具有整周回转能力的3T1R并联机构运动学分析
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摘要
设计了一种可实现整周回转运动且便于模块化装配的3T1R并联机构。首先,提出一种仅含转动副的二维移动放缩单元,模块化组合与扩展后,构造得到一种平面二维移动放缩机构,将平面二维移动放缩机构作为支链,设计得到一种新型3T1R并联机构;其次,对该3T1R机构进行拓扑结构分析,在保证机构基本功能(方位特征集和自由度)不变的情况下对其进行降耦设计,得到耦合度为1的机构;最后,基于序单开链法对降耦机构进行位置分析,同时,基于导出的机构位置反解公式,分析机构的工作空间和转动能力,并绘制转动能力图谱,根据转动能力图谱筛选出机构可实现整周回转运动的工作空间范围,为该型机构的设计和实际工程应用提供理论依据。
There is a wide range of industrial application for the 4-DOF parallel mechanism( PM) which can achieve SCARA type output motion( i. e.,three translations and one rotation). However,due to the constraints of kinematic chains,most of them have small rotational capacity and cannot meet the actual demand sometimes. A type of 3T1R PM which can realize full cycle rotary motion was proposed. Firstly,a two-dimensional moving unit which consisted of revolute joint only was constructed. According to the mechanisms and machine theory,modular principle of the pantograph mechanism for scaling twodimensional planar graph was explained as the mechanism can be divided into three types of modules which were all derived from the two-dimensional moving unit. And then a 3T1R PM with four legs was designed by taking the obtained pantograph mechanisms as sub-chains. Secondly,the structure couplingreducing optimization design for this PM was performed,whose POC and DOF were unchanged with lower coupling degree( k = 1). Finally,the modeling method and the numerical solutions for forward and inverse position equations of the PM were established based on ordered single-open-chain( SOC) units.The working space and the rotational ability of this parallel mechanism were obtained and the rotational capacity map was drawn by using the inverse position equations. According to the map,the range of workspace that can realize the full rotational capability was selected which can be treated as a theoretical basis for the design and applications for this mechanism.
There is a wide range of industrial application for the 4-DOF parallel mechanism( PM) which can achieve SCARA type output motion( i. e.,three translations and one rotation). However,due to the constraints of kinematic chains,most of them have small rotational capacity and cannot meet the actual demand sometimes. A type of 3T1R PM which can realize full cycle rotary motion was proposed. Firstly,a two-dimensional moving unit which consisted of revolute joint only was constructed. According to the mechanisms and machine theory,modular principle of the pantograph mechanism for scaling twodimensional planar graph was explained as the mechanism can be divided into three types of modules which were all derived from the two-dimensional moving unit. And then a 3T1R PM with four legs was designed by taking the obtained pantograph mechanisms as sub-chains. Secondly,the structure couplingreducing optimization design for this PM was performed,whose POC and DOF were unchanged with lower coupling degree( k = 1). Finally,the modeling method and the numerical solutions for forward and inverse position equations of the PM were established based on ordered single-open-chain( SOC) units.The working space and the rotational ability of this parallel mechanism were obtained and the rotational capacity map was drawn by using the inverse position equations. According to the map,the range of workspace that can realize the full rotational capability was selected which can be treated as a theoretical basis for the design and applications for this mechanism.
引文
[1] PIERROT F,COMPANY O. H4:a new family of 4-DOF parallel robots[C]∥Proceedings of the 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics,1999:508-513.
[2] KRUT S,COMPANY O,BENOIT M,et al. I4:a new parallel mechanism for scara motions[C]∥Proceedings of the 2003 IEEE International Conference on Robotics and Automation,2003:1875-1880.
[3] NABAT V,RODRIGUEZ M,COMPANY O,et al. Par4:very high speed parallel robot for pick-and-place[C]∥Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems,2005:553-558.
[4] KRUT S,COMPANY O,NABAT V,et al. Heli4:a parallel robot for scara motions with a very compact travelling plate and a symmetrical design[C]∥Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems,2006:1656-1661.
