改进的固体各向同性材料惩罚模型（Solid isotropic material with penalization,SIMP）,以柔顺机构的互应变能最大化作为目标函数,采用P范数方法对所有单元的局部应力凝聚化成一个全局化应力约束,利用自适应约束缩放法使得P范数应力更加接近最大应力,以机构的最大应力和体积作为约束,建立柔顺机构最大应力约束拓扑优化模型,采用全局收敛移动渐近线算法求解柔顺机构最大应力约束拓扑优化问题。结果表明,采用P范数方法进行柔顺机构最大应力约束拓扑优化设计,能够有效抑制类铰链结构。随着应力约束极限值减少,获得机构构型由集中式柔顺机构逐渐转变为分布式柔顺机构,应力分布更加均匀,但机构的互应变能逐渐减小。     

基于磁-机耦合效应的大行程多稳态机构非线性跳跃分析

跳跃非线性是制约多稳态特性(包括稳态个数、位置、阈值和行程)设计的难点。针对多稳态机构存在的关键稳态特征不可控问题,提出一种基于磁-机耦合效应的新型大行程多稳态机构及其设计方法,即引入空间变化磁场来调整系统局部能量极值点的分布状态,实现多稳态特性的精确设计。基于磁荷理论和伪刚体模型法,考虑结构几何大变形对空间磁场分布的影响,建立考虑位移补偿的多稳态非线性跳跃特性分析模型,分析磁结构参数、磁体数量与布置方式对多稳态特性的影响。基于能量变分原理提出多稳态特性设计的能量判据,揭示稳态与伪稳态之间的关系,得到稳态特征存在的条件。研制一种新型大行程7稳态机构样件,理论与试验结果基本一致,验证所提出的多稳态机构设计方法的可行性和有效性。     

用李群李代数分析具有空间柔性变形杆件的机器人动力学

用李群李代数理论方法研究具有三维空间柔性变形杆件的机器人的动力学分析问题。首先用李群李代数法描述空间二柔性杆件机器人的运动学,然后给出空间柔性杆件微小段的质量密度和刚性密度,通过积分得到空间二柔性杆件的动能和势能。用Rayleigh-Ritz方法进一步研究柔性杆件动力学,并用MATHEMATICA软件仿真 分析机器人末端点的空间变形和空间位置,与ANSYS/ADAMS联合仿真的结果进行对比,证明了建模方法的有效性。