General forward kinematic algorism for three-chain parallel manipulator
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摘要: 针对含复合铰链的3RPS并联机构在制造装配中实际结构参数不等于名义结构参数的问题,设计了一种考虑全部结构参数的一般三支链并联正解算法.一般三支链并联机构是3条支链共同支撑1个平台,每个支链结构均为一般5自由度串联机器人,其中只有一个运动副是主动副驱动的三支链并联机构.算法基于对偶四元数和DH方法表达支链方程,该算法考虑了一般三支链并联机构总共78项几何参数.可用于一般三支链并联机构的精度分析、精度综合、精度补偿和精确的运动仿真.算法经过反复计算验证,具有准确、稳定、速度快的特点,并且将3RPS,3_5R,3_RPUR,3_RPRRR等构型统一在一个数学模型中.Abstract: To solve the problem that actual geometric parameters are not equal to nominal ones in parallel manipulator, a general forward kinematic algorism, containing all of the geometric parameters, was proposed. The general 3RPS parallel manipulator, with compound spherical joints, was taken as an example. The manipulator consists of a base platform, a mobile platform and three chains, and every chain is a 5-DOF serial manipulator with only 1-DOF being active. The algorism is based on dual quaternion and DH method and contains a total of 78 geometric parameters, and hence it is able to be used for accuracy analysis, accuracy synthesis, accuracy calibration and accurate kinematic simulation of parallel manipulator. Finally, the precise, stability and rapidness of the algorism were verified through iterative calculation. The forward kinematic algorism of 3RPS, 3_5R, 3_RPUR, 3_RPRRR,and so on can be expressed in a same form on the basis of the proposed algorism.
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Key words:
- 3RPS mechanism /
- dual quaternion /
- DH method /
- parallel mechanism /
- forward kinematics
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[1] Hunt K H. Structural kinematics of in-parallel-actuated robot-arms[J].Journal of Mechanisms Transmissions and Automation in Design, 1983, 105(4):705-712 [2] Kim J, Park F C.Direct kinematic analysis of 3-RS parallel mechanisms[J].Mechanism and Machine Theory, 2001, 36(10): 1121-1134 [3] 孙永生, 韩先国, 陈五一, 等.并联机构大范围收敛高效正解算法[J].计算机集成制造系统, 2012, 18(5):981-987 Sun Yongsheng, Han Xianguo, Chen Wuyi, et al.High efficient approach of direct problem with extensive convergence on parallel mechanism[J].Computer Integrated Manufacturing Systems, 2012, 18(5):981-987(in Chinese) [4] Zhan T S, Kao C C.Modified PSO method for robust control of 3RPS parallel manipulators[J].Mathematical Problems in Engineering, 2010:302430-1-25 [5] 黄俊杰, 赵俊伟.3-PRS 并联机构位置正解分析[J].河南理工大学学报:自然科学版, 2012, 31(4):434-436, 452 Huang Junjie, Zhao Junwei.Research on kinematic forward solution for 3-PRS parallel mechanism[J].Journal of Henan Polytechnic University:Natural Science, 2012, 31(4):434-436, 452(in Chinese) [6] 李新友, 陈五一, 韩先国.基于正交设计的3-RPS并联机构精度分析与综合[J].北京航空航天大学学报, 2011, 37(8):979-984 Li Xinyou, Chen Wuyi, Han Xianguo.Accuracy analysis and synthesis of 3-RPS parallel machine based on orthogonal design[J].Journal of Beijing University of Aeronautics and Astronautics, 2011, 37(8):979-984(in Chinese) [7] 黄真, 赵永生, 赵铁石.高等空间机构学[M].北京:高等教育出版社, 2006:262-268 Huang Zhen, Zhao Yongsheng, Zhao Tieshi.Advanced spatial mechanism[M].Beijing:Higher Education Press, 2006:262-268(in Chinese) [8] Li S H, Ma N, Ding W H.Kinematic analysis of a novel 3-DOF 3-RPUR translational parallel mechanism[C]//IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM.Piscataway, NJ:IEEE, 2008:516-521 [9] Wang J, Masory O.On the accuracy of a stewart platform, Part 1:the effect of manufacturing tolerances[C]//Proceedings of the IEEE International Conference on Robotics and Automation.Piscataway, NJ:IEEE, 1993(1):114-120 [10] Gan D M, Liao Q Z, Wei S M, et al.Dual quaternion-based inverse kinematics of the general spatial 7R mechanism[J].Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2008, 222(8):1593-1598 [11] 廖启征, 倪振松, 李洪波, 等.四元数的复数形式及其在6R机器人反解中的应用[J].系统科学与数学, 2009, 24(9):1286-1296 Liao Qizheng, Ni Zhensong, Li Hongbo, et al.An application of dual quaternions on the reverse displacement analysis of 6R robots[J].J Sys Sci & Math Scis, 2009, 24(9):1286-1296(in Chinese) [12] Aspragathos N A, Dimitros J K.A comparative study of three methods for robot kinematis[J].IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics, 1998, 28(2):135-145 [13] Clifford W K.Application of Grassmann's extensive algebra[J].American Journal of Mathematics, 1878, 1(4):350-358 [14] Danevit J, Hartenberg R S.A kinematic notation for lower-pair mechanisms based on matrices[J].Trans ASME J of Applied Mechanics, 1955, 22:215-221
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