6支链台体型Stewart衍生构型位置正解半解析算法
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摘要
目前6支链Stewart并联机构位置正解无全解析解或全解析解推导困难,不利于程式化分析计算,本文设计4种6支链台体型Stewart衍生构型,并构建了一种数值法和解析法相结合的半解析算法。通过添加6条虚拟支链,4种衍生构型可重构为同一种12-6台体型拓扑构型;推导了重构构型的协调方程,并针对4种衍生构型,推导了虚拟支链长度的数值解;基于动平台上特征点之间的拓扑关系,推导了重构构型位置正解的全解析解。进一步对比分析了半解析算法与传统数值法在计算位姿正解时的精度、效率和稳定性。数值算例表明,半解析算法的精度与稳定性优于传统数值法至少2倍,但传统数值法的效率是半解析算法的7倍;同时得到了半解析算法的3点构型选取原则。
According to the present problems that the forward displacement analysis of most platform Stewart parallel mechanisms with six links can not be described with whole analytical solutions,and a very few of them can be described with whole analytical solutions and also with these difficulties,including calculation and programming,four kinds of platform Stewart derivative configurations with six links were designed,and a semi-analytic algorithm which combined with numerical method and analytical method was established. By adding six virtual links, the four derivative configurations can be reconstructed into the same kind of 12-6 platform topological configuration. Compatibility equations of reconstructed configuration were derived,and aimed at four kinds of derivative configurations,the numerical solution of the length of the virtual links was derived. Based on the topological relations between feature points on the moving platform,the whole analytical solution of the forward displacement analysis of the reconstructed configuration was derived. Furthermore,the accuracy,efficiency and stability of the semi-analytic algorithm and the traditional numerical method were compared and analyzed respectively. Numerical examples showed that the accuracy and stability of the semi-analytic algorithm was at least two times of that of the traditional numerical method,but the efficiency of the traditional numerical method was seven times of that of the semi-analytic algorithm. Meanwhile,three selection principles of configurations were obtained,which established theoretical foundation for the engineering application of six links parallel mechanism.
According to the present problems that the forward displacement analysis of most platform Stewart parallel mechanisms with six links can not be described with whole analytical solutions,and a very few of them can be described with whole analytical solutions and also with these difficulties,including calculation and programming,four kinds of platform Stewart derivative configurations with six links were designed,and a semi-analytic algorithm which combined with numerical method and analytical method was established. By adding six virtual links, the four derivative configurations can be reconstructed into the same kind of 12-6 platform topological configuration. Compatibility equations of reconstructed configuration were derived,and aimed at four kinds of derivative configurations,the numerical solution of the length of the virtual links was derived. Based on the topological relations between feature points on the moving platform,the whole analytical solution of the forward displacement analysis of the reconstructed configuration was derived. Furthermore,the accuracy,efficiency and stability of the semi-analytic algorithm and the traditional numerical method were compared and analyzed respectively. Numerical examples showed that the accuracy and stability of the semi-analytic algorithm was at least two times of that of the traditional numerical method,but the efficiency of the traditional numerical method was seven times of that of the semi-analytic algorithm. Meanwhile,three selection principles of configurations were obtained,which established theoretical foundation for the engineering application of six links parallel mechanism.
引文
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[2]张英,廖启征,魏世民.一般6-4台体型并联机构位置正解分析[J].机械工程学报,2012,48(9):26-32.ZHANG Ying,LIAO Qizheng,WEI Shimin.Forward displacement analysis of a general 6-4 in-parallel platform[J].Journal of Mechanical Engineering,2012,48(9):26-32.(in Chinese)
[3]WEN Ke,DU Fuzhou,ZHANG Xianzhi.Algorithm and experiments of six-dimensional force/torque dynamic measurements based on a Stewart platform[J].Chinese Journal of Aeronautics,2016,29(6):1840-1851.
[4]ENFERADI J,NIKROOZ R.The performance indices optimization of a symmetrical fully spherical parallel mechanism for dimensional synthesis[J].Journal of Intelligent&Robotic Systems,2018,90(3-4):305-321.
