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.     

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.     

A complex solution framework for the kinetostatic synthesis of a compliant four-bar mechanism

This paper presents a systematic solution framework for the kinetostatic synthesis of compliant four-bar mechanisms. The goal of the kinetostatic synthesis is to find feasible compliant mechanism solutions for a given set of kinematic and force/energy specifications. Similar to the synthesis of rigid body linkages, we first classify kinetostatic synthesis problems into three major categories: function, motion and path generations. The kinetostatic synthesis equations are derived by combining the kinematic synthesis and static equilibrium equations. We then propose a comprehensive framework based on polynomial solvers for obtaining solutions to these synthesis equations. When kinematic and static equations are decoupled, we solve first kinematic equations independently and then solve static equations for springs' stiffness. While they are coupled, we transform them into a polynomial form and solve them simultaneously with polynomial solvers. For this case a parameter continuation is devised to avoid computing for the junk solutions. At last, three representative examples are provided to demonstrate the solution process and verify the solution framework.     

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.     

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.     

Design of a low-cost nano-manipulator which utilizes a monolithic, spatial compliant mechanism

This paper presents the design of a novel, low-cost nano-manipulator which uses a six-axis compliant mechanism which is driven by electromagnetic actuators. The mechanism's monolithic, planar geometry is easily fabricated via planar manufacturing processes, enables compact packaging and incorporates a flexure mechanism for achieving small transmission ratios. The manipulator tolerates ±1 mm actuator misalignment with less than 0.1% full-scale position error. Measurements over a 100 nm × 100 nm × 100 nm work volume show resolution better than our measurement capability of 5 nm and open-loop parasitic errors less than 5 nm. Measurements over a 100 μm × 100 μm × 100 μm work volume show open loop errors less than 0.2% full-scale. The mechanism's equilateral symmetry and planar geometry make it possible to limit thermal drift in position and orientation to less than 23 nm and 4 μrad over a 30 min start up period. The nano-manipulator, built at US$ 2000 cost (excludes electronics), is used as an ultra-precision fiber optic aligner.     

Accurate low DOF modeling of a planar compliant mechanism with flexure hinges: the equivalent beam methodology

A methodology for accurate and efficient finite elements method (FEM) simulations of planar compliant mechanisms with flexure hinges is presented. First, using symmetry/antisymmetry boundary conditions and 3D elements, one-eighth of a single hinge is simulated to determine its true stress/stiffness characteristics. A set of fictitious beams is derived, which have the identical characteristics. This set is used in conjunction with other beams that model relatively stiff links to generate an equivalent model of an entire mechanism consisting of the beam elements only. The model has a low number of degrees-of-freedom (DOF) and appears to be more accurate than any 2D FEM models, even those with very large number of DOF. The methodology has been developed specifically for the right circular flexure hinge; however, it can be applied to all types of revolute flexure hinges.     

空间RSSR机构向球面4R机构的转化

根据空间RSSR机构建立机构运动的数学模型,推导出空间RSSR机构的位移方程。同时分析空间RSSR机构转化为球面4R机构的必要条件,并从理论上证明通过对机构设计参数的特殊选取,空间RSSR机构可以转化为轴线相交一点的球面4R机构,然后推导出空间RSSR机构为主动曲柄件时,空间RSSR机构转化为4R机构的各个设计参数应满足的条件,为实际工程应用提供理论依据。根据空间RSSR机构转化为球面4R机构的方法,通过理论计算和试验仿真分析,设计出适应高速剑杆织机的空间引纬机构。以高速剑杆织机的空间引纬机构设计为实例,对以空间4R机构代替空间RSSR机构的设计方法进行验证,验证结果显示,该方法设计的球面4R机构能够满足空间RSSR机构的运动规律要求,并具有更好的运动性能以及可加工性与可装配性。从结构、工艺、维护以及运动学与动力学性能等方面比较空间RSSR机构和球面4R机构的性能与特点,结果显示了使用球面4R机构代替空间RSSR机构的优越性,并为将来空间复杂驱动机构的设计提供了参考。     

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.     

