Design and development of compliant mechanisms for electromagnetic force balance sensor

Compared with the lever-type amplifier, the rhombus-type amplifier has attracted more attention by virtue of large displacement amplification ratio, compact structure, and linear output displacement. In this paper, a novel electromagnetic force balance sensor (EFBS) based on the rhombus-type amplifier is presented to measure the mass with high precision. First, the structure and operating principle of the EFBS are described, and the requirements for the design and manufacture of the amplifier are put forward. Then, the analytical models of the two-stage rhombus-type amplifier are given out, and two guiding mechanisms are analyzed and modeled. Furthermore, the validity of the established model is verified by finite element analysis (FEA). Thanks to the theoretical guidance, an electromagnetic force balance sensor based on the two-stage rhombus-type amplifier and double parallelogram flexure mechanism is designed and tested. The experimental results demonstrate that the developed EFBS can measure the mass of the objects with high precision, and also verifies the correctness of the analytical model. This provides a new concept for the structural design of the EFBS.     

Nonlinear modeling of compliant mechanisms incorporating circular flexure hinges with finite beam elements

Modeling of compliant mechanisms incorporating flexure hinges is mainly focused on linear methods. However, geometrically nonlinear effects cannot be ignored generally. This work shows that nonlinear behavior plays an important role in the deformation and stress analysis, which consequently impacts the design of compliant mechanisms. In this study a nonlinear higher order finite beam element based modeling approach is presented strongly reducing the computation time of nonlinear models. Planar deformation and mechanical stress of a single circular flexure hinge under a wide range of loads is modeled and computed with the proposed approach. A comparison with a 3D-nonlinear finite element model shows very good agreement and validates the beam model. It is shown that the linear and nonlinear deformation behavior of a single flexure hinge deviate marginally so that linear modeling approaches are sufficient. Furthermore a planar displacement amplification mechanism incorporating circular flexure hinges is studied by means of the same method highlighting the distinct deviation of the behavior of the geometrically nonlinear model from its linear prediction. In conclusion the nonlinear behavior at the system level can not longer be neglected. Finally, a study shows that different designs of the displacement amplification mechanism are achieved when linear or nonlinear modeling approaches are applied.     

一种新型6-PRRS并联机器人正解研究

介绍了一种新型的6-PPRS并联机器人,位置正解是该并联机器人的重要研究内容,讨论了人工神经网络在其位置正解求解中的应用.在BP网络中,利用位置逆解结果作为样本,经过学习训练,找到输入滑块与运动平台的非线性映射关系,最终求得并联机器人的位置正解.采用迭代计算进行误差补偿的方法,提高正解精度.计算结果表明,该法迭代次数少、精度高,算例验证了解法的有效性与可行性.     

Investigation of the forward kinematics of the Gough‐Stewart manipulator with natural coordinates

In this paper, we propose a forward kinematics model with natural coordinates for the Gough–Stewart manipulator and other spatial parallel mechanisms. The prevailing merits of this model are that the constraint equations are either quadratic or linear and the coordinates are fully Cartesian. As a result, the derivative matrix of the constraint equations only consists of linear or constant elements, which shows remarkable advantages in kinematic and dynamic analysis over those built through the rotation matrix, the elements of which often contain quadratic or transcendental functions. Application examples show that the virtues are obvious in the analysis of the kinematics of spatial parallel manipulators, especially for those with six full degrees of freedom (DoFs), including three translational DoFs and three rotational DoFs. In reality, this method is easily understood and will be widely used in engineering applications.     

Design and analysis of a multi-notched flexure hinge for compliant mechanisms

This article presents a new multi-notched flexure hinge, which consists of two right circular and two parabolic notches, for positioning stages based on compliant mechanisms. First, the configuration of the presented multi-notched hinge is obtained using topology optimization, and the final shape is proposed based on post-processing. Second, the dimensionless empirical equations for the stiffness, rotational precision and stress levels of the flexure hinges are developed using finite element analysis (FEA). Third, based on the established equations, the influences of the geometric parameters on the performance of the flexure hinge are investigated. Finally, to further understand the characteristics of this type of flexure hinge, comparisons with flexure hinges of various shapes are performed in terms of stiffness, rotational precision and stress levels.     

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.     