[5]沈惠平,许可,杨廷力,等.一种零耦合度且运动解耦的新型3T1R并联操作手2-(RPa3R)3R的设计及其运动学[J].机械工程学报.http:∥kns.cnki.net/kcms/detail/11.2187.TH.20180904.1444.004.html.SHEN Huiping,XU Ke,YANG Tingli,et al.New 3T1R parallel manipulator 2-(RPa3R)3R with zero coupling degree and partial decoupling:design and kinematics[J].Journal of Mechanical Engineering.http:∥kns.cnki.net/kcms/detail/11.2187.TH.20180904.1444.004.html(in Chinese)
[6]KALANI H,REZAEI A,AKBARZADEH A.Improved general solution for the dynamic modeling of Gough-Stewart platform based on principle of virtual work[J].Nonlinear Dynamics,2016,83(4):2393-2418.
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[8]尤晶晶.基于冗余并联机构的压电式六维加速度传感器研究[D].南京:南京航空航天大学,2013.YOU Jingjing.Research on piezoelectric six-axis accelerometer based on redundant parallel mechanism[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2013.(in Chinese)
[9]尤晶晶.基于6-SPS并联机构的压电式六维加速度传感器的研究[D].南京:南京航空航天大学,2010.YOU Jingjing.Research on a piezoelectric six-axis accelerometer based on 6-SPS parallel mechanism[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2010.(in Chinese)
[10]CHAPSKY V,PORTMAN V T,SANDLER B Z.Single-mass 6-DOF isotropic accelerometer with segmented PSD sensors[J].Sensors&Actuators A Physical,2007,135(2):558-569.
[11]HAN Hongwei,DANG Shuwen.Research on performance of motion platform of 3-RPS flight simulator[C]∥IEEEInternational Conference on Computational Intelligence and Security,2017:340-344.
[12]周昌春,方跃法,叶伟,等.6-RRS超冗余驱动飞行模拟器的性能分析[J].机械工程学报,2016,52(1):34-40.ZHOU Changchun,FANG Yuefa,YE Wei,et al.Performance analysis of 6-RRS over-redundant actuation flight simulator[J].Journal of Mechanical Engineering,2016,52(1):34-40.(in Chinese)
[13]倪涛,李骁鹏,张红彦,等.基于立体视觉的遥操作机器人力感示教控制策略[J/OL].农业机械学报,2013,44(1):244-247.NI Tao,LI Xiaopeng,ZHANG Hongyan,et al.3-D vision-based kinesthesis teaching control strategy for telerobotics[J/OL].Transactions of the Chinese Society for Agricultural Machinery,2013,44(1):244-247.http:∥www.j-csam.org/jcsam/ch/reader/view_abstract.aspx?flag=1&file_no=20130145&journal_id=jcsam.DOI:10.6041/j.issn.1000-1298.2013.01.045.(in Chinese)
[14]RYDEN F,STEWART A,CHIZECK H J.Advanced telerobotic underwater manipulation using virtual fixtures and haptic rendering[C]∥IEEE Oceans,2013:1-8.
[15]戴文伟,吴洪涛,杨小龙.6-3型Stewart平台并联机构的运动学正解[J].机械设计与制造工程,2012,41(17):43-46.DAI Wenwei,WU Hongtao,YANG Xiaolong.Numerical method for forward kinematics of 6-3 Stewart platform parallel manipulator[J].Machine Design and Manufacturing Engineering,2012,41(17):43-46.(in Chinese)
[16]MERLET J P.Parallel robots[M].Springer,2006.
