Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine

In this paper, error modeling and analysis of a typical 3-degree of freedom translational Parallel Kinematic Machine is presented. This mechanism provides translational motion along the Cartesian X-, Y- and Z-axes. It consists of three limbs each having an arm and forearm with prismatic-revolute-revolute-revolute joints. The moving or tool platform maintains same orientation in the entire workspace due to its joint arrangement. From inverse kinematics, the joint angles for a given position of tool platform necessary for the error modeling and analysis are obtained. Error modeling is done based on the differentiation of the inverse kinematic equations. Variation of pose errors along X, Y and Z directions for a set of dimensions of the parallel kinematic machine is presented. A non-dimensional performance index, namely, global error transformation index is used to study the influence of dimensions and its corresponding global maximum pose error is reported. An attempt is made to find the optimal dimensions of the Parallel Kinematic Machine using Genetic Algorithms in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the Parallel Kinematic Machine under study.     

Multi-objective optimization of a 3-DOF translational parallel kinematic machine

In this paper, stiffness modelling and analysis of a typical 3-DOF parallel kinematic machine (PKM) that provides translational motion along X, Y and Z axes is presented. The mechanism consists of three limbs each having an arm and a forearm with prismatic-revoluterevolute-revolute joints (PRRR). The joint arrangement is in such a way that the moving or tool platform maintains same orientation in the entire workspace. Through inverse kinematics, the joint angles for a given position of tool platform necessary for the stiffness modelling and analysis are obtained. The stiffness modelling is based on the compliance matrices of arm and forearm of each limb. Typical non-dimensional performance indices, namely, workspace volume index (WVI), global translational stiffness index (GTSI), and global rotational stiffness index (GRSI), are introduced and used to study the influence of dimensions. Attempts are also made to find the optimal dimensions of the translational PKM using multi-objective optimization based on the genetic algorithms (MOGA) in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the PKM under study.     

Design optimization of a 2-DOF parallel kinematic machine based on natural frequency

In this paper, kinematics, workspace, and dynamic analysis of a two degree of freedom (2-DOF) translational parallel robot are carried out. The mechanism of the 2-DOF translational parallel robot consists of four links. Links 1 and 2 consist of three revolute joints and link 3 and 4 consist of three revolute joints and one prismatic joint. These four links are attached to the end effector. The inverse kinematics analysis is carried out to find the joint positions for a particular position of the moving platform. Using stiffness and dynamic mass matrices, the natural frequencies of the parallel kinematic machine (PKM) are obtained. Since the first natural frequency is responsible for higher vibrations, the first natural frequency is considered as performance measure of the PKM i.e. global natural frequency index (GNFI). Using GNFI as the objective, the optimal dimensions of the PKM are obtained.

     

高温发汗润滑体单胞接触应力分析模型研究

采用“无限大板”中孤立小孔应力集中方法,建立了一种新的以特征参数λ表征的厚壁单胞体接触应力理论模型;以高温发汗润滑体为对象,采用该模型仿真分析了单胞体在特征参数λ≤0.4情况下的胞内应力分布状态。结果表明：随着外载荷的增大,接触半径逐渐增大,且接触区域的各向应力（绝对值）均逐渐变大;最大剪应力逐渐从胞体表面向胞体内部迁移,其y向最大应力从接触中心逐渐向孔边θ=0和θ=-π,r=r₂处转移,x向最大应力从接触中心逐渐向孔边θ=-π/2,r=r₂处转移;该应力集中区逐渐取代胞体接触表面而成为微裂纹诱发源。λ对胞体接触应力分布也有很大影响：当λ=0.4时,孔穴应力集中区与胞体接触区的y向应力差值最大;当λ=0.1时,两处的x向应力差值最大;当外载荷大于1000N时,λ=0.2的胞体内的最大剪应力具有最小值。     

移动型3—UPU并联机构的刚度分析

分析了移动型3—UPU并联机构刚度矩阵的特点和刚度矩阵主轴的变化规律。结果表明,并联机构几何参数的变化只对工作空间的大小和形状有影响,而对刚度矩阵的特征向量大小及方向几乎没有影响,最小刚度方向分布在垂直于静平台平面的锥体内。移动型3—UPU并联机构刚度矩阵分析对并联机构的设计具有一定的指导作用。     

Tricept机械手静刚度解析建模方法

以Tricept机械手的3自由度球坐标型并联机构为例,提出含恰约束支链的球坐标型并联构型装备静刚度解析建模方法。该方法首先借助子结构综合思想将末端执行器位姿变形分解为无约束主动支链的拉压变形、恰约束支链的弯曲变形及其扭转变形3个部分,然后利用虚功原理和结构矩阵法建立各子结构系统的静柔度模型,最后借助线性叠加原理组集整机末端静柔度模型。在建模过程中,侧重研究恰约束支链弯曲刚度以及铰链刚度的建模方法。在此基础上,考察了Tricept机械手中3自由度并联机构静刚度在工作空间中的变化规律,并借助全局性能指标评价了主要构件柔度对整机柔度的贡献。     

