Error Modeling and Sensitivity Analysis of a Parallel Robot with SCARA(Selective Compliance Assembly Robot Arm) Motions

Parallel robots with SCARA（selective compliance assembly robot arm） motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.

Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method

Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.

A numerical error analysis method and its application on a 4RRR parallel kinematic machine

To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method and genetic algorithm are introduced for the forward kinematic solution.Based onthe inverse and forward kinematic solutions,the end-effector s error calculation procedure is developed.To solve the accuracy problem caused by the length and angular parameters' different units,a normalizationmethod is proposed based on the manufacturing tolerance.Comparison between the error analysis resultscalculated by the traditional method and the numerical method for a 4RRR PKM shows that,this numericalerror analysis method is more accurate,simpler,and can evaluate the machine s real error basedon the manufacturing tolerance.

Error Analysis of Three Degree-of-Freedom Changeable Parallel Measuring Mechanism

A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.

Calibration of parallel kinematics machine using generalized distance error model

This paper focus on the accuracy enhancement of parallel kinematics machine through kinematics calibration. In the calibration processing, well-structured identification Jacobian matrix construction and end-effector position and orientation measurement are two main difficulties. In this paper, the identification Jacobian matrix is constructed easily by numerical calculation utilizing the unit virtual velocity method. The generalized distance errors model is presented for avoiding measuring the position and orientation directly which is difficult to be measured. At last, a measurement tool is given for acquiring the data points in the calibration processing. Experimental studies confirmed the effectiveness of method. It is also shown in the paper that the proposed approach can be applied to other typed parallel manipulators.

Error modeling, sensitivity analysis and assembly process of a class of 3-DOF parallel kinematic machines with parallelogram struts

This paper presents an error modeling methodology that enables the tolerance design, assembly and kinematic calibration of a class of 3-DOF parallel kinematic machines with parallelogram struts to be integrated into a unified framework. The error mapping function is formulated to identify the source errors affecting the uncompensable pose error. The sensitivity analysis in the sense of statistics is also carried out to investigate the influences of source errors on the pose accuracy. An assembly process that can effectively minimize the uncompensable pose error is proposed as one of the results of this investigation.

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 Kine- matic 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.

改进型Delta并联机构误差建模及灵敏度分析

以改进型Delta并联机构为研究对象,为提高其动平台中心处末端执行器的位置精度和探究各种误差源对位姿误差的影响程度,采用矢量法建立机构的运动链矢量方程,通过对该方程中变量进行一阶线性摄动,从而构建该机构各种尺寸和姿态误差与机构末端执行器位姿误差的误差映射模型;通过对建立的误差映射模型进行灵敏度分析,可以利用具体数值直观地衡量各个误差源对机构末端位姿误差的影响程度。此研究成果对该机构的运动位置精度设计有指导意义。分析表明,主动臂的姿态误差对机构末端执行器误差影响较大,而构件的杆长误差对机构运动精度影响较小。

基于数字孪生控制的精密机床热误差模型

已有的研究结果表明,机床的热误差约占其总加工误差的40%~70%,且机床越精密,其热误差所占比例就越大,因此,通过控制热误差以提升机床的加工精度很有必要。针对机床热误差模型的预测精度不高和泛化能力不强的问题,提出了一种引入主轴转速,并可嵌入数字孪生控制系统的机床热误差建模方法。首先,对模糊聚类分析(FCA)、灰色关联分析(GCA)及主成分回归(PCR)方法进行了理论分析;然后,以某立式加工中心为对象,通过热特性实验,获得了转速图谱下的温度数据和热误差数据,并采用模糊聚类分析结合灰色关联分析的方法选取了其温度敏感点;最后,以主轴转速和温度敏感点的温升值为输入变量,采用PCR方法建立了机床热误差模型,并将其与多元线性回归(MLR)模型进行了效果对比。研究结果表明:相比于MLR模型,所建立的PCR模型的预测精度提升9.5%,证明该模型拥有更高的预测精度和更强的泛化能力;可将模型嵌入到数字孪生控制系统中,对机床进行实时热误差预测和热误差控制。

Geometric error analysis of an over-constrained parallel tracking mechanism using the screw theory

This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore,two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.

可重构混联机械手——TriVariant的误差建模与灵敏度分析

针对少自由度并联构型装备,必须通过误差建模将影响末端可控和不可控误差的几何误差源进行分离,从而指导机构的精度设计和运动学标定的问题,以5自由度混联机械手TriVariant为对象,研究一种少自由度并联构型装备的误差建模方法。该方法可有效分离出影响末端不可控误差的几何误差源,得到由UP支链连架胡克铰的加工和装配误差,以及套筒导轨扭角误差引起的末端姿态误差为不可控误差,从而得到仅需控制恰约束支链的制造和装配误差,便可有效抑制末端的不可控姿态误差的重要结论。在此基础上,借助灵敏度分析方法,在统计意义下定量揭示出上述几何误差源对末端不可控姿态误差的影响。分析结果表明,胡克铰两轴线不相交误差对末端不可控误差的影响最大。

