基于D-H矩阵的Stewart型并联机床位姿误差计算模型

针对6自由度Stewart型并联机床,以D-H变换矩阵为建模工具,建立起包含铰座位姿参数、杆件D-H参数的机床动平台位姿方程.采用矩阵微分方法推导出一个机床位姿误差线性化计算模型.该模型不仅使铰座位姿参数误差、杆件D-H参数误差等几何误差全部进入机床位姿误差计算方程,而且将机床位姿误差与几何误差之间的非线性隐式函数关系简化为线性显式函数关系.基于支链杆长方程建立起一个能描述机床位姿误差与几何误差之间实际映射关系的非线性计算模型,以其作为参考模型对线性化计算模型的有效性进行检验.仿真表明:在小误差条件下,线性化模型可以很好地逼近非线性模型,由于具有形式简洁、分析与计算方便等特点,基于D-H变换矩阵的位姿误差线性化计算模型可用于Stewart型并联机床的精度分析、精度综合及运动学标定.仿真结果还表明:当对机床位姿精度要求较高时,需要考虑杆件的全部D-H参数误差对机床位姿的影响.     

一种少自由度飞行模拟运动平台误差分析

将一种少自由度并联机构3-PRS用作飞行模拟运动平台,为使该平台运动精度满足系统要求,对其进行误差分离与灵敏度分析。通过研究平台运动学逆解模型获得驱动雅克比矩阵与约束雅克比矩阵,采用空间闭环误差矢量链的误差建模方法,对运动平台进行误差建模,获得各个几何误差源与终端输出位姿误差之间的映射函数,在所建立的全误差源模型的基础上,利用解析法去除冗余误差源后,借助驱动雅克比矩阵与约束雅克比矩阵将影响该平台末端可补偿位姿误差的误差源和不可补偿位姿误差的误差源分离。最后,在整个运动空间内,借助灵敏度分析,获得影响末端不可补偿位姿误差源的全局灵敏度影响系数。根据灵敏度影响系数可指导前期设计阶段各零部件公差等级的选择以及装配阶段装配公差的确定,研究结果对同类少自由度并联机构具有指导意义。     

基于机构精度通用算法的机器人位姿误差分析

在Denavit-Hartenberg参数法建立的机器人末端位姿变换方程的基础上,利用机构通用精度算法建立了机器人末端位姿误差模型。通过矩阵运算,建立了机器人末端位姿误差与各杆件运动学参数误差之间的函数关系式。在SCARA机器人上的实验表明,用此方法建立的误差模型进行误差标定和补偿,可以提高机器人的定位精度。     

基于敏感度的运动模拟台误差综合

位姿误差是影响运动模拟台性能的重要因素。用矩阵微分法推导了平台位姿误差和42种原始误差之间的关系式，定义了平台位姿误差对各种原始误差的敏感度，并建立基于敏感度约束条件的原始误差优化目标函数，给出了按敏感度的比例对原始误差进行综合的优化方法，通过实例验证了基于敏感度的误差综合方法的有效性。基于敏感度的误差综合方法对六自由度运动模拟台的精度设计具有参考作用。     

基于D-H矩阵的球面5R并联机构误差建模及灵敏度分析

以D-H变换矩阵为建模工具,采用环路增量法,建立了包含杆件D-H参数的球面5R并联机构的误差模型,该模型不仅考虑了机构的结构参数误差,还考虑了由于加工和装配等原因出现的各转动副轴线和球心之间的偏差,使得误差模型更接近于工程实际;根据误差模型进一步计算得到了各从动件运动参数误差以及轴向间隙量的显式函数关系;最后对该机构进行灵敏度分析,研究了各几何误差源对该机构末端执行器位姿误差的影响程度。研究结果为该机构样机的标定、运动学补偿及应用提供了理论基础。      

并联运动模拟台几何误差的正交特性

分析了一台冗余电机驱动的新型六维正交并联运动模拟台,根据其位置反解的数学模型,导出了末端平台的位姿误差与机构各运动部件几何参数误差之间的函数关系,并基于模拟台的位置正解验证了误差模型的正确性.最后,以误差模型为基础,分析了运动模拟台六条支链几何误差的正交特性,为运动学标定和误差补偿提供了理论依据.     