新型三维微动台的设计与试验分析

研究设计一种新型的、以压电陶瓷为驱动器的三维微动台结构。该微动台以柔性铰链为弹性导轨实现了微定位。 分析所采用的直圆柔性铰链的参数变化对其造成的性能影响;提出一种新型柔性铰链结构,利用有限元分析软件AN SYS对这种新型结构进行理论分析和试验测试。试验表明:采用这种柔性铰链结构的微动台刚度比较小、运动耦合误差 小,定位精度优于±0.01μm。     

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。     

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。     

连杆机构运动分析的解析设计

建立连杆机构运动分析的计算模型，并应用VB语言进行求解，提高设计精度。     

Design and nonlinear analysis of a 6-DOF compliant parallel manipulator with spatial beam flexure hinges

In this paper, a compliant parallel manipulator with six compliant limbs is proposed for micro positioning applications. The load–displacement model of a single compliant limb is established using a nonlinear closed-form spatial beam model. The inverse solution to the compliant parallel manipulator is then implicitly derived by applying load equilibrium to the moving platform. Finally, the compliant model of the limb and the implicit inverse kinematic solution of the manipulator are fully tested by FEA. Discrepancies between results of the presented models and the FEA are analyzed within planned workspaces. The validations demonstrate that accuracies of the proposed models are acceptable and can be improved by shrinking the planned workspace.     

BP神经网络求6PTRT型并联机器人正运动学精确解

采用BP神经网络,利用位置逆解结果,通过训练学习,实现操作从关节变量空间到工作变量空间的非线性映射,从而求出6PTRT型并联机器人的正运动学解.计算实例表明单用BP神经网络得到的精度并不高,所以为提高正解结果精度,引入误差补偿算法,并设计相应软件,所得数据表明,该算法计算精度高.     

Modeling and analysis of an over-constrained flexure-based compliant mechanism

Bridge-type micro-displacement amplifier with flexure hinges is a classic displacement amplification mechanism. Existing theoretic models cannot predict its amplification ratio and input stiffness accurately and make it very difficult to confirm the amplifier’s performance and error compensation by means of these models, which is very significant in ultra-precision positioning. This paper focuses on the development of design equations that can accurately calculate the ideal displacement amplification ratio and input stiffness of the amplifier based on the thought of statically indeterminate structure. Force Method, Maxwell–Mohr Method, principle of superposition and deformation compatibility are used together to establish uncanonical linear homogeneous equations. The analytical results are verified by FEA simulations. The influence of the geometric parameters on the amplifier performance is investigated. It is noted that amplifier performance is more sensitive to the longitudinal distance of flexure hinges. Besides, two same-sized amplifiers with the opposite output directions can be clearly differentiated by these equations.     

指向机构微调平台的结构设计与分析

针对提高指向机构定位精度的要求,充分利用压电陶瓷驱动器和柔性铰链的优点,设计一套基于压电陶瓷驱动的新型高精度的两自由度微调平台,并实现了微调平台的机构、驱动、检测的一体化。采用余弦矩阵法,对微调平台的机械结构进行运动学分析,并利用Ansys软件建立有限元模型进行静力分析,求出各关键零、部件的微位移和应力分布,验证了设计方案能够满足工作空间和强度准则的要求。     

Y型柔性铰链的设计与实验

为设计一种高精度、结构简单的大变形柔性铰链,提高并联平台的运动精度和零件使用寿命,本文提出了一种Y型柔性铰链。首先,借助ANSYS和ADAMS进行柔性铰链的回转中心、安装方式和行程要求的分析研究。接着,利用数控机床进行柔性铰链的加工制作。然后,利用光学坐标测量仪OPTOTRAK进行柔性铰链的轴漂测量实验。最后,进行了转动副并联平台、单片簧柔性铰链并联平台和Y型柔性铰链并联平台的圆轨迹实验。实验结果表明:Y型柔性铰链回转误差最大值为0.5962mm,Y型柔性铰链并联平台圆轨迹的误差最大值比转动副并联平台减小了42.7%。Y型柔性铰链可以很好地替换并联平台中的转动副,提高并联平台运动精度。     

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.     

On the modeling of flexure hinge mechanisms with finite beam elements of variable cross section

In this paper, a modeling technique for flexure hinge mechanisms is studied. Beam elements of variable cross sections are deployed within a finite element procedure to model a circular flexure hinge. The resulting finite element model has very few degrees of freedom and is accurate in both static and dynamic analysis. Furthermore the modeling approach is applied to an amplifier mechanism. Comparing the results of the proposed model with a 3D finite element reference model, high accuracy for a broad spectrum of hinge parameters is reported while reducing the number of degrees of freedom immensely.     

三自由度微定位工作台的设计与特性分析

设计一种用于平面磨削主动控制的新型数控微定位工作台。该工作台采用三个安装在底座上的压电陶瓷 (PZT)驱动器驱动动平台 ,三个圆形凹槽弹性铰链构成的弹性环节实现对压电陶瓷驱动器的预紧。为了提高定位精度采用三个高精度的电容式位移传感器用来测量动平台的输出 ,从而形成闭环控制系统。采用有限元分析软件ANSYS对微定位工作台的静、动态特性进行了数值分析。