Calibration of a hexapod machine tool using a redundant leg

Parallel configurations are recently being applied to the machine tool with the hopes of greater rigidity, stability, and accuracy than conventional multi-axis structures allow. However, the many calibration methods presently available for serial machine tools are not applicable to hexapod type structures. A calibration method is presented that uses a ball–bar or other simple length measuring device to act as an ‘extra leg,’ allowing calibration of the hexapod's true kinematic parameters. This method utilizes a total least squares minimization, does not require any special hexapod configuration or difficult six degree of freedom pose measurements, and is effective with as few as one additional length sensor. Selection of calibration pose sets is briefly discussed, as well as the influence of measurement noise on calibration accuracy. Simulations show the potential for this algorithm to significantly reduce errors to the point where machining errors are within 5–10 times the measurement errors.     

A systematic optimization approach for the calibration of parallel kinematics machine tools by a laser tracker

Parallel kinematics machine has attracted attention as machine tools because of the outstanding features of high dynamics and high stiffness. Although various calibration methods for parallel kinematics machine have been studied, the influence of inaccurate motion of joints is rarely considered in these studies. This paper presents a high-accuracy and high-effective approach for calibration of parallel kinematics machine. In the approach, a differential error model, an optimized model and a statistical method are combined, and the errors of parallel kinematics machine due to inaccurate motion of joints can be reduced by this approach. Specifically, the workspace is symmetrically divided into four subspaces, and a measurement method is suggested by a laser tracker to require the actual pose of the platform in these subspaces. An optimized model is proposed to solve the kinematic parameters in symmetrical subspaces, and then arithmetical mean method is proposed to calculate the final kinematic parameter. In order to achieve the global optimum quickly and precisely, the initial value of the optimal parameter is directly solved based on the differential error model. The proposed approach has been realized on the developed 5-DOF hexapod machine tool, and the experiment result proves that the presented method is very effective and accurate for the calibration of the hexapod machine tool.     

Kinematic calibration of a hexapod of simple design

To benefit from the advantages of parallel kinematic machines (PKM) in industrial applications an efficient kinematic calibration is of particular importance. In this paper a new approach for kinematic calibration of PKM is presented that has been developed and successfully tested on a hexapod at the IWM Dresden. The approach particularly respects the concept of simple design that aims at a cost-effective and economic over-all solution. Aspects of calibration that are in many cases not explicitly accounted for are considered. A simple and robust double-ball-bar (DBB) is used for data acquisition while continuously moving the platform on a specific trajectory in 6 degrees of freedom (dof). The measuring trajectory is optimized to ensure the identifiability of kinematic parameters, respecting their sensitivity and orthogonality in the workspace. Parameter identification is based on Genetic algorithms with customized genetic operators as well as real and simulated measurements. A significant rise of motion accuracy was obtained in the whole workspace. We would like to thank the German Research Foundation (DFG) for their kind support.     

Stewart型并联机床伸缩杆伸长量误差在线测量

标定作为提高Stewart型并联机床静态精度的有效方法，包括建模、测量、参数识别和补偿等环节。其中伸缩杆伸长量误差的测量准确性直接影响标定效果。本文提出间接方法准确测量其值。首先选择激光跟踪系统精确测量并联机床不同位姿对应的伸缩杆绝对伸长量，再辅以符号运算，最终达到测量机床伸缩杆伸长量误差的目的。     

六自由度工业机器人本体标定实验的研究

目前六自由度工业机器人普遍具重复定位精度较高,但绝对定位精度较低的特性,所以为了提高离线编程的精度,需要通过运动学建模、实际测量、参数辨识、误差补偿四步进行机器人本体标定。文中在概括总结现有的工业机器人本体标定技术的基础上,运用MATLAB进行运动学仿真建模,Leica AT960绝对激光跟踪仪系统进行实际测量,SA软件实现参数辨识,外部控制器进行关节补偿,完成本体标定实验。并在此基础上,按照GB/T12642-2013进行标定前后机器人位姿特性检测,通过Robot Check软件处理检测数据,对比前后结果,验证了本体标定实验。     

基于光学坐标测量机的STEWART机构标定研究

为提高大型Stewart机构的定位精度,建立了误差模型并提出了基于光学坐标测量机的标定方法.仿真和试验研究表明,本方法姿态测量过程简便,算法的收敛速度快,系统的定位精度明显提高,为Stewart机构的标定提供了一种解决方案.     