[5] PIERROT F,NABAT V,COMPANY O,et al. Optimal design of a 4-DOF parallel manipulator:from academia to industry[J].IEEE Transactions on Robotics,2009,25(2):213-224.
[6] LI Y H,MA Y,LIU S T,et al. Integrated design of a 4-DOF high-speed pick-and-place parallel robot[J]. CIRP AnnalsManufacturing Technology,2014,63(1):185-188.
[7]赵铁石,黄真.一种新型四自由度并联平台机构及其位置分析[J].机械科学与技术,2000,19(6):927-929.ZHAO Tieshi,HUANG Zhen. A novel spatial four-DOF parallel mechanism and its position analysis[J]. Mechanical Science and Technology for Aerospace Engineering,2000,19(6):927-929.(in Chinese)
[8]黄田,赵学满,梅江平,等.一种具有三维平动一维转动的并联机构:CN202528189U[P]. 2012-11-14.
[9]刘辛军,谢福贵,王立平.一种可实现SCARA运动的四自由度单动平台并联机构:CN102922513A[P]. 2013-02-13.
[10]沈惠平,熊坤,孟庆梅,等.并联机构运动解耦设计方法与应用研究[J/OL].农业机械学报,2016,47(6):348-356.SHEN Huiping,XIONG Kun,MENG Qingmei,et al. Design methods for kinematic decoupled parallel mechanisms and its applications[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2016,47(6):348-356. http:∥www.j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20160646&journal_id=jcsam. DOI:10. 6041/j. issn.1000-1298. 2016. 06. 046.(in Chinese)
[11]沈惠平,曾氢菲,李菊,等.典型并联机构拓扑结构特征分析[J/OL].农业机械学报,2016,47(8):388-398.SHEN Huiping,ZENG Qingfei,LI Ju,et al. Topological structure characteristics analysis for typical and practical parallel mechanisms[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2016,47(8):388-398. http:∥www.j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20160851&journal_id=jcsam. DOI:10. 6041/j. issn.1000-1298. 2016. 08. 051.(in Chinese)
[12]沈惠平,朱小蓉,尹洪波,等.并联机构的结构降耦原理及其设计方法[J].机械工程学报,2016,52(23):102-113.SHEN Huiping,ZHU Xiaorong,YIN Hongbo,et al. Principle and design method for structure coupling-reducing of parallel mechanisms[J]. Journal of Mechanical Engineering,2016,52(23):102-113.(in Chinese)
[13]沈惠平,尹洪贺,邵国为,等.低耦合度3T1R并联操作手设计与运动学分析[J/OL].农业机械学报,2017,48(5):405-412.SHEN Huiping,YIN Honghe,SHAO Guowei,et al. Design and kinematics analysis of a novel 3T1R parallel manipulator with lower coupling degree[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2017,48(5):405-412. http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20170552&journal_id=jcsam. DOI:10. 6041/j.issn. 1000-1298. 2017. 05. 052.(in Chinese)
[14]沈惠平,张震,杨廷力,等. 3T1R并联机构结构降耦设计与运动学分析[J/OL].农业机械学报,2017,48(10):380-389,400.SHEN Huiping,ZHANG Zhen,YANG Tingli,et al. Structure coupling-reducing design and kinematics analysis of 3T1R parallel mechanism[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2017,48(10):380-389,400.http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20171049&journal_id=jcsam. DOI:10.6041/j. issn. 1000-1298. 2017. 10. 049.(in Chinese)
[15]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,2019,55(5):53-64.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,2019,55(5):53-64.(in Chinese)
[16]沈惠平,吕蒙,朱小蓉,等.一种单自由度3T1R并联机构的拓扑设计及其运动学[J].中国机械工程,2019,30(8):961-968.SHEN Huiping,LüMeng,ZHU Xiaorong,et al. Topological design and kinematics of 3T1R PM with single degree of freedom[J]. China Mechanical Engineering,2019,30(8):961-968.(in Chinese)
[17]杨廷力,刘安心,罗玉峰,等.机器人机构拓扑结构设计[M].北京:科学出版社,2012.
