全适应性双稳态微机构及其假刚体模型

概述了双稳态微机构的定义、优点及分类。介绍了全适应性双稳态微机构的特征及其建模技术，重点分析了假刚体模型的思想及其在适应性机构设计中的应用，并对全适应性双稳态微机构假刚体模型的优化方法进行了一定的研究。     

模拟柔顺机构中柔顺杆件末端特征的2R伪刚体模型

柔顺机构是一种新型机构,其中包含的柔顺杆件会因为产生大变形而导致分析起来十分复杂。伪刚体模型能够简化柔顺杆件的大变形分析。基于伪刚体模型的原理,针对柔顺机构中的柔顺杆件,提出以末端转角参数化近似方法为基础的2R伪刚体模型。该模型用两个不同劲度系数的扭转弹簧连接3个不同长度的刚性杆件,并用特征半径系数表征刚性杆件的长度,用刚度系数表征扭簧的扭转能力,通过二维搜索得到模型的最优特征半径系数,应用线性回归方法得到模型的刚度系数。该模型能准确模拟柔顺机构中柔顺杆件的末端变形轨迹和变形角度。推导柔顺杆件和伪刚体模型变形时的应变能公式,通过数值对比,从能量角度评价伪刚体模型储存应变能的能力。     

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.     

Finding the optimal characteristic parameters for 3R pseudo-rigid-body model using an improved particle swarm optimizer

Compliant mechanisms have been used in many engineering areas where high precision and sensitivity are required. One of the major challenges of designing compliant mechanisms lies in understanding and analyzing the nonlinear deflections of flexible members. The pseudo-rigid-body model (PRBM) method, which simplifies the modeling of the nonlinear deflection by approximating it as motion of rigid links, has been accepted as one of the most important tools for synthesis and analysis of compliant mechanisms. In this paper, a review of various PRBMs is presented. The 3R PRBM whose characteristic parameters are independent of external loads is discussed in detail. For the purpose of finding the optimal set of the characteristic parameters for the 3R PRBM, a six-dimensional objective function is formulated by combining the approximation errors of both tip point and tip slope for the two extreme load cases, i.e., pure moment load and pure vertical force load. A particle swarm optimizer was employed to conduct a continuous search on the objective function. The resulting 3R PRBM with the optimized characteristic parameters shows better performance in predicting large deflections of cantilever beams over the original 3R PRBM.     

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.     

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.     

A new type of compliant spatial four-bar (RSSR) mechanism

This paper presents a novel study on the analysis and design of a new type compliant spatial four-bar (RSSR) mechanism. To the best of our knowledge, any research on compliant spatial mechanisms which possesses out of plane motions is not available in the literature. This study introduces enumeration and novel approach for the analysis and design of such mechanisms. The analysis and design are performed with the pseudo-rigid-body model (PRBM). Since there are numerous applications of rigid spatial four bar mechanisms, it is strongly believed that a compliant version of such mechanisms may find many applications.     

双稳态平面并联机构

以提高多自由度并联机构的运动性能为目标,探索柔顺双稳态机构在克服并联机构力奇异问题中的应用。提出一种双稳态凸轮柔顺机构,利用双稳态机构在非稳态位形的非零内力,为并联机构提供柔顺过驱动输入,利用柔顺过驱动输入消除并联机构在运动奇异和力奇异位形时的运动或操作力不确定性。以平面五杆2-DOF并联机构为例进行了机构工作空间分析、运动奇异位形分析、以及力奇异位形分析。计算结果证明采用提出的双稳态凸轮柔顺机构能实现该平面2-DOF机构奇异位形的控制。     

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.     