五轴并联机床的标定仿真

建立标定模型,用逆向运动学标定方式模拟了一新型五轴并联机床的标定过程,结果表明这种标定方法的算法收敛快、鲁棒性好.由于将并联机床的固定参考系的姿态参数也考虑进标定模型中,使得这一模型可以消除测量的系统误差对并联机器人标定精度的影响,进一步提高并联机器人的标定精度.这些分析结果为并联机床的标定试验提供理论分析基础.     

Calibration system based on a laser interferometer for kinematic accuracy assessment on machine tools

This paper deals with a method for the dynamic calibration of the kinematic accuracy of lathes and thread grinding machines in screw-cutting mode but free of load. It utilizes a precision polygon mounted on the spindle, in conjunction with a trigger device to generate angular pulses. A laser interferometer system assesses the longitudinal position of the saddle with respect to a cube-corner affixed on the chuck. As the spindle rotates, a string of pulses is generated by the angular trigger device. These pulses are used for triggering the laser interferometer. A software package has been elaborated to enable on-the-fly data acquisition and to display the kinematic errors in graphical form. The components of the kinematic error considered are the progressive pitch error, the cyclic error and spindle-free float. Application of this kinematic error calibrator on a universal and a CNC lathe has been carried out. Test results are presented and commented.     

Force Free Add-on Position Measurement Device for the TCP of Parallel Kinematic Manipulators

The position of the tool center point (TCP) of a parallel kinematic manipulator (PKM) is traditionally being measured indirectly by means of the position measurement of the drives. Cutting forces and acceleration forces cause displacements of the TCP, which cannot be detected from the position measurement of the drives. To improve the position accuracy of the TCP a force free add-on position measurement device is suggested. The kinematic design of such a measurement device, the calibration and its application for feedback control and improved TCP positioning in the presence of external forces is described. Experimental results are presented to illustrate the expected improvements in TCP positioning.     

运动学误差模型变体下的机械臂标定精度研究

为进一步提高机械臂运动学标定精度,研究不同D-H建模方式下运动学误差辨识精度的差异,为运动学误差准确建模提供理论依据。围绕SD-H和MD-H运动学误差模型的各种变体形式,量化对比各模型变体的性态水平和线性化误差,并分析二者对运动学标定精度的综合影响。研究结果表明：x-z-y欧拉变换会破坏MD-H运动学误差模型最小性,不适用于运动学标定;其余满秩MD-H模型性态水平优于SD-H模型两个数量级;MD-H建模时引入的线性化误差与SD-H数量级等同;在模型性态水平和线性化误差综合作用下,较强测量噪声环境中的SD-H模型运动学标定精度(0.1%~39.3%)优于MD-H模型(0.1%~71.2%);角度类与位置类的运动学参数误差的辨识精度差异显著。研究成果为机械臂标定的精确建模以及误差类型与辨识方法的合理匹配提供了理论依据。     

Identification strategy of error parameter in volumetric error compensation of machine tool based on laser tracker measurements

This paper presents a new method for volumetric verification of machine tools. Beyond the consideration of a particular machine, a general verification methodology is presented based on the type of machine to verify the number and movement of axes and different techniques that can be used.A scheme and kinematic model with the inclusion of the measurement system depending on the kinematics of the machine are presented. The model describes the geometry and kinematics of a real milling machine based on a parametric synthetic data generator, which generates a test with known geometric errors and noise to enable a study of different optimisation techniques and models.Similarly, different errors identification techniques and volumetric verification models are presented and analysed.The paper shows the improvement that occurs in verification by considering optimisation phases, the appropriateness of using new techniques of feedback, and the influence of optimisation parameters. Chebyshev polynomials and its characteristics are presented, as well as a regression function for the new verification model. The new developed technique allows the characterisation of the different errors in the whole workspace of the machine and in less time than direct verification methods.     