[17]尤晶晶,符周舟,吴洪涛,等.12-6台体型Stewart冗余并联机构正向运动学研究[J/OL].农业机械学报,2017,48(12):395-402.YOU Jingjing,FU Zhouzhou,WU Hongtao,et al.Forward kinematics of general 12-6 Stewart redundant parallel mechanism[J/OL].Transactions of the Chinese Society for Agricultural Machinery,2017,48(12):395-402.http:∥www.j-csam.org/jcsam/ch/reader/view_abstract.aspx?flag=1&file_no=20171249&journal_id=jcsam.DOI:10.6041/j.issn.1000-1298.2017.12.049.(in Chinese)
[18]刘芳华,张星,魏玉平,等.基于牛顿迭代的6-UPS并联机构运动学正解的研究[J].机械设计与制造,2013(5):173-176.LIU Fanghua,ZHANG Xing,WEI Yuping,et al.The forward kinematics analysis of 6-UPS parallel mechanism based on Newton iteration[J].Machinery Design&Manufacture,2013(5):173-176.(in Chinese)
[19]耿明超,赵铁石,王唱,等.基于拟Newton法的并联机构位置正解[J].机械工程学报,2015,51(9):28-36.GENG Mingchao,ZHAO Tieshi,WANG Chang,et al.Direct position analysis of parallel mechanism based on quasi-Newton method[J].Journal of Mechanical Engineering,2015,51(9):28-36.(in Chinese)
[20]韩方元,赵丁选,李天宇.3-RPS并联机构正解快速数值算法[J].农业机械学报,2011,42(4):229-233.HAN Fangyuan,ZHAO Dingxuan,LI Tianyu.A fast forward algorithm for 3-RPS parallel mechanism[J].Transactions of the Chinese Society for Agricultural Machinery,2011,42(4):229-233.(in Chinese)
[21]ZHOU Wanyong,CHEN Wuyi,LIU Huadong,et al.A new forward kinematics algorithm for a general Stewart platform[J].Mechanism and Machine Theory,2015,87:177-190.
[22]YANG Xiaolong,WU Hongtao,LI Yao,et al.A dual quaternion solution to the forward kinematics of a class of six-DOFparallel robots with full or reductant actuation[J].Mechanism and Machine Theory,2017,107:27-36.
[23]李明磊,贾育秦.6-SPS并联机构位置正解的改进粒子群算法[J].现代制造工程,2009(5):106-110.LI Minglei,JIA Yuqin.Improved particle swarm optimization algorithm for forward positional analysis of 6-SPS parallel manipulators[J].Modern Manufacturing Engineering,2009(5):106-110.(in Chinese)
[24]程世利,吴洪涛,姚裕.6-SPS并联机构运动学正解的一种解析化方法[J].机械工程学报,2010,46(9):26-31.CHENG Shili,WU Hongtao,YAO Yu.An analytical method for the forward kinematics analysis of 6-SPS parallel mechanisms[J].Journal of Mechanical Engineering,2010,46(9):26-31.(in Chinese)
[25]HUANG Tian,WANG Manxin,YANG Shuofei,et al.Force/motion transmissibility analysis of six degree of freedom parallel mechanisms[J].Journal of Mechanisms and Robotics,2014,6(3):1-5.
[26]黄昔光,廖启征,魏世民,等.一般6-6型平台并联机构位置正解代数消元法[J].机械工程学报,2009,45(1):56-61.HUANG Xiguang,LIAO Qizheng,WEI Shimin,et al.Forward kinematics analysis of the general 6-6 platform parallel mechanism based on algebraic elimination[J].Chinese Journal of Mechanical Engineering,2009,45(1):56-61.(in Chinese)
[27]尤晶晶,李成刚,吴洪涛.基于四面体构型的冗余并联机构的运动学分析[J].中国机械工程,2013,24(8):1097-1101.YOU Jingjing,LI Chenggang,WU Hongtao.Kinematics analysis of redundant parallel mechanism based on tetrahedral configuration[J].China Mechanical Engineering,2013,24(8):1097-1101.(in Chinese)
[28]沈惠平,尹洪波,王振,等.基于拓扑结构分析的求解6-SPS并联机构位置正解的研究[J].机械工程学报,2013,49(21):70-80.SHEN Huiping,YIN Hongbo,WANG Zhen,et al.Research on forward position solutions for 6-SPS parallel mechanisms based on topology structure analysis[J].Journal of Mechanical Engineering,2013,49(21):70-80.(in Chinese)
[2]张英,廖启征,魏世民.一般6-4台体型并联机构位置正解分析[J].机械工程学报,2012,48(9):26-32.ZHANG Ying,LIAO Qizheng,WEI Shimin.Forward displacement analysis of a general 6-4 in-parallel platform[J].Journal of Mechanical Engineering,2012,48(9):26-32.(in Chinese)
[3]WEN Ke,DU Fuzhou,ZHANG Xianzhi.Algorithm and experiments of six-dimensional force/torque dynamic measurements based on a Stewart platform[J].Chinese Journal of Aeronautics,2016,29(6):1840-1851.