固定-导向柔顺杆件6R伪刚体模型

为提高固定-导向型伪刚体模型的计算精度,基于伪刚体模型的原理提出了一种固定-导向6R伪刚体模型。建立了该模型的运动学方程,并根据逆运动学分析方法及优化算法求解了模型的4个最优特征半径系数和3个扭簧刚度系数。通过数值算例模拟固定-导向6R伪刚体模型的末端动作路径,并将其与固定-导向2R伪刚体模型及柔顺杆件的末端路径进行对比。结果表明,固定-导向6R伪刚体模型能够更加精确地模拟相应柔顺杆件的末端动作过程,且其相对误差几乎为0。最后,通过ANSYS有限元分析实例验证了该模型在实际计算中的精确性。     

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.     

Modeling of cross-spring pivots subjected to generalized planar loads

Cross-spring pivots, formed by crossing two identical flexural beams at their midpoint, have been broadly used in precision engineering and aerospace fields. Many researches have been conducted on modeling and analysis of cross-spring pivots. However the influence of application position and magnitude of the external loads on the load-rotation and parasitic motion characteristics has not yet been discussed. In order to reveal the effect of the external loads, this paper develops the accurate load-rotation and center shift models of cross-spring pivots, with generalized planar loads applied including bending moment, horizontal and vertical forces. Firstly, by using the energy method, the load-displacement models of the pivot are derived with the assumption of small rotational angles. Based on the models, the influence of generalized planar loads on the load-rotation relationship is discussed, which shows that both application position and magnitude of the vertical and horizontal forces influence the load-rotation behaviors. Then the accurate center shift expressions of the pivot with generalized planar loads are developed, which shows that the rotational angle is the dominant term for both components of the center shift while the vertical and horizontal forces are small. Finally, the accuracy of the proposed model is validated by finite element analysis(FEA). Comparing the model data with the results obtained from FEA, the relative error of the load-rotation is less than 6% even if the rotational angle reaches 20°; the relative errors of the two components of center shift are less than 5% and 10% respectively when the rotational angle reaches 10°. The proposed model and analytical conclusions can be used to analyze and preliminarily design the compliant mechanisms containing cross-spring pivots.     

基于局部截面构型优化的双稳态结构跳跃阈值控制与设计*

双稳态结构正反行程跳跃阈值不相等引起的驱动困难是制约其工程应用的瓶颈问题。基于大变形有限元理论分析了影响双稳态结构跳跃过程的关键因素,引入跳跃阈值力、稳态保持力以及双稳态特征系数(二者的比值)作为描述双稳态特征的指标,提出了基于局部单元截面构型优化的双稳态跳跃阈值控制方法,建立了具有特定跳跃力学特征的双稳态结构优化设计模型,以局部单元的截面尺寸、个数及位置为设计变量,采用分步优化的方法,得到了几类具有不同双稳态特征系数的余弦梁新构型,分析了变截面单元厚度及布置方式对跳跃阈值及路径的影响关系。数值仿真结果表明,局部截面构型改变前后双稳态结构的跳跃时间及振动频率变化不大。考虑试验加载位置与夹持条件对双稳态特征系数的影响,仿真与试验结果基本一致,验证了所提出的双稳态结构跳跃力控制方法的有效性。     

Integrating mechanism synthesis and topological optimization technique for stiffness-oriented design of a three degrees-of-freedom flexure-based parallel mechanism

This paper introduces a new design approach to synthesize multiple degrees-of-freedom (DOF) flexure-based parallel mechanism (FPM). Termed as an integrated design approach, it is a systematic design methodology, which integrates both classical mechanism synthesis and modern topology optimization technique, to deliver an optimized multi-DOF FPM. This design approach is separated into two levels. At sub-chain level, a novel topology optimization technique, which uses the classical linkage mechanisms as DNA seeds, is used to synthesize the compliant joints or limbs. At configuration level, the optimal compliant joints are used to form the parallel limbs of the multi-DOF FPM and another stage of optimization was conducted to determine the optimal space distribution between these compliant joints so as to generate a multi-DOF FPM with optimized stiffness characteristic. In this paper, the design of a 3-DOF planar motion FPM was used to demonstrate the effectiveness and accuracy of this proposed design approach.     