Exechon并联模块的静刚度建模与分析*

为研究Exechon并联模块的刚度性能,采用子结构综合方法建立该模块的刚度解析模型。分别采用虚拟关节法和有限元法计入各关节和支链体的柔性,并通过推导动平台和支链装配体间的变形协调方程构建出系统的弹性静力学模型。由系统方程抽取出动平台刚度矩阵,据此预估Exechon并联模块在典型位姿和工作全域内的刚度性能,并将其与有限元仿真结果进行对比。结果表明,所建解析模型具有较高计算精度,可快速预估机构工作全域的刚度特性;Exechon并联模块在工作空间任一截面内的刚度关于x轴对称分布,且沿w方向的刚度受机构位形影响较小。     

三维平动球平台机器人的位置与工作空间分析

提出一种新颖的三维平动球平台机器人并分析其位置与工作空间问题。该新型机器人是DELTA机器人的一种变异形式，结合其结构布局特点，建立了其位置正反解方程式，分析其工作空间及其影响因素，为其设计和实用化提供理论依据。该新型机器人运动平台无过约束，在三雏平动微动机器人、并联机床和振动环境模拟台等领域有广阔的应用前景。     

Pre-deformation for assembly performance of machine centers

The current research of machine center accuracy in workspace mainly focuses on the poor geometric error subjected to thermal and gravity load while in operation, however, there are little researches focusing on the effect of machine center elastic deformations on workspace volume. Therefore, a method called pre-deformation for assembly performance is presented. This method is technically based on the characteristics of machine tool assembly and collaborative computer-aided engineering （CAE） analysis. The research goal is to enhance assembly performance, including straightness, positioning, and angular errors, to realize the precision of the machine tool design. A vertical machine center is taken as an example to illustrate the proposed method. The concept of travel error is defined to obtain the law of the guide surface. The machine center assembly performance is analyzed under cold condition and thermal balance condition to establish the function of pre-deformation. Then, the guide surface in normal direction is processed with the pre-deformation function, and the machine tool assembly performance is measured using a laser interferometer. The measuring results show that the straightness deviation of the Z component in the Y-direction is 158.9% of the allowable value primarily because of the gravity of the spindle head, and the straightness of the X and Y components is minimal. When the machine tool is processed in pre-deformation, the straightness of the Z axis moving component is reduced to 91.2%. This research proposes a pre-deformation machine center assembly method which has sufficient capacity to improving assembly accuracy of machine centers.     

Comparison of Parallel Kinematic Machines with Three Translational Degrees of Freedom and Linear Actuation

The development of new robot structures, in particular of parallel kinematic machines(PKM), is widely systematized by different structure synthesis methods. Recent research increasingly focuses on PKM ...     

一种三自由度并联机床的工作空间分析

提出了一种新型三自由度并联机床，该机床具有x、y、z三个方向的平动自由度，运用Pro/E软件对其进行了建模，求得了其运动学反解的封闭形式，运动学反解方程形式简单，易于实时控制，并对该机床的工作空间进行了分析和研究，可以用于指导实际的样机制作。     

基于RGRR-Ⅰ并联双自由度转动机构的混联五轴机床研究

传统的串联式数控机床存在刚度低的缺点.并联双自由度转动机构RGRR-Ⅰ刚度高,且有着工作空间/机构尺寸比大、耦合为零、制造容易等一系列的优点.运用RGRR-Ⅰ构造的并联双自由度转动刀头摆动精度高、工作空间大.基于混联五轴联动车床的工作要求,研究能实现绕xyz三个直线运动坐标移动,两个运动轴坐标回转的混联五轴联动机床,分析其工作机理,建立有关模型.该研究也可为其他混联机床的设计与制造提供借鉴.     

一种新型3-DOF混联机械臂的运动学基础分析

机械臂运动学基础性能分析是其控制和应用的基础。分析了一种新型3一DOF混联机械臂的运动学传递性能，定义了这种混联机械臂的速度传递性能评价指标，并研究了评价指标在定姿态工作空间内的分布规律，为这种混联机械臂的设计与控制奠定了理论基础。这种新型3-DOF混联机械臂具有工作空间大、运动灵活、刚度大和工艺性好等优点。     

新型并联机床静刚度特性的有限元分析及优化设计

静刚度分析是机床设计的重要内容之一,对一种新型龙门式并联机床的平面并联机构进行了研究,通过位置逆解求出了广义全工作空间;建立了整机静刚度的有限元模型,得到动平台在广义工作空间下的刚度分布规律;找出影响Z向位置精度的关键因素并进行了优化设计,为进一步改进并联机床提供重要的依据。     

