2UPR-RRU并联机构及其运动学分析
|
摘要
针对航天制造中轻金属材料搅拌摩擦焊的焊接需求,提出一种以2UPRRRU构型的1T2R三自由度并联机构为主要执行机构的焊接装备。基于螺旋理论分析了该构型在一般位型和特殊位型下的约束螺旋系和自由度性质,指出该构型是具有两转一移的全周自由度机构。建立2UPR-RRU并联机构运动学模型,利用闭环矢量法建立动平台位姿与各驱动支链的关系,推导其运动学的正反解;在正解过程中构造优化目标函数,采用粒子群优化(PSO)算法分析了位姿输出与驱动关节输入的关系,得到了驱动输入的精确解。基于输入/输出速度雅可比矩阵分析了机构的奇异性问题,指出该构型避免存在驱动奇异的条件,研究表明该机构具有较好的运动学特性和驱动特性,具备良好的应用潜力。
To actualize the requirement of friction stir welding for light metal materials in aerospace manufacturing,this paper proposed a novel 2UPR-RRU parallel mechanism with IT2R 3-DOF as the manipulator of the welding equipment. Based on screw theory,the mechanism of one translational and two rotational fullcycle DOFs was found on general position and special position. Kinematic model of 2UPR-RRU parallel mechanism was constructed. Then the relationship between platform's positions and driving joints was analyzed by closed loop vector method and forward/inverse kinematics solutions were deduced. The optimal objective function was established in the process of forward kinematics,particle swarm optimization( PSO) algorithm was used to analyze the relationship between platform outputs and driving joints inputs,and finally the exact solution was found. Based on the input/output velocity Jacobi matrix,the motion singularity of 2UPR-RRU was analyzed,and especially the conditions to avoid driving singularity were discussed in detail. The research shows that 2UPR-RRU parallel mechanism,which is an important full-cycle DOF mechanism,possesses excellent kinetic characteristics,driving characteristics and high potential application.
To actualize the requirement of friction stir welding for light metal materials in aerospace manufacturing,this paper proposed a novel 2UPR-RRU parallel mechanism with IT2R 3-DOF as the manipulator of the welding equipment. Based on screw theory,the mechanism of one translational and two rotational fullcycle DOFs was found on general position and special position. Kinematic model of 2UPR-RRU parallel mechanism was constructed. Then the relationship between platform's positions and driving joints was analyzed by closed loop vector method and forward/inverse kinematics solutions were deduced. The optimal objective function was established in the process of forward kinematics,particle swarm optimization( PSO) algorithm was used to analyze the relationship between platform outputs and driving joints inputs,and finally the exact solution was found. Based on the input/output velocity Jacobi matrix,the motion singularity of 2UPR-RRU was analyzed,and especially the conditions to avoid driving singularity were discussed in detail. The research shows that 2UPR-RRU parallel mechanism,which is an important full-cycle DOF mechanism,possesses excellent kinetic characteristics,driving characteristics and high potential application.
引文
[1]杨坤玉,贺地求.飞机蒙皮铝合金超声辅助搅拌摩擦焊试验分析[J].北京航空航天大学学报,2017,43(10):1987-1993.YANG K Y,HE D Q.Test analysis for ultrasonic assisted friction stir welding of aircraft skin aluminum alloy[J].Journal of Beijing University of Aeronautics and Astronautics,2017,43(10):1987-1993(in Chinese).
[2]SALIH O S,OU H,SUN W,et al.A review of friction stir welding of aluminium matrix composites[J].Materials&Design,2015,86:61-71.
[3]GIBSON B T,LAMMLEIN D H,PRATER T J,et al.Friction stir welding:Process,automation,and control[J].Journal of Manufacturing Processes,2014,16(1):56-73.
[4]刘辛军,谢福贵,汪劲松.当前中国机构学面临的机遇[J].机械工程学报,2015,51(13):2-12.LIU X J,XIE F G,WANG J S.Current opportunities in the field of mechanisms in China[J].Journal of Mechanical Engineering,2015,51(13):2-12(in Chinese).
[5]LONGHURST W R.Force control of friction stir welding[D].Nashville:Vanderbilt Universitys,2009.
[6]BACKER J D,CHRISTIANSSON A,OQUEKA J,et al.Investigation of path compensation methods for robotic friction stir welding[J].Industrial Robot:An International Journal,2012,39(6):601-608.
[7]MENDES N,NETO P,LOUREIRO A,et al.Machines and control systems for friction stir welding:A review[J].Materials&Design,2016,90:256-265.
[8]杨会,房海蓉,李典,等.一新型并联灌注机器人运动学分析和多目标优化[J].北京航空航天大学学报,2018,44(3):568-575.YANG H,FANG H R,LI D,et al.Kinematics analysis and multi-objective optimization of a novel parallel perfusion robot[J].Journal of Beijing University of Aeronautics and Astronautics,2018,44(3):568-575(in Chinese).