[4]ENFERADI J,NIKROOZ R.The performance indices optimization of a symmetrical fully spherical parallel mechanism for dimensional synthesis[J].Journal of Intelligent&Robotic Systems,2018,90(3-4):305-321.
[5]沈惠平,许可,杨廷力,等.一种零耦合度且运动解耦的新型3T1R并联操作手2-(RPa3R)3R的设计及其运动学[J].机械工程学报.http:∥kns.cnki.net/kcms/detail/11.2187.TH.20180904.1444.004.html.SHEN Huiping,XU Ke,YANG Tingli,et al.New 3T1R parallel manipulator 2-(RPa3R)3R with zero coupling degree and partial decoupling:design and kinematics[J].Journal of Mechanical Engineering.http:∥kns.cnki.net/kcms/detail/11.2187.TH.20180904.1444.004.html(in Chinese)
[6]KALANI H,REZAEI A,AKBARZADEH A.Improved general solution for the dynamic modeling of Gough-Stewart platform based on principle of virtual work[J].Nonlinear Dynamics,2016,83(4):2393-2418.
[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,2014.
[8]尤晶晶.基于冗余并联机构的压电式六维加速度传感器研究[D].南京:南京航空航天大学,2013.YOU Jingjing.Research on piezoelectric six-axis accelerometer based on redundant parallel mechanism[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2013.(in Chinese)
[9]尤晶晶.基于6-SPS并联机构的压电式六维加速度传感器的研究[D].南京:南京航空航天大学,2010.YOU Jingjing.Research on a piezoelectric six-axis accelerometer based on 6-SPS parallel mechanism[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2010.(in Chinese)
[10]CHAPSKY V,PORTMAN V T,SANDLER B Z.Single-mass 6-DOF isotropic accelerometer with segmented PSD sensors[J].Sensors&Actuators A Physical,2007,135(2):558-569.
[11]HAN Hongwei,DANG Shuwen.Research on performance of motion platform of 3-RPS flight simulator[C]∥IEEEInternational Conference on Computational Intelligence and Security,2017:340-344.
[12]周昌春,方跃法,叶伟,等.6-RRS超冗余驱动飞行模拟器的性能分析[J].机械工程学报,2016,52(1):34-40.ZHOU Changchun,FANG Yuefa,YE Wei,et al.Performance analysis of 6-RRS over-redundant actuation flight simulator[J].Journal of Mechanical Engineering,2016,52(1):34-40.(in Chinese)
[13]倪涛,李骁鹏,张红彦,等.基于立体视觉的遥操作机器人力感示教控制策略[J/OL].农业机械学报,2013,44(1):244-247.NI Tao,LI Xiaopeng,ZHANG Hongyan,et al.3-D vision-based kinesthesis teaching control strategy for telerobotics[J/OL].Transactions of the Chinese Society for Agricultural Machinery,2013,44(1):244-247.http:∥www.j-csam.org/jcsam/ch/reader/view_abstract.aspx?flag=1&file_no=20130145&journal_id=jcsam.DOI:10.6041/j.issn.1000-1298.2013.01.045.(in Chinese)
[14]RYDEN F,STEWART A,CHIZECK H J.Advanced telerobotic underwater manipulation using virtual fixtures and haptic rendering[C]∥IEEE Oceans,2013:1-8.
[15]戴文伟,吴洪涛,杨小龙.6-3型Stewart平台并联机构的运动学正解[J].机械设计与制造工程,2012,41(17):43-46.DAI Wenwei,WU Hongtao,YANG Xiaolong.Numerical method for forward kinematics of 6-3 Stewart platform parallel manipulator[J].Machine Design and Manufacturing Engineering,2012,41(17):43-46.(in Chinese)
[16]MERLET J P.Parallel robots[M].Springer,2006.