(2PRR)~2+R平面并联机构的刚度与固有频率

基于两移动一转动三自由度平面并联机构构造了一种新型五自由度串并混联机器人并对其并联部分,一具有运动冗余和驱动冗余两种不同模式的平面并联机构(2PRR)~2+R进行了运动学分析。首先,建立了三自由度平面并联机构的运动学模型,基于机构的运动学模型推导得到了冗余和非冗余驱动并联机构的刚度矩阵,并且通过求取并联机构各组成构件的等效质量,得到并联机构的质量矩阵;然后,借助系统刚度矩阵和质量矩阵建立的并联机构动力学方程,求得了机构的固有频率方程;最后,通过数值仿真对冗余和非冗余驱动并联机构的刚度及固有频率进行对比分析。结果显示:冗余驱动分支对机构绕Z轴方向角刚度和系统的一阶固有频率均值影响最大,其增幅分别为88.46%和31.50%;对X轴方向的线刚度和系统的二阶固有频率均值影响最小,其增幅分别为52.34%和1.90%。因此,冗余驱动分支有助于提高并联机构的整体刚度,改善机构的动态性能。     

3-DOF并联机构运动学与新型混联机床构想

在机械制造领域,混联机床结合了并联机床和传统机床的主要优点,它既有高的刚度,也有大的工作空间,混联机床成为下一代机床极佳的选择.根据三自由度(3 -DOF)空间并联机构的运动学求解特点,将已提出和应用的3-DOF空间并联机构分为四类,并在分类的基础上提出一种新型的混联机床,它是由一个空间三自由度(两个移动和一个转动)的...     

球铰刚度计算模型及靠冗余支链实现并联机床刚度的改善

以Stewart机构为例提出一种基于解析法和有限元法的刚度分析新方法。应用有限元软件模拟球铰内的非线性接触变形,将计算结果抽象成一个特征参数带入机构的刚度解析模型中,然后得到机构的刚度矩阵,以解决在解析模型中无法处理铰链刚性的问题,并采用有限元软件证实该方法的可靠性。如果在解析模型中忽略球铰变形,则整个机构的刚度解析结果将产生较大误差。在此基础上,应用该方法定量研究采用主动冗余支链对提高并联机床刚性的效果。结果表明,在一定工作空间范围内,主动冗余支链可以显著提高并联机床的刚性。     

Improved Stiffness Modeling for An Exechon-Like Parallel Kinematic Machine(PKM) and Its Application

Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy, stiffness and workspace of machining equipment. Therefore, a 5-DOF(degrees of freedom) parallel kinematic machine(PKM) with redundant constraints is proposed. Based on the kinematics analysis of the parallel mechanism using intermediate variables, the kinematics problems of the PKM are solved through equivalent kinematics model. The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM, where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis. And the stiffness model of the parallel mechanism is improved by correction coefficient matrix, each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism. The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively. The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism. To enhance the machining accuracy of the PKM, the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece. A plate workpiece taken as example is examined in the case study section, which demonstrates the effectiveness of optimization method.     

4自由度混联机器人静刚度分析

研究一种新型混联机器人模块-Bicept的半解析刚度建模方法。该模块由一含恰约束支链的2自由度平面并联机构和一与动平台末端串接的2自由度转头构成,是Tricept机器人的一种二维形式,具有制造成本低,工作空间大的特点,配以长行程导轨,可用于飞机壁板数字化自动制孔等场合。在完成2自由度并联机构位置逆解分析和变形分析基础之上,基于全变形雅可比矩阵建立该机构的静刚度半解析模型。建模中考虑了所有支链构件及铰链的弹性贡献,并侧重研究其恰约束支链弯曲刚度的精确建模问题。通过算例获得Bicept机器人面内静刚度在工作空间中的分布规律,并通过ANSYS有限元分析软件验证了计算结果的正确性。     

On-machine measurement of microtool wear and cutting edge chipping by using a diamond edge artifact

This paper presents precision on-machine measurement of microwear and microcutting edge chipping of the diamond tool used in a force sensor integrated fast tool servo (FS-FTS) mounted on a three-axis diamond turning machine. A diamond edge artifact with a nanometric sharpness is mounted on the machine spindle with its axis of rotation along the Z-axis to serve as a reference edge artifact. The diamond tool is placed in the tool holder of the FS-FTS to generate cutting motion along the Z-axis. By moving the X-slide on which the FS-FTS is mounted, the reference edge can be scanned by the diamond tool. During the scanning, the Z-directional position of the tool is closed-loop controlled by the FS-FTS in such a way that the contact force between the tool tip and the reference edge is kept constant based on the force sensor output of the FS-FTS. The tool edge contour can be obtained from the scan trace of the tool tip, whose X- and Z-directional coordinates are provided by the output of the linear encoder of the X-slide and that of the displacement sensor in the FS-FTS, respectively. Since the reference edge artifact has a good hardness and a nanometric sharpness to ensure the lateral resolution of measurement, a microwear on the cutting edge of the diamond tool can be indentified from the measured tool edge contour. Experiments of on-machine measurement of tool edge contour and microtool wear are carried out to demonstrate the feasibility of the proposed system.