[9]李秦川,柴馨雪,陈巧红.两转一移三自由度并联机构研究进展[J].科学通报,2017,62(14):1507-1519.LI Q C,CHAI X X,CHEN Q H.Review on 2R1T 3-DOF parallel mechanisms[J].Chinese Science Bulletin,2017,62(14):1507-1519(in Chinese).
[10]HUNT K H.Structural kinematics of in-parallel-actuated robotarms[J].Journal of Mechanisms Transmissions,and Automation in Design,1983,105(4):705-712.
[11]王瑞,纪校娟.一种改进型混联铣床的主轴运动学分析[J].组合机床与自动化加工技术,2009(6):22-25.WANG R,JI X J.Kinematics analysis on an improved parallelserial milling spindle[J].Modular Machine Tool&Automatic Manufacturing Technique,2009(6):22-25(in Chinese).
[12]程刚,万勇健,葛世荣.3-RPS对称并联支撑结构误差灵敏度研究[J].光电工程,2009,36(9):146-150.CHENG G,WAN Y J,GE S R.Error sensitivity of 3-RPS symmetrical parallel supporting structure[J].Opto-Electronic Engineering,2009,36(9):146-150(in Chinese).
[13]李艳文.几类空间并联机器人的奇异研究[D].秦皇岛:燕山大学,2005.LI Y W.On singularity of several kinds of spacial parallel manipulators[D].Qinhuangdao:Yanshan University,2005(in Chinese).
[14]邹成.基于2UPR/RPS并联机构的搅拌摩擦焊机器人设计与研究[D].秦皇岛:燕山大学,2016.ZOU C.Design and study of FSW robot based on 2UPR/RPSparallel mechanism[D].Qinhuangdao:Yanshan University,2016(in Chinese).
[15]张扬.无伴随运动对称两转一移并联机构的研究[D].秦皇岛:燕山大学,2016.ZHANG Y.Study on symmetrical 2R1T parallel mechanism without parasitic motion[D].Qinhuangdao:Yanshan University,2016(in Chinese).
[16]吴金波,韩鹏.一平动两转动3-UPU并联机构奇异性分析[J].机械科学与技术,2016,35(9):1313-1317.WU J B,HAN P.Singularity analysis of a 3-UPU parallel manipulator with one translation and two rotations[J].Mechanical Science and Technology for Aerospace Engineering,2016,35(9):1313-1317(in Chinese).
[17]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.HUANG Z,ZHAO Y S,ZHAO T S.Advanced spatial mechanism[M].Beijing:Higher Education Press,2014(in Chinese).
[18]LIU G,WANG Y,ZHANG Y,et al.Real-time solution of the forward kinematics for a parallel haptic device using a numerical approach based on neural networks[J].Journal of Mechanical Science&Technology,2015,29(6):2487-2499.
[19]王启明,苏建,张兰,等.基于L-M算法的正交Stewart平台位姿正解的初值补偿[J].吉林大学学报(工学版),2017,47(1):97-104.WANG Q M,SU J,ZHANG L,et al.Forward kinematics of orthogonal stewart platform based on L-M algorithm[J].Journal of Jilin University(Engineering and Technology Edition),2017,47(1):97-104(in Chinese).
[20]吴小勇,谢志江,宋代平,等.基于改进蚁群算法的3-PPR并联机构位置正解研究[J].农业机械学报,2015,46(7):339-344.WU X Y,XIE Z J,SONG D P,et al.Forward kinematics of 3-PPR parallel mechanism based on improved ant colony algorithm[J].Transactions of The Chinese Society of Agricultural Machinery,2015,46(7):339-344(in Chinese).
[21]YANG T L,LIU A,SHEN H,et al.General formula of degrees of freedom for spatial mechanisms[M].Singapore:Topology Design of Robot Mechanisms,2018.
[22]黄真,刘婧芳,曾达幸.基于约束螺旋理论的机构自由度分析的普遍方法[J].中国科学(E辑:技术科学),2009(1):84-93.HUANG Z,LIU J F,ZENG D X.General methodology for the freedom synthesis of parallel manipulators based on reciprocal screw theory[J].Science in China(Series E:Technological Sciences),2009(1):84-93(in Chinese).
[2]SALIH O S,OU H,SUN W,et al.A review of friction stir welding of aluminium matrix composites[J].Materials&Design,2015,86:61-71.
[3]GIBSON B T,LAMMLEIN D H,PRATER T J,et al.Friction stir welding:Process,automation,and control[J].Journal of Manufacturing Processes,2014,16(1):56-73.
[4]刘辛军,谢福贵,汪劲松.当前中国机构学面临的机遇[J].机械工程学报,2015,51(13):2-12.LIU X J,XIE F G,WANG J S.Current opportunities in the field of mechanisms in China[J].Journal of Mechanical Engineering,2015,51(13):2-12(in Chinese).
[5]LONGHURST W R.Force control of friction stir welding[D].Nashville:Vanderbilt Universitys,2009.