Integrated post-processor for 5-axis machine tools with geometric errors compensation

Geometric errors of 5-axis machine tools introduce great deviation in real workpiece manufacture and on-machine measurement like touch-trigger probe measurement. Compensation of those errors by toolpath modification is an effective and distinguished method considering the machine calibration costs and productivity. Development of kinematic transformation model is involved in this paper to clarify the negative influences caused by those errors at first. The deviation of the designed toolpath and the real implemented toolpath in workpiece coordinate system is calculated by this model. An iterative compensation algorithm is then developed through NC code modification. The differential relationship between the NC code and the corresponding real toolpath can be expressed by Jacobi matrix. The optimal linear approximation of the compensated NC code is calculated by utilizing the Newton method. Iteratively applying this approximation progress until the deviation between the nominal and real toolpath satisfies the given tolerance. The variations of the geometric errors at different positions are also taken into account. To this end, the nominal toolpath and the geometric errors of the specific 5-axis machine tool are considered as the input. The new compensated NC code is generated as the output. The methodology can be directly utilized as the post-processor. Experimental results demonstrate the sensibility and effectiveness of the compensation method established in this study.     

Configuration analysis of five-axis machine tools using a generic kinematic model

Five-axis machine tools are designed in a large variety of kinematic configurations and structures. Regardless of the type of the intended analysis, a kinematic model of the machine tool has to be developed in order to determine the translational and rotational joint movements required to achieve a specified position and orientation of the cutting tool relative to the workpiece. A generic and unified model is developed in this study as a viable alternative to the particular solutions that are only applicable to individual machine configurations. This versatile model is then used to verify the feasibility of the two rotational joints within the kinematic chain of three main types of five-axis machine tools: the spindle rotating, rotary table, and hybrid type. A numerical measure of total translational joint movement is proposed to evaluate the kinematic performance of a five-axis machine tool. The corresponding kinematic analyses have confirmed the advantages of the popular machine design that employs intersecting rotational axes and the common industrial practice during setup that minimizes the characteristic rotating arm length of the cutting tool and/or workpiece.     

Free-leg Hexapod: A novel approach of using parallel kinematic platforms for developing miniature machine tools for special purpose operations

The paper reports on the development, calibration and exploitation of a novel configuration of parallel kinematic platform, Free-leg Hexapod (FreeHex), on which the base (fixed) platform has been removed; thus, each leg can be individually positioned on workpiece surfaces of non-flat geometries. To enable the utilisation of FreeHex as a miniature machine tool, calibration methods (to reference the platform against the workpiece), work volume calculations, and collision assessment procedures have been developed. The concept of this novel miniature machine tool was demonstrated by generating standard test pieces as well as freeform surfaces followed by accuracy assessments.     

Relationships between straightness and angular kinematic errors in machines

The software compensation approach for the improvement of machine tool and coordinate measuring machine accuracy depend to some extent on machine error modelling and measurement methodologies. The currently established methodology is based on the derivation of tool position error (for machine tools) or stylus tip position error (for coordinate measuring machines) by the combination of individual axis joint kinematic error parameters. The purpose of this paper is to propose a machine error analysis based on error classification. This taxonomic approach forms a conceptual basis for an analysis of machine errors with a deeper understanding of error mechanisms at more fundamental levels. The relevance of this approach is investigated through the case study of the coupling mechanism between joint kinematic angular and straightness errors of machine linear axes. The limitations of the joint kinematic straightness and angular error modelling based on purely abstract mathematical dependence principles are explored through simulations and experiments.     

基于三坐标测量仪的Stewart平台标定技术

针对空间对接半物理仿真系统中Stewart平台的运动精度问题,提出一种基于三坐标测量仪的低成本标定方法.利用通用的三坐标测量仪获取运动平台的位姿信息,构造一个统一度量的残差方程,辨识出运动平台的几何参数并进行误差补偿.此方法的特点是能够保证所有几何参数的可辨识性,不再需要设计和加工专门用于标定的各种辅助机构和冗余传感器,具有较强的通用性和可操作性.本文阐述了该标定方法的标定过程,对残差方程的构造方式进行了讨论,仿真表明标定后平台的运动精度能够达到测量噪声的量级.最后将此方法用于某实际运动平台的标定,经过误差补偿后其精度提高了5倍以上.     