空间 RSSR和球面 RRRR机构的计算机三维位形动态模拟

虽然空间RSSR和球面RRRR机构的解析方法是比较成熟的，但是对于具体机构而言由于设计和分析的结果是用方程和函数表达的，因此具有不直观、难以检验和不可靠的缺点。针对这种情况，这里提出了对机构位形作三维动态模拟的计算机算法。作者已在此基础上在AutoCAD图形系统中编制出了相应的软件程序。用该软件程序模拟出的机构位形可以用AutoCAD命令显示和直接检验。     

Analysis of parasitic motion in parallelogram compliant mechanism

In this paper, an analytical method for parasitic rotation and displacement calculations of parallelogram compliant mechanisms is formulated. Mathematical model is proposed for the geometrical parametric study of parasitic motion, through which the approach to reduce parasitic motion is obtained. The formulations for calculating the locations of the points on end-effectors with no theoretical parasitic displacement are presented. The analytical model predictions are confirmed by the finite element analysis. Theoretical basis is built for improving the output precision of parallelogram compliant mechanisms.     

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.     

空间RSSR机构的装配偏差区间分析

针对空间RSSR曲柄摇杆机构装配偏差分析问题,首先基于区间分析法和三角模糊数的概念建立了包含间隙和杆长尺寸偏差变动信息的区间模型,构建了偏差回路和非线性区间参数方程组,并对非线性区间参数方程组进行了求解.其次,对空间RSSR机构进行了运动仿真,得出了输出角的名义数据,并与非线性区间参数方程组的求解结果进行对照,绘制出了角位移曲线及不同隶属度情形下的角位移偏差对比曲线.最后,分析了关节处间隙变动和杆长偏差对机构输出角位移偏差的影响.分析结果表明:在机构输出角位移曲线的极小值与极大值点附近,间隙与杆长的变动对输出角位移偏差的影响较显著,且间隙与杆长误差越大,角位移偏差受到影响也越大;调整隶属度数值至合适数值,机构输出角位移偏差有明显改善.     

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.     

按K和[γ]的一类特殊空间曲柄摇杆RSSR机构设计

进一步挖掘和揭示出“辅助角方法”具有普遍的适应性和有效性 ,提出了按许用传动角 [γ]对一类特殊空间曲柄摇杆RSSR机构的设计方法     

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.     

A compliant end-effector for microscribing

A new end-effector was designed and built for microscribing processes using principles of compliant mechanisms. Initial testing of a chemomechanical microscribing process showed that low forces produce lines that are significantly smoother, more uniform, and exhibit less material chipping. From the testing it is apparent that there is a need for a specialized precision end-effector that (1) is passively controlled, (2) has low axial stiffness, and (3) has high lateral stiffness. To meet these needs a three segment folded-beam compliant mechanism was chosen. This design is passively controlled, has a high axial/lateral stiffness ratio, is ideal for clean sensitive applications, and can be designed for a range of low forces. The axial stiffness of the end-effector was modeled using both the compliant mechanism pseudo-rigid body model and linear-elastic beam theory. The lateral stiffness was modeled using FEA techniques. Ratios of lateral stiffness to axial stiffness were found to be nearly 1000:1. A fatigue analysis was also performed and it was determined that the mechanism could reach approximately 1 billion cycles before failure. The compliant end-effector design is a significant improvement over existing scribing alternatives and can produce smooth and uniform scribed lines that exhibit less material chipping.     

一种新型平面连杆机构——四偏心机构

为扩大传统平面连杆机构的应用范围、丰富其结构形式,通过完全采用以偏心构件代替连杆,以转动副代替铰接,构成一种新型的四偏心式平面四连杆机构,即带有大转动副的微型平面四连杆机构.为促进此机构向实用阶段转化,给出了两种基本的结构形式,并对其进行了初步的结构分析、运动分析、CAE仿真以及实验验证.给出了各构件的基本尺寸关系和结构优化的方法,求出了从动构件的转角位移运动方程和曲线.通过仿真获得了与理论推导结果相同的从动构件的转角位移运动曲线;同时得出了此机构与传统平面田连杆机构的运动仿真轨迹曲线一致.指出了此机构相对于传统四连杆机构的特点和实施要点.上述分析证明此机构与传统平面田连杆机构的运动规律在本质上具有一致性.     

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.