[18]杨廷力,刘安心,沈惠平,等.基于方位特征方程的3T-1R并联机构的拓扑结构综合[J].机械工程学报,2017,53(21):54-64.YANG Tingli,LIU Anxin,SHEN Huiping,et al. Topological structural synthesis of 3T-1R parallel mechanism based on POC equations[J]. Journal of Mechanical Engineering,2017,53(21):54-64.(in Chinese)
[19]朱小蓉,宋月月,沈惠平,等.基于POC方法的少自由度无过约束并联机构构型综合[J/OL].农业机械学报,2016,47(8):370-377.ZHU Xiaorong,SONG Yueyue,SHEN Huiping,et al. Structural synthesis based on POC set for lower-mobility nonoverconstrained parallel mechanisms[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2016,47(8):370-377. http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20160849&journal_id=jcsam.DOI:10. 6041/j. issn. 1000-1298. 2016. 08. 049.(in Chinese)
[20]朱小蓉,胡旸,沈惠平,等. 3T1R并联机构降耦设计与分析[J/OL].农业机械学报,2018,49(12):393-401.ZHU Xiaorong,HU Yang,SHEN Huiping,et al. Design and analysis of structure coupling reduction on novel 3T1R parallel mechanism[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2018,49(12):393-401. http:∥www.j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20181247&journal_id=jcsam. DOI:10. 6041/j. issn.1000-1298. 2018. 12. 047.(in Chinese)
[21]贺磊盈,涂叶凯,叶伟,等.一种可整周回转的新型3T1R并联机构运动学分析[J].机械工程学报,2018,54(11):151-160.HE Leiying,TU Yekai,YE Wei,et al. Kinematics analysis of a novel 3T1R parallel manipulator with full rotational capability[J]. Journal of Mechanical Engineering,2018,54(11):151-160.(in Chinese)
[2] KRUT S,COMPANY O,BENOIT M,et al. I4:a new parallel mechanism for scara motions[C]∥Proceedings of the 2003 IEEE International Conference on Robotics and Automation,2003:1875-1880.
[3] NABAT V,RODRIGUEZ M,COMPANY O,et al. Par4:very high speed parallel robot for pick-and-place[C]∥Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems,2005:553-558.
[4] KRUT S,COMPANY O,NABAT V,et al. Heli4:a parallel robot for scara motions with a very compact travelling plate and a symmetrical design[C]∥Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems,2006:1656-1661.
[5] PIERROT F,NABAT V,COMPANY O,et al. Optimal design of a 4-DOF parallel manipulator:from academia to industry[J].IEEE Transactions on Robotics,2009,25(2):213-224.
[6] LI Y H,MA Y,LIU S T,et al. Integrated design of a 4-DOF high-speed pick-and-place parallel robot[J]. CIRP AnnalsManufacturing Technology,2014,63(1):185-188.
[7]赵铁石,黄真.一种新型四自由度并联平台机构及其位置分析[J].机械科学与技术,2000,19(6):927-929.ZHAO Tieshi,HUANG Zhen. A novel spatial four-DOF parallel mechanism and its position analysis[J]. Mechanical Science and Technology for Aerospace Engineering,2000,19(6):927-929.(in Chinese)
[8]黄田,赵学满,梅江平,等.一种具有三维平动一维转动的并联机构:CN202528189U[P]. 2012-11-14.
[9]刘辛军,谢福贵,王立平.一种可实现SCARA运动的四自由度单动平台并联机构:CN102922513A[P]. 2013-02-13.