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     

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。     

Preload characteristics identification of the piezoelectric-actuated 1-DOF compliant nanopositioning platform

Packaged piezoelectric ceramic actuators (PPCAs) and compliant mechanisms are attractive for nanopositioning and nanomanipulation due to their ultra-high precision. The way to create and keep a proper and steady connection between both ends of the PPCA and the compliant mechanism is an essential step to achieve such a high accuracy. The connection status affects the initial position of the terminal moving plate, the positioning accuracy and the dynamic performance of the nanopositioning platform, especially during a long-time or high-frequency positioning procedure. This paper presents a novel external preload mechanism and tests it in a 1-degree of freedom (1-DOF) compliant nanopositioning platform. The 1-DOF platform utilizes a parallelogram guiding mechanism and a parallelogram load mechanism to provide a more accurate actual input displacement and output displacement. The simulation results verify the proposed stiffness model and dynamic model of the platform. The values of the preload displacement, actual input displacement and output displacement can be measured by three capacitive sensors during the whole positioning procedure. The test results show the preload characteristics vary with different types or control modes of the PPCA. Some fitting formulas are derived to describe the preload displacement, actual input displacement and output displacement using the nominal elongation signal of the PPCA. With the identification of the preload characteristics, the actual and comprehensive output characteristics of the PPCA can be obtained by the strain gauge sensor (SGS) embedded in the PPCA.     

A novel flexure beam module with low stiffness loss in compliant mechanisms

Flexure mechanisms provide guided motion via elastic deformation of thin beams. Due to the employment of compliant elements, these mechanisms cannot sufficiently maintain acceptable constraint stiffness level in the entire range of motion. The stiffness deterioration afflicts the performance of flexure mechanisms in terms of motion range, accuracy and constraint characteristics. This paper presents a novel flexure beam module with improved constraint behavior in beam-based flexure mechanisms. The proposed module alleviates the problem of stiffness loss in large displacements and provides a better motion performance. The mathematical model governing the static behavior of the module is developed using the principle of virtual work. The geometric nonlinearity associated with large midplane stretching is taken into account. Closed-form solutions are derived for load-displacement relationships, providing a powerful design tool for the novel flexure. Also a nonlinear expression is obtained for the strain energy of the flexure in terms of end displacements. The functionality of the presented module is exploited in a multi-beam parallelogram mechanism. The constraint behavior of the parallelogram is analytically quantified and considerable improvements in stiffnesses and error motions are observed. The analytical results provided in this paper are verified via finite element simulations. The proposed novel module can be used as the building block of more complex flexures to improve their stiffness characteristics, diminish their error motions and widen their stability region.     

Manufacturing error analysis of compliant 3-DOF microrobot

In the fields of micro/nanopositioning application, error analysis is an effective way to enhance the precision of micromanipulators. Manufacturing imperfections, which are inevitable, are the most important factors influencing the accuracy. Therefore, various manufacturing imperfections were studied by taking a planar 3 degrees of freedom (3-DOF) flexure hinge-based microrobot as a case. By formulating static stiffness of the robot, mapping between manufacturing imperfections and end-effector positioning accuracy was obtained. Using the theoretical calculation and finite element method (FEM), effects of various machining imperfection types on end-effector positioning accuracy were evaluated. The results showed that errors of the radium of the hinges and angular differences of the centerline of the hinges were dominant factors resulting in output errors. Conclusions drawn from the experiments can be used to instruct the design of compliant parallel mechanisms by distributing various manufacturing differences of configurable parameters to guarantee precision in the positioning of the end-effector within the required range; they may also be helpful while calibrating this kind of manipulator. __________ Translated from Journal of Beijing University of Aeronautics and Astronautics, 2005, 31(7) (in Chinese)     

三自由度砂带磨床的设计与分析

介绍了一种用于复杂空间曲面磨削加工的新型机器人柔性磨削系统,重点对系统中三自由度砂带磨床的三自由度转位机构、砂带跑偏调整机构和砂带张紧机构进行了设计和分析,对砂带磨床的控制系统也做了介绍.