3-HSS并联机构位置正解几何法的研究
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摘要
与串联机器人不同,并联机器人位置正解的推导过程复杂。常见的并联机构位置正解的求解方法有解析法和数值法。解析法推导过程十分繁琐,容易出现错误且不易排查;数值法对奇异点的处理存在缺陷。为了避免以上的缺点,以3-HSS并联机构为研究对象,根据平行四边形结构的特点对3-HSS并联机构模型进行简化。将立体几何问题简化为多个相关的平面几何问题,得到了基于几何法的3-HSS并联机构位置正解的显式方程组。使用Matlab进行编程,进行了仿真实验验证了算法的正确性和可靠性。
Different from the serial robot,the derivation process of the positive solution of the parallel robot is very complicated. Analytical and numerical methods are used to solve the positive solution of parallel mechanism.The derivation process of the analytical method is very complicated,and it is easy to be wrong and not easy to check.The numerical method is weake on solving the the singularity. In order to avoid the above shortcomings,this paper took 3-HSS parallel mechanism as the research object,and simplified the 3-HSS parallel mechanism model according to the characteristics of parallelogram structure. The stereoscopic geometry problem was transformed into a number of related plane geometric problems,and got the explicit equations of the positive solution of the position for the 3-HSS parallel mechanism based on the geometric method.And the simulation results show the reliability of the geometry method.
Different from the serial robot,the derivation process of the positive solution of the parallel robot is very complicated. Analytical and numerical methods are used to solve the positive solution of parallel mechanism.The derivation process of the analytical method is very complicated,and it is easy to be wrong and not easy to check.The numerical method is weake on solving the the singularity. In order to avoid the above shortcomings,this paper took 3-HSS parallel mechanism as the research object,and simplified the 3-HSS parallel mechanism model according to the characteristics of parallelogram structure. The stereoscopic geometry problem was transformed into a number of related plane geometric problems,and got the explicit equations of the positive solution of the position for the 3-HSS parallel mechanism based on the geometric method.And the simulation results show the reliability of the geometry method.
引文
[1]薛明瑞,高奇峰,胡红钱.基于几何法Delta并联机器人运动学分析[J].机械设计与制造,2017(3):258-260.(Xue Ming-rui,Gao Qi-feng,Hu Hong-qian.Knematics analysisof delta parallel robot based on geometric solution[J].Machinery Design&Manufacture,2017(3):258-260.)
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[3]郭玉,赵新华,李彬.一种过约束3自由度并联机构的位置正解研究[J].天津理工大学学报,2012(2):20-22.(Guo Yu,Zhao Xin-hua,Li Bin.Orward position analysis of an over·constrained 3-DOF parallel mechanism[J].Journal of Tianjin University of Technology,2012(2):20-22.)
[4]周万勇,陈五一,刘华东.一般三支链并联机构正解算法[J].北京航空航天大学学报,2014(4):461-466.(Zhou Wan-yong,Chen Wu-yi,Liu Hua-dong.General forward kinematic algorism for three-chain parallel manipulator[J].Journal of Beijing University of Aeronautics and Astronautics,2014(4):461-466.)
[5]孙付伟,赵俊伟,陈国强.3-PRS并联机构运动学正解可视化分析[J].河南理工大学学报:自然科学版,2017(1):80-85.(Sun Fu-wei,Zhao Jun-wei,Chen Guo-qiang.Visualization analysis of positive solution of 3-PRS parallel mechanism kinematics[J].Journal of Henan Polytechnic University:Natural Science,2017(1):80-85.)
[6]耿明超,赵铁石,王唱.基于拟Newton法的并联机构位置正解[J].机械工程学报,2015(9):28-36.(Geng Ming-chao,Zhao Tie-shi,Wang Chang.Direct position analysis of parallel mechanism based on Qasi-Newton method[J].Journal of Mechanical Engineering,2015(9):28-36.)
[7]康件丽,陈国强,赵俊伟.3-PRS并联机构正解的数值方法[J].现代制造工程,2015(2):36-42.(Kang Jian-li,Chen Guo-qiang,Zhao Jun-wei.Forward kinematics of3-PRS mechanism based on numerical method[J].Modern Manufacturing Engineering,2015(2):36-42.)