一种新型3-PRS并联机构的位姿误差分析

针对一种新型3-PRS并联机构的3个基座位置可调、工作空间可变的特点,分析该机构的末端位姿误差,提出了采用几何解析法求该机构的运动学正解,进而推导出动平台末端位姿误差的分析方法,并运用软件仿真3个基座在不同位置时的动平台末端位置和方向。结果表明,3个基座在取不同参数时,末端的位姿误差有明显变化。此研究对该新型3-PRS并联机构的误差补偿提供了有益指导。     

基于三坐标定位器的大部件调姿机构误差分析

针对基于3个三坐标定位器联动实现大型部件位姿调整机构的位姿误差问题,采用多体运动学理论分析了机构运动学关系,在不考虑大部件变形的情况下,利用矩阵微分法并结合冗余驱动的特点建立了该调姿机构的位姿误差模型,从而可定量分析各原始误差对调姿对象位姿误差的影响,并通过蒙特卡洛法对调姿误差进行了仿真研究。为获取各原始误差对调姿误差的影响比重,对机构进行了误差敏感度分析,研究结果表明,各导轨的直线度、平行度及三坐标轴间的垂直度等引起的角误差对应的敏感度较大。     

新型一平移一转动并联机构的精度分析

根据并联机器人机构结构综合理论,以单开链支路为单元,改进了一种能实现空间一维移动和一维转动的二自由度并联机构。采用传递矩阵法研究了推拿机器人末端位姿误差。基于机器人末端执行器位置反解结果,通过全微分误差分析理论,建立误差模型,进行求解计算,构造了机器人末端执行器并联机构输出位姿误差与各误差源之间的对应关系。为将该并联机构用作中医推拿机器人的末端执行器,有效完成多种推拿动作提供重要保障。     

6-THRT并联机器人的误差模型研究

针对Stewart平台式的6-THRT型并联机构的研究,提出了一种中心轴测量模型。采用一般工业机器人位姿误差分析法,建立并联机构的误差模型,并结合单杆固定法来获取末端位姿信息,该模型包含了杆的制造、安装及铰链的位置安装等几何参数误差。通过Matlab软件进行仿真运算,分析了影响末端位姿的主要误差源。该研究为并联机器人的误差补偿提供了一定的理论依据。     

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。     

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.     

机器人手臂误差分析及误差补偿

本文对机器人手臂的误差和影响误差的因素作了分析,建立起机器人夹持器(手)的运动误差与各种原始误差的函数式,文章着重于推导作为误差传递函数的各种偏导数矩阵,得到了统一的表达式。这种形式特别适合电子计算机计算。文章最后讨论了误差补偿方法和导出了补偿计算的公式。     

<Emphasis Type="Bold">Roundness Error Prediction with a Volumetric Error Model Including Spindle Error Motions of a Machine Tool</Emphasis>

This paper proposes a modified volumetric error model that includes spindle error motions as well as geometric errors. The model is constructed using rigid-body kinematics and homogeneous transformation matrices and an additional error matrix describing spindle error motions is included. The suggested model predicts the positioning errors at a given axis position as a function of both the axis position and the engaged spindle rotation angle. Two circular interpolation tests (inner and outer circle of the same radius) are simulated and the machined part profiles are predicted. To verify the simulation results, machining tests are performed according to the ISO 10791-7 standard. The error model with spindle errors shows a better agreement, between the simulated and measured roundness errors, than the simple geometric model. It can be seen that the geometric errors determine the basic part profiles and the spindle errors change the basic profiles according to the magnitude of the errors and the spindle rotation angle.     

考虑基坐标系误差的机器人运动学标定方法

提出了一种基于机器人几何参数误差与基坐标系位姿误差的六轴串联型机器人误差标定方法.首先基于MD-H方法建立了IRB6700机器人几何参数误差模型,得到机器人连杆几何参数误差到机器人末端位姿误差的映射关系;然后进一步考虑了基坐标系的位姿误差,并建立了考虑基坐标系误差的机器人误差模型;此外,针对传统标定方法操作繁琐、偶然误...     