改进Delta并联机构运动可靠性分析

运动精度是评价机构质量的重要考核指标。以往并联机构运动精度分析中,往往不考虑输入误差的随机性,造成评价结果不准确。首先应用齐次坐标变换,推导了改进Delta并联机构的位置反解公式。基于位置反解和一阶泰勒展开,建立了包含机构尺寸误差、转动副间隙误差和驱动误差的机构位置误差计算模型。利用该误差模型,考虑各个原始输入误差的随机性,推导了机构运动可靠性数学模型,给出了评价机构运动可靠性高低的量度和计算方法。运动可靠性是机构运动精度高低的更本质的衡量指标。运动可靠性分析是机构优化设计和误差补偿的基础。

一种新型并联机构位姿误差建模及灵敏度分析

利用齐次坐标变换推导了一种新型五自由度平动、转动独立的复合机构的位姿反解。基于位姿反解和一阶泰勒展开,建立了考虑机构形位尺寸误差、转动副间隙误差和驱动误差的位姿误差计算模型。应用误差模型能够得出末端执行器位姿误差和各个误差源之间的显式映射关系,定量地分析各个误差源对机构运动精度的影响程度,从而确定机构中影响其运动精度的关键环节。应用差分法就机构位置误差对主要设计变量的灵敏度进行了分析计算。灵敏度分析有助于合理确定机构的设计参数。位姿误差建模及灵敏度分析为该复合机构的优化设计和误差补偿提供了理论基础。

Delta并联机构精度标定方法研究

以Delta并联机构为对象,研究一类合平行四边形支链的3自由度并联机构误差建模技术,所建模型可有效分离出影响末端姿态误差的几何误差源。在此基础上提出一种精度标定方法,该方法利用并联机构操作空间与关节空间非线性映射的性质,仅需检测末端沿z向的位置误差、以及在初始位形下的姿态误差便可识别出几何参数,并可通过修改系统输入实现末端位置误差补偿。给出算例以验证该方法的有效性。

并联机床驱动杆铰链位置误差分析

为提高并联机床运动精度,解决其铰链误差对运动精度的影响问题,以东北大学开发的3-PTP并联机床为分析对象,采用叠加原理,建立三自由度并联机构驱动杆铰链误差模型;采用矩阵范数分析驱动杆铰链误差对动平台终端运动精度的影响规律.分析表明,结构参数λ大,不利于减小工作空间内动平台位置误差的最小值,但对其最大值影响不大.该误差模型的建立为此并联机床进一步优化机构设计参数以及误差补偿奠定了基础.

3-RRRU并联机器人运动学建模与误差分析

针对3-RRRU并联机器人控制精度问题,基于空间矢量法建立运动学正解模型以及误差模型,详细分析了机器人各结构误差源对控制精度的影响。仿真结果表明:驱动角度误差分布在0.001°~0.01°时,第一支链的驱动角误差对被控终端的精度影响最大为84.2um;连杆加工误差在0.01mm^0.1mm变化时,靠近动平台的被动杆为0.1mm时对被控终端精度影响最大,其最大误差值为137.2um;静、动平台的外接圆半径加工误差为0.1mm时,机器人终端最大误差为568.4um。因此,对于线性连杆加工误差和角度误差源,连杆加工误差对多支链、多连杆机器人精度的影响高于角度误差,且静、动平台的加工误差对机器人的终端控制精度影响最大,为后续机器人结构的最优化设计提供了理论依据。

有误差的螺旋锥齿轮传动接触分析

以多体系统误差建模理论和齿轮啮合原理为基础,提出含有机床运动几何误差以及齿轮副安装误差的螺旋锥齿轮齿面接触分析(Error tooth contact analysis,ETCA)方法。以SGM法(大轮展成法加工,小轮变形法加工)加工的弧齿锥齿轮为例,通过ETCA分析,得到机床运动误差和安装误差对螺旋锥齿轮齿面加工质量影响的定量关系,对ETCA和TCA的结果进行对比分析,结果表明机床运动误差和安装误差对螺旋锥齿轮的齿面接触质量有较大的影响,为了通过齿面接触分析达到更准确的反调加工参数的目的,采用ETCA的分析结果指导加工参数反调更为合理。

基于区间分析的一类三转动自由度并联机构的精度设计(邀请论文)

面向大型结构件调姿、天线跟踪及快速定位等应用需求,研究三转动自由度并联机构3-PSU&S的精度设计方法.首先,利用螺旋理论建立该机构的误差映射模型,并将影响机构末端姿态精度的几何误差分离为可补偿误差与不可补偿误差2类.其次,借助区间分析理论,提出不可补偿误差的灵敏度指标,并通过全域灵敏度分析揭示各项不可补偿误差对机构末端姿态精度的影响规律.然后,以灵敏度指标值为分配权重,建立各项不可补偿误差的优化分配模型,在给定精度约束下,借助遗传算法将难以实现的不可补偿误差的公差值松弛至最大可行区间.最后,通过蒙特卡洛仿真验证了所提出精度设计方法的有效性.

一种串并联型机床及其误差分析

多杆件并联及串并联型机床是正在致力研究和开发的新型加工设备。分析了一种新研制的串并联型机床的结构及空间误差 ,推导并验证了主轴平台空间运动误差的数学模型 。

Delta并联机械手几何误差建模及灵敏度分析

以一类含平行四边形支链的Delta并联机械手为对象,利用空间矢量链分析方法,构造出机构末端位置和姿态误差与几何误差之间的映射关系,明确揭示出影响机构末端不可补偿误差的几何误差源,并借助灵敏度分析定量揭示几何误差对末端位姿误差的影响.研究成果对指导同类装备的设计与制造具有普遍的意义.