[8]张永文.五自由度并联机构正解新数值算法[J].装备制造技术,2015(11):53-57.(Zhang Yong-wen.A new numerical algorithm for forward kinematics of five DOF parallel mechanisms[J].Equipment Manufacturing Technology,2015(2):36-42.)
[9]韩霄,李虹,李瑞琴.基于BP法的3-RRP并联机构位置正解研究[J].组合机床与自动化加工技术,2015(2):94-96.(Han Xiao,Li Hong,Li Rui-qin.A solution for forward kinematics of 3-RSR parallel robot based on BP algorithm[J].Modular Machine Tool&Automatic Manufacturing Technique,2015(2):94-96.
[10]黄涛,沈惠平,余同柱.5-3型6-SPS并联机构位置分析的正逆解析解[J].常州大学学报:自然科学版,2013(2):72-76.(Huang Tao,Shen Hui-ping,Yu Tong-zhu.Analytical solutions to the forward and inverse positions of 5-3 type 6-SPS parallel mechanism[J].Journal of Changzhou University:Natural Science Edition,2013(2):72-76.)
[2]高征,高峰.球面3自由度并联机构的正解分析新方法[J].机械设计与制造,2006(9):122-124.(Gao Zheng,Gao Feng.New method of forward position analysis of the3-DOF spheical parallel manipulator[J].Machinery Design&Manufacture,2006(9):122-124.)
[3]郭玉,赵新华,李彬.一种过约束3自由度并联机构的位置正解研究[J].天津理工大学学报,2012(2):20-22.(Guo Yu,Zhao Xin-hua,Li Bin.Orward position analysis of an over·constrained 3-DOF parallel mechanism[J].Journal of Tianjin University of Technology,2012(2):20-22.)
[4]周万勇,陈五一,刘华东.一般三支链并联机构正解算法[J].北京航空航天大学学报,2014(4):461-466.(Zhou Wan-yong,Chen Wu-yi,Liu Hua-dong.General forward kinematic algorism for three-chain parallel manipulator[J].Journal of Beijing University of Aeronautics and Astronautics,2014(4):461-466.)
[5]孙付伟,赵俊伟,陈国强.3-PRS并联机构运动学正解可视化分析[J].河南理工大学学报:自然科学版,2017(1):80-85.(Sun Fu-wei,Zhao Jun-wei,Chen Guo-qiang.Visualization analysis of positive solution of 3-PRS parallel mechanism kinematics[J].Journal of Henan Polytechnic University:Natural Science,2017(1):80-85.)
[6]耿明超,赵铁石,王唱.基于拟Newton法的并联机构位置正解[J].机械工程学报,2015(9):28-36.(Geng Ming-chao,Zhao Tie-shi,Wang Chang.Direct position analysis of parallel mechanism based on Qasi-Newton method[J].Journal of Mechanical Engineering,2015(9):28-36.)
[7]康件丽,陈国强,赵俊伟.3-PRS并联机构正解的数值方法[J].现代制造工程,2015(2):36-42.(Kang Jian-li,Chen Guo-qiang,Zhao Jun-wei.Forward kinematics of3-PRS mechanism based on numerical method[J].Modern Manufacturing Engineering,2015(2):36-42.)
[8]张永文.五自由度并联机构正解新数值算法[J].装备制造技术,2015(11):53-57.(Zhang Yong-wen.A new numerical algorithm for forward kinematics of five DOF parallel mechanisms[J].Equipment Manufacturing Technology,2015(2):36-42.)
[9]韩霄,李虹,李瑞琴.基于BP法的3-RRP并联机构位置正解研究[J].组合机床与自动化加工技术,2015(2):94-96.(Han Xiao,Li Hong,Li Rui-qin.A solution for forward kinematics of 3-RSR parallel robot based on BP algorithm[J].Modular Machine Tool&Automatic Manufacturing Technique,2015(2):94-96.
[10]黄涛,沈惠平,余同柱.5-3型6-SPS并联机构位置分析的正逆解析解[J].常州大学学报:自然科学版,2013(2):72-76.(Huang Tao,Shen Hui-ping,Yu Tong-zhu.Analytical solutions to the forward and inverse positions of 5-3 type 6-SPS parallel mechanism[J].Journal of Changzhou University:Natural Science Edition,2013(2):72-76.)