3UPS-RPR并联机构的静力学分析
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摘要
由于3UPS-RPR并联机构中间是一条RPR摆动支链,存在较大的工作空间与机构体积比,为了提高其力学灵敏度,进而提高其工作精度,对其进行静力学研究.采用闭环矢量法建立了该机构的逆位置模型,得到了逆位置解析解;在此基础上,运用反螺旋方法求得了该机构的完整雅可比矩阵;由虚功原理得到机构的输入与输出之间完整的力映射模型,建立静力学评价指标;最后,对力传递性能进行仿真,综合评估,得到机构优选的静动平台半径比λ在3~5之间,末端位姿参数α范围-0.5~0.5 rad,为机构后续静刚度分析和尺度综合奠定了基础.
3 UPS-RPR parallel mechanism has a RPR wobbling chain, and it has larger workspace and the volume ratio. In order to improve its mechanical sensitivity to achieve high working accuracy, so 3 UPS-RPR parallel mechanism is studied on the static analysis. The inverse position model is established with the close-loop vector and the inverse position analysis of the parallel mechanism is gotten. Base on these, the global Jacobian matrix of the parallel mechanism is established by applying the inverse screw. The force-mapping model between the input and the output is obtained according to the principle of virtual work. Then, the statics index is founded. At last, the force transfer property is simulated and overall results are obtained that the optimal radius ratio λ of static and dynamic platform is from 3 to 5 and the scope of the parameter α of end position from-0.5 to 0.5 rad. The study paves the way for the subsequent static stiffness analysis and dimensional synthesis.
3 UPS-RPR parallel mechanism has a RPR wobbling chain, and it has larger workspace and the volume ratio. In order to improve its mechanical sensitivity to achieve high working accuracy, so 3 UPS-RPR parallel mechanism is studied on the static analysis. The inverse position model is established with the close-loop vector and the inverse position analysis of the parallel mechanism is gotten. Base on these, the global Jacobian matrix of the parallel mechanism is established by applying the inverse screw. The force-mapping model between the input and the output is obtained according to the principle of virtual work. Then, the statics index is founded. At last, the force transfer property is simulated and overall results are obtained that the optimal radius ratio λ of static and dynamic platform is from 3 to 5 and the scope of the parameter α of end position from-0.5 to 0.5 rad. The study paves the way for the subsequent static stiffness analysis and dimensional synthesis.
引文
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[2]李永刚,宋轶民,冯志友,等.4自由度非全对称并联机构的完整雅可比矩阵[J].机械工程学报,2007,43(6):37-40.LI Y G,SONG Y M,FENG Z Y,et al.Complete Jacobian matrix of 4 degree of freedom non symmetric parallel mechanism[J].Journal of Mechanical Engineering,2007,43(6):37-40(in Chinese).
[3]孙涛,宋轶民,李永刚.3RUU机构雅可比矩阵与奇异性分析[J].机械设计与研究,2009(增刊):54-56.SUN T,SONG Y M,LI Y G.Jacobian matrix and singularity analysis of 3RUU mechanism[J].Machine Design and Research,2009(S):54-56(in Chinese).
[4]YANG G,CHEN I M,LIN W,et al.Singularity analysis of three-legged parallel robots based on passive-joint velocities[J].IEEE Transactions on Robotics&Automation,2001,17(4):413-422.
[5]姜子强,李永刚,许立新.基于齐次量纲雅可比矩阵的四自由度并联机构运动灵巧度分析[J].机械与电子,2014(6):43-47.JIANG Z Q,LI Y G,XU L X.Kinematic dexterity analysis of four degree of freedom parallel mechanism based on homogeneous dimensional Jacobian matrix[J].Machinery and Electronics,2014(6):43-47(in Chinese).
[6]CECCARELLI M,OTTAVIANO E,GALVAGNO M.A 3-DOF parallel manipulator as earthquake motion simulator[J].International Conference on Control,2003,2(4):944-949.
[7]曲海波,梁艺瀚,方跃法,等.4-RRS冗余球面并联机构的静力学与刚度分析[J].机械工程学报,2015,51(11):8-15.QU H B,LIANG Y H,FANG Y F,et al.Statics and stiffness analysis of 4-RRS redundant spherical parallel mechanism[J].Journal of Mechanical Engineering,2015,51(11):8-15(in Chinese).
[8]路光达,张爱梅,周静,等.3RSS-S并联机构的静力学分析与实验研究[J].机械设计,2013,30(3):26-31.LU G D,ZHANG A M,ZHOU J,et al.Statics analysis and experimental research of 3RSS-S parallel mechanism[J].Journal of Mechanical Design,2013,30(3):26-31(in Chinese).
[9]王中林,张宁斌,李秦川,等.2UPR-RPU并联机构的静力学分析[J].浙江理工大学学报,2016,35(3):372-378.WANG Z L,ZHANG N B,LI Q C,et al.Statics analysis of2UPR-RPU parallel mechanism[J].Journal of Zhejiang University of Technology,2016,35(3):372-378(in Chinese).
[10]HUBERT J,MERLET J P.Static of parallel manipulators and closeness to singularity[J].Journal of Mechanisms&Robotics,2009,1(1):212-240.
[11]艾青林,黄伟锋,张洪涛,等.并联机器人刚度与静力学研究现状与进展[J].力学进展,2012,42(5):583-592.AI Q L,HUANG W F,ZHANG H T,et al.The status and progress of the parallel robot stiffness and statics research[J].Journal of Mechanics,2012,42(5):583-592(in Chinese).
[12]邓昱,陈修龙,孙先洋,等.4-UPS-RPS并联机器人机构及其静力学分析[J].北京工业大学学报,2013,39(10):1464-1467.DENG Y,CHEN X L,SUN X Y,et al.4-UPS-RPS parallel robot mechanism and its statics analysis[J].Journal of Beijing University of Technology,2013,39(10):1464-1467(in Chinese).
[13]NINOMIYA T,HIGASHI T,HARADA K,et al.Analysis of the static and dynamic characteristics of push-pull parallel resonant converters[C]//Annual Power Electronics Specialists Conference.Vancouver:PESC,1986:367-374.
[14]LI Y,XU Q.Kinematic analysis of a 3-PRS parallel manipulator[J].Robotics and Computer-Integrated Manufacturing,2007,23(4):395-408.
[15]LIU H T,HUANG T,ZHAO X M,et al.Optimal design of the trivariant robot to achieve a nearly axial symmetry of kinematic performance[J].Mechanism&Machine Theory,2007,42(12):1643-1652.
[16]黄真,孔令富,方跃法.并联机器人机构学理论及控制[M].北京:机械工业出版社,1997.HUANG Z,KONG L F,FANG Y F.The Theory and Control of Parallel Robot Mechanism[M].Beijing:China Machine Press,1997(in Chinese).