Analysis–synthesis of dimensional deviation of the machining feature for discrete-part manufacturing processes

Dimensional deviation analysis has been an active and important research topic in mechanical design, manufacturing processes, and manufacturing systems. This paper proposes a comprehensive dimensional deviation evaluation framework for discrete-part manufacturing processes (DMP). A generic, explicit, and transmission model is developed to describe the dimensional deviation accumulation of machining processes by means of kinematic analysis of relationships between fixture error, datum error, machine tool geometric error, fixturing force inducing error and the dimensional quality of the product. The developed modeling technology can deal with general fixture configurations. In addition, the local contact deformations of the workpiece–fixture system are determined by solving a nonlinear programming problem of minimizing the total complementary energy of the frictional workpiece–fixture subsystem in machining system. Moreover, the deviation of an arbitrary point on machining feature can be also evaluated based on a point deviation model with prediction dimension deviation from the transmission model. The dimensional error transmission within the machining process is quantitatively described in this model. A systematic procedure to construct the model is presented and validated. This model can be also applied to process design evaluation for complicated machining processes.     

基于双目视觉和距离误差模型的工业机器人运动学参数标定方法

基于距离误差模型的标定技术,建立机器人末端距离误差与机器人运动学参数误差间的模型关系,避免了标定过程中坐标系的转换误差,能显著提高标定精度。视觉测量技术具有测量精度高、非接触性、实时性强等特点,与传统的机器人末端测量手段相比,具有成本低、操作简单等优势。研究一种将距离误差模型与视觉测量技术相结合的机器人标定方法,用于提高工业机器人特定工作空间的精度。采用双目视觉系统,将相机外置于机器人进行测量。基于距离误差模型进行机器人参数标定,利用标定结果进行运动学参数补偿。结果表明:特定标定工作空间内的距离误差都有所改善;在标定轨迹上,绝对距离误差的平均值从0.279 9 mm减少为0.104 4 mm,非标定轨迹的误差降幅高达50%以上,验证了该方法的可行性。     

A new calibration method for parallel kinematics machine tools using orientation constraint

This paper considers the problem of improving the accuracy of parallel kinematics machine tools through a low-cost and effective calibration method. A novel orientation constraint of keeping two attitude angles of the end-effector constant is presented to derive the calibration algorithm with special insight on the effect of using various combinations of two angles. The orientation constraint of the selected combination is realized physically through leveling a commercial biaxial inclinometer installed on the end-effector. Benefits of the proposed method include exempting the needs for precise pose (position and orientation) measurement and for mechanical fixtures, as well as rendering the independence of the measuring range and angular positioning accuracy of the inclinometer. Simulation based on the geometry of the Stewart platform of XJ-HEXA shows the position and orientation accuracy can reach 0.1 mm and 0.01° after calibration, when using an inclinometer with the repeatability of 0.001° and measuring the leg lengths with the precision of 0.002 mm at 80 configurations. Experiments on XJ-HEXA further verify the effectiveness of the proposed method.     

Kinematical calibration of a hybrid machine tool with Regularization method

The hybrid machine tools, combining the advantages of serial and parallel type machine tools, provide more and more application opportunities for less-freedom parallel mechanism. Accuracy performance is still an important index of hybrid machine tool for industry application. In this study, configuration of a 3-P(4R)S-XY hybrid machine tool is first introduced. The 3-P(4R)S parallel mechanism can be simplified to a 3-PRS mechanism on kinematical calibration. Based on that, error model and error kinematics are derived to introduce all possible manufacturing and assembling errors into calibration. Then, identification matrix is derived by differentiating kinematical equations. Combining the advantages of calibration schemes based on both inverse and forward kinematics model, a new measurement scheme is put forward, in which not all freedoms of motions needs to be measured and error identification could be efficiently accomplished in one time measurement. In order to solve the ill-posed problem in error identification, practical Regularization methods are adopted. Finally, the kinematical calibration experiment of the prototype machine tool is performed with a combined measuring tool. The results of RTCP accuracy test reveal that the positioning accuracy is less than 0.05 mm in the 30° cone workspace. Calibration experiments for the prototype verify feasibility and effectivity of the more precise kinematical error model, the low-cost measurement scheme, and the error identification solution with Regularization method.