[6]BACKER J D,CHRISTIANSSON A,OQUEKA J,et al.Investigation of path compensation methods for robotic friction stir welding[J].Industrial Robot:An International Journal,2012,39(6):601-608.
[7]MENDES N,NETO P,LOUREIRO A,et al.Machines and control systems for friction stir welding:A review[J].Materials&Design,2016,90:256-265.
[8]杨会,房海蓉,李典,等.一新型并联灌注机器人运动学分析和多目标优化[J].北京航空航天大学学报,2018,44(3):568-575.YANG H,FANG H R,LI D,et al.Kinematics analysis and multi-objective optimization of a novel parallel perfusion robot[J].Journal of Beijing University of Aeronautics and Astronautics,2018,44(3):568-575(in Chinese).
[9]李秦川,柴馨雪,陈巧红.两转一移三自由度并联机构研究进展[J].科学通报,2017,62(14):1507-1519.LI Q C,CHAI X X,CHEN Q H.Review on 2R1T 3-DOF parallel mechanisms[J].Chinese Science Bulletin,2017,62(14):1507-1519(in Chinese).
[10]HUNT K H.Structural kinematics of in-parallel-actuated robotarms[J].Journal of Mechanisms Transmissions,and Automation in Design,1983,105(4):705-712.
[11]王瑞,纪校娟.一种改进型混联铣床的主轴运动学分析[J].组合机床与自动化加工技术,2009(6):22-25.WANG R,JI X J.Kinematics analysis on an improved parallelserial milling spindle[J].Modular Machine Tool&Automatic Manufacturing Technique,2009(6):22-25(in Chinese).
[12]程刚,万勇健,葛世荣.3-RPS对称并联支撑结构误差灵敏度研究[J].光电工程,2009,36(9):146-150.CHENG G,WAN Y J,GE S R.Error sensitivity of 3-RPS symmetrical parallel supporting structure[J].Opto-Electronic Engineering,2009,36(9):146-150(in Chinese).
[13]李艳文.几类空间并联机器人的奇异研究[D].秦皇岛:燕山大学,2005.LI Y W.On singularity of several kinds of spacial parallel manipulators[D].Qinhuangdao:Yanshan University,2005(in Chinese).
[14]邹成.基于2UPR/RPS并联机构的搅拌摩擦焊机器人设计与研究[D].秦皇岛:燕山大学,2016.ZOU C.Design and study of FSW robot based on 2UPR/RPSparallel mechanism[D].Qinhuangdao:Yanshan University,2016(in Chinese).
[15]张扬.无伴随运动对称两转一移并联机构的研究[D].秦皇岛:燕山大学,2016.ZHANG Y.Study on symmetrical 2R1T parallel mechanism without parasitic motion[D].Qinhuangdao:Yanshan University,2016(in Chinese).
[16]吴金波,韩鹏.一平动两转动3-UPU并联机构奇异性分析[J].机械科学与技术,2016,35(9):1313-1317.WU J B,HAN P.Singularity analysis of a 3-UPU parallel manipulator with one translation and two rotations[J].Mechanical Science and Technology for Aerospace Engineering,2016,35(9):1313-1317(in Chinese).
[17]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.HUANG Z,ZHAO Y S,ZHAO T S.Advanced spatial mechanism[M].Beijing:Higher Education Press,2014(in Chinese).
[18]LIU G,WANG Y,ZHANG Y,et al.Real-time solution of the forward kinematics for a parallel haptic device using a numerical approach based on neural networks[J].Journal of Mechanical Science&Technology,2015,29(6):2487-2499.
[19]王启明,苏建,张兰,等.基于L-M算法的正交Stewart平台位姿正解的初值补偿[J].吉林大学学报(工学版),2017,47(1):97-104.WANG Q M,SU J,ZHANG L,et al.Forward kinematics of orthogonal stewart platform based on L-M algorithm[J].Journal of Jilin University(Engineering and Technology Edition),2017,47(1):97-104(in Chinese).
[20]吴小勇,谢志江,宋代平,等.基于改进蚁群算法的3-PPR并联机构位置正解研究[J].农业机械学报,2015,46(7):339-344.WU X Y,XIE Z J,SONG D P,et al.Forward kinematics of 3-PPR parallel mechanism based on improved ant colony algorithm[J].Transactions of The Chinese Society of Agricultural Machinery,2015,46(7):339-344(in Chinese).
[21]YANG T L,LIU A,SHEN H,et al.General formula of degrees of freedom for spatial mechanisms[M].Singapore:Topology Design of Robot Mechanisms,2018.
[22]黄真,刘婧芳,曾达幸.基于约束螺旋理论的机构自由度分析的普遍方法[J].中国科学(E辑:技术科学),2009(1):84-93.HUANG Z,LIU J F,ZENG D X.General methodology for the freedom synthesis of parallel manipulators based on reciprocal screw theory[J].Science in China(Series E:Technological Sciences),2009(1):84-93(in Chinese).