[17]尤晶晶,符周舟,吴洪涛,等.12-6台体型Stewart冗余并联机构正向运动学研究[J/OL].农业机械学报,2017,48(12):395-402.YOU Jingjing,FU Zhouzhou,WU Hongtao,et al.Forward kinematics of general 12-6 Stewart redundant parallel mechanism[J/OL].Transactions of the Chinese Society for Agricultural Machinery,2017,48(12):395-402.http:∥www.j-csam.org/jcsam/ch/reader/view_abstract.aspx?flag=1&file_no=20171249&journal_id=jcsam.DOI:10.6041/j.issn.1000-1298.2017.12.049.(in Chinese)
[18]刘芳华,张星,魏玉平,等.基于牛顿迭代的6-UPS并联机构运动学正解的研究[J].机械设计与制造,2013(5):173-176.LIU Fanghua,ZHANG Xing,WEI Yuping,et al.The forward kinematics analysis of 6-UPS parallel mechanism based on Newton iteration[J].Machinery Design&Manufacture,2013(5):173-176.(in Chinese)
[19]耿明超,赵铁石,王唱,等.基于拟Newton法的并联机构位置正解[J].机械工程学报,2015,51(9):28-36.GENG Mingchao,ZHAO Tieshi,WANG Chang,et al.Direct position analysis of parallel mechanism based on quasi-Newton method[J].Journal of Mechanical Engineering,2015,51(9):28-36.(in Chinese)
[20]韩方元,赵丁选,李天宇.3-RPS并联机构正解快速数值算法[J].农业机械学报,2011,42(4):229-233.HAN Fangyuan,ZHAO Dingxuan,LI Tianyu.A fast forward algorithm for 3-RPS parallel mechanism[J].Transactions of the Chinese Society for Agricultural Machinery,2011,42(4):229-233.(in Chinese)
[21]ZHOU Wanyong,CHEN Wuyi,LIU Huadong,et al.A new forward kinematics algorithm for a general Stewart platform[J].Mechanism and Machine Theory,2015,87:177-190.
[22]YANG Xiaolong,WU Hongtao,LI Yao,et al.A dual quaternion solution to the forward kinematics of a class of six-DOFparallel robots with full or reductant actuation[J].Mechanism and Machine Theory,2017,107:27-36.
[23]李明磊,贾育秦.6-SPS并联机构位置正解的改进粒子群算法[J].现代制造工程,2009(5):106-110.LI Minglei,JIA Yuqin.Improved particle swarm optimization algorithm for forward positional analysis of 6-SPS parallel manipulators[J].Modern Manufacturing Engineering,2009(5):106-110.(in Chinese)
[24]程世利,吴洪涛,姚裕.6-SPS并联机构运动学正解的一种解析化方法[J].机械工程学报,2010,46(9):26-31.CHENG Shili,WU Hongtao,YAO Yu.An analytical method for the forward kinematics analysis of 6-SPS parallel mechanisms[J].Journal of Mechanical Engineering,2010,46(9):26-31.(in Chinese)
[25]HUANG Tian,WANG Manxin,YANG Shuofei,et al.Force/motion transmissibility analysis of six degree of freedom parallel mechanisms[J].Journal of Mechanisms and Robotics,2014,6(3):1-5.
[26]黄昔光,廖启征,魏世民,等.一般6-6型平台并联机构位置正解代数消元法[J].机械工程学报,2009,45(1):56-61.HUANG Xiguang,LIAO Qizheng,WEI Shimin,et al.Forward kinematics analysis of the general 6-6 platform parallel mechanism based on algebraic elimination[J].Chinese Journal of Mechanical Engineering,2009,45(1):56-61.(in Chinese)
[27]尤晶晶,李成刚,吴洪涛.基于四面体构型的冗余并联机构的运动学分析[J].中国机械工程,2013,24(8):1097-1101.YOU Jingjing,LI Chenggang,WU Hongtao.Kinematics analysis of redundant parallel mechanism based on tetrahedral configuration[J].China Mechanical Engineering,2013,24(8):1097-1101.(in Chinese)
[28]沈惠平,尹洪波,王振,等.基于拓扑结构分析的求解6-SPS并联机构位置正解的研究[J].机械工程学报,2013,49(21):70-80.SHEN Huiping,YIN Hongbo,WANG Zhen,et al.Research on forward position solutions for 6-SPS parallel mechanisms based on topology structure analysis[J].Journal of Mechanical Engineering,2013,49(21):70-80.(in Chinese)