3-UPS/S并联稳定平台满载工况误差分析与运动学标定

当负载达到一定数值时,并联机构的变形误差相对于几何误差对动平台输出精度的影响是不可忽略的。以电液驱动型3-UPS/S并联稳定平台为研究对象,分别建立了稳定平台几何误差与变形误差的传递模型,并通过线性叠加得到了总的误差传递模型。基于几何误差传递模型,建立了稳定平台满载工况下的运动学标定模型。在满载工况下进行了运动学标定实验,测量了动平台参考点的位置,计算得到动平台姿态误差δH0,通过分离变形误差δH1得到了几何误差δH,通过最小二乘法完成了稳定平台几何误差参数标定。     

基于广义几何误差模型的微机器人精度分析

提出了一个用于微机器人精度分析的通用方法,该方法以广义几何误差的形式描述各种误差源对机器人本体产生的影响,通过任两座标系间的向后微分关系,利用运动学方程以及并联机构的环路特性,建立了微机器人的广义几何误差模型。基于此模型,对工作空间中的位姿误差进行了仿真分析,验证了该法的有效性。此方法虽然是针对微机器人,但可推广应用到一般并联机器人的误差建模和精度分析。     

Product of exponential model for geometric error integration of multi-axis machine tools

This paper proposes a product of exponential (POE) model to integrate the geometric errors of multi-axis machine tools. Firstly, three twists are established to represent the six basic error components of each axis in an original way according to the geometric definition of the errors and twists. The three twists represent the basic errors in x, y, and z directions, respectively. One error POE model is established to integrate the three twists. This error POE formula is homogeneous and can express the geometric meaning of the basic errors, which is precise enough to improve the accuracy of the geometric error model. Secondly, squareness errors are taken into account using POE method to make the POE model of geometric errors more systematic. Two methods are proposed to obtain the POE models of squareness errors according to their geometric properties: The first method bases on the geometric definition of errors to obtain the twists directly; the other method uses the adjoint matrix through coordinate system transformation. Moreover, the topological structure of the machine tools is introduced into the POE method to make the POE model more reasonable and accurate. It can organize the obtained 14 twists and eight POE models of the three-axis machine tools. According to the order of these POE models multiplications, the integrated POE model of geometric errors is established. Finally, the experiments have been conducted on an MV-5A three-axis vertical machining center to verify the model. The results show that the integrated POE model is effective and precise enough. The error field of machine tool is obtained according to the error model, which is significant for the error prediction and compensation.     

Concept for the integration of geometric and servo dynamic errors for predicting volumetric errors in five-axis high-speed machine tools: an application on a XYC three-axis motion trajectory using programmed end point constraint measurements

A modelling approach for volumetric error prediction taking into account geometric and servo dynamic errors in a five-axis high-speed machine tool is proposed in this paper. Polynomial functions are used to represent and then predict the geometric errors. A simple second-order transfer function model is used to model and predict the servo dynamic error. The servo dynamic errors are added to the axis position geometric errors and propagated to the tool and workpiece using matrix transformations. The validity of the error integration concept is tested for a XYC three-axis motion trajectory. Two experimental setups are used. The first experimental test used the KGM grid encoder instrument to estimate the parameters of the servo dynamic error models of the X- and Y-axes. The second experimental test used a programmed end point constraint procedure with measurement of the 3D volumetric positioning errors between a point on the tool holder and another fixed to the machine table. The tests involve maintaining the nominal coincidence of these two points whilst exercising the three axes. These last tests are used to estimate the geometric error parameters and also to validate the prediction performance of the integrated geometric and dynamic model. The result shows the effectiveness of the error integration concept.     

Accuracy modeling,analysis and radical error distribution of 3-RPR planar parallel mechanism

Output accuracy performance is directly determined by geometric errors and working poses of a mechanism. Accuracy sensitivity as geometric error transmission coefficient, closely relates to pose configuration and geometric parameters. This research focuses on accuracy of a 3-RPR planar parallel mechanism: firstly, established 3 models in an analytic form, to describe relationship between output errors and geometric ones, then they are mutually verified statistically. Secondly, the anisotropy and periodic fluctuation of position errors, independently contributed by each category of geometric errors, are illustrated; and mirror symmetric trajectories and poses generating output errors with mirror symmetry, are also revealed by numerical simulation. Finally, the radical accuracy model in an analytic form, was established through variance and covariance analysis on output errors. We concluded that the radical error of the movable platform in central symmetric poses, follows Rayleigh distribution pattern. Through statistical comparison with Monte Carlo simulation, the radical error model was demonstrated, that provided a reference for accuracy design for other planar parallel mechanism.