Abstract：This paper described the kinematic calibration of the measurement trajectory and error compensation of a 5-axis hybrid machine tool. The kinematics model was based on the closed loop vector kinematic equations while the error model was based on the linear perturbation method. An index to evaluate the measurement trajectory was developed from a non-orthogonal index of the trajectory vectors. Two calibration tests were performed using different trajectories. Two error compensation schemes were based on the forward and inverse kinematics. The calibration tests show that the error compensation scheme based on the inverse kinematics has higher compensation accuracy. Finally, a test of machining an "S"-shape test specimen shows that 94% of the detected points are acceptable. The results verify the effectiveness of the index and the error compensation scheme.
刘宇哲, 吴军, 王立平, 汪劲松. 5轴混联机床运动学标定的测量轨迹评价及误差补偿[J]. 清华大学学报（自然科学版）, 2016, 56(10): 1047-1054.
LIU Yuzhe, WU Jun, WANG Liping, WANG Jinsong. Measurement trajectory evaluation and error compensation for kinematic calibration of a 5-axis hybrid machine tool. Journal of Tsinghua University(Science and Technology), 2016, 56(10): 1047-1054.
 Ramesh R, Mannan M A, Poo A N. Error compensation in machine tools: A review: Part I: Geometric, cutting-force induced and fixture-dependent errors [J]. International Journal of Machine Tools and Manufacture, 2000, 40(9): 1235-1256.
 WU Jun, CHEN Xiaolei, WANG Liping, et al. Dynamic load-carrying capacity of a novel redundantly actuated parallel conveyor [J]. Nonlinear Dynamics, 2014, 78(1): 241-250.
 WU Jun, WANG Jinsong, WANG Liping, et al. Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy [J]. Mechanism and Machine Theory, 2009, 44(4): 835-849.
 谢福贵, 刘辛军, 陈禹臻. 一种新型虚拟中心并联机构的误差灵敏度分析 [J]. 机械工程学报, 2013, 49(17): 85-91.XIE Fugui, LIU Xinjun, CHEN Yuzhen. Error sensitivity analysis of novel virtual center mechanism with parallel kinematics [J]. Chinese Journal of Mechanical Engineering, 2013, 49(17): 85-91. (in Chinese)
 WU Jun, WANG Dong, WANG Liping. A control strategy of a two degrees-of-freedom heavy duty parallel manipulator [J]. Journal of Dynamic Systems, Measurement, and Control, 2015, 137(6), 061007.
 黄鹏, 汪劲松, 王立平, 等. 3-PRS 并联机构误差运动学分析及辨识 [J]. 清华大学学报: 自然科学版, 2010, 50(11): 1811-1814.HUANG Peng, WANG Jingsong, WANG Liping, et al. Kinematical error analysis and identification of a 3-PRS parallel mechanism [J]. J Tsinghua Univ: Sci and Tech, 2010, 50(11): 1811-1814. (in Chinese)
 邵珠峰, 唐晓强, 王立平, 等. 平面柔性3-RRR并联机构自标定方法[J]. 机械工程学报, 2009, 45(3): 150-155. SHAO Zhufeng, TANG Xiaoqiang, WANG Liping, et al. Self-calibration method of planar flexible 3-RRR parallel manipulator [J]. Chinese Journal of Mechanical Engineering, 2009, 45(3): 150-155. (in Chinese)
 CHEN Yuzhen, XIE Fugui, LIU Xinjun, et al. Error modeling and sensitivity analysis of a parallel robot with SCARA (selective compliance assembly robot arm) motions [J]. Chinese Journal of Mechanical Engineering, 2014, 27(4): 693-702.
 Menq C H, Borm J H, Lai J Z. Identification and observability measure of a basis set of error parameters in robot calibration [J]. Journal of Mechanisms, Transmissions, and Automation in Design, 1989, 111(4): 513-518.
 Driels M R, Pathre U S. Significance of observation strategy on the design of robot calibration experiments [J]. Journal of Robotic Systems, 1990, 7(2): 197-223.
 Bennett D J, Hollerbach J M. Autonomous calibration of single-loop closed kinematic chains formed by manipulators with passive endpoint constraints [J]. IEEE Transactions on Robotics and Automation, 1991, 7(5): 597-606.
 CHANG Peng, WANG Jinsong, LI Tiemin, et al. Step kinematic calibration of a 3-DOF planar parallel kinematic machine tool [J]. Science in China Series E: Technological Sciences, 2008, 51(12): 2165-2177.
 LIU Dawei, WANG Liping, LI Tiemin, et al. A numerical error modeling method for parallel kinematic machines and its applications [J]. Tsinghua Sci and Tech, 2010, 15(5): 489-497.
 高猛, 李铁民, 郑浩峻, 等. 并联机床铰链制造误差的补偿 [J]. 清华大学学报: 自然科学版, 2003, 43(5): 617-620.GAO Meng, LI Tiemin, ZHENG Haojun, et al. Compensation for joint manufacturing errors in parallel kinematic machines [J]. J Tsinghua Univ: Sci and Tech, 2003, 43(5): 617-620. (in Chinese)