[10]沈惠平,熊坤,孟庆梅,等.并联机构运动解耦设计方法与应用研究[J/OL].农业机械学报,2016,47(6):348-356.SHEN Huiping,XIONG Kun,MENG Qingmei,et al. Design methods for kinematic decoupled parallel mechanisms and its applications[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2016,47(6):348-356. http:∥www.j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20160646&journal_id=jcsam. DOI:10. 6041/j. issn.1000-1298. 2016. 06. 046.(in Chinese)
[11]沈惠平,曾氢菲,李菊,等.典型并联机构拓扑结构特征分析[J/OL].农业机械学报,2016,47(8):388-398.SHEN Huiping,ZENG Qingfei,LI Ju,et al. Topological structure characteristics analysis for typical and practical parallel mechanisms[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2016,47(8):388-398. http:∥www.j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20160851&journal_id=jcsam. DOI:10. 6041/j. issn.1000-1298. 2016. 08. 051.(in Chinese)
[12]沈惠平,朱小蓉,尹洪波,等.并联机构的结构降耦原理及其设计方法[J].机械工程学报,2016,52(23):102-113.SHEN Huiping,ZHU Xiaorong,YIN Hongbo,et al. Principle and design method for structure coupling-reducing of parallel mechanisms[J]. Journal of Mechanical Engineering,2016,52(23):102-113.(in Chinese)
[13]沈惠平,尹洪贺,邵国为,等.低耦合度3T1R并联操作手设计与运动学分析[J/OL].农业机械学报,2017,48(5):405-412.SHEN Huiping,YIN Honghe,SHAO Guowei,et al. Design and kinematics analysis of a novel 3T1R parallel manipulator with lower coupling degree[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2017,48(5):405-412. http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20170552&journal_id=jcsam. DOI:10. 6041/j.issn. 1000-1298. 2017. 05. 052.(in Chinese)
[14]沈惠平,张震,杨廷力,等. 3T1R并联机构结构降耦设计与运动学分析[J/OL].农业机械学报,2017,48(10):380-389,400.SHEN Huiping,ZHANG Zhen,YANG Tingli,et al. Structure coupling-reducing design and kinematics analysis of 3T1R parallel mechanism[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2017,48(10):380-389,400.http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20171049&journal_id=jcsam. DOI:10.6041/j. issn. 1000-1298. 2017. 10. 049.(in Chinese)
[15]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,2019,55(5):53-64.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,2019,55(5):53-64.(in Chinese)
[16]沈惠平,吕蒙,朱小蓉,等.一种单自由度3T1R并联机构的拓扑设计及其运动学[J].中国机械工程,2019,30(8):961-968.SHEN Huiping,LüMeng,ZHU Xiaorong,et al. Topological design and kinematics of 3T1R PM with single degree of freedom[J]. China Mechanical Engineering,2019,30(8):961-968.(in Chinese)
[17]杨廷力,刘安心,罗玉峰,等.机器人机构拓扑结构设计[M].北京:科学出版社,2012.
[18]杨廷力,刘安心,沈惠平,等.基于方位特征方程的3T-1R并联机构的拓扑结构综合[J].机械工程学报,2017,53(21):54-64.YANG Tingli,LIU Anxin,SHEN Huiping,et al. Topological structural synthesis of 3T-1R parallel mechanism based on POC equations[J]. Journal of Mechanical Engineering,2017,53(21):54-64.(in Chinese)
[19]朱小蓉,宋月月,沈惠平,等.基于POC方法的少自由度无过约束并联机构构型综合[J/OL].农业机械学报,2016,47(8):370-377.ZHU Xiaorong,SONG Yueyue,SHEN Huiping,et al. Structural synthesis based on POC set for lower-mobility nonoverconstrained parallel mechanisms[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2016,47(8):370-377. http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20160849&journal_id=jcsam.DOI:10. 6041/j. issn. 1000-1298. 2016. 08. 049.(in Chinese)
[20]朱小蓉,胡旸,沈惠平,等. 3T1R并联机构降耦设计与分析[J/OL].农业机械学报,2018,49(12):393-401.ZHU Xiaorong,HU Yang,SHEN Huiping,et al. Design and analysis of structure coupling reduction on novel 3T1R parallel mechanism[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2018,49(12):393-401. http:∥www.j-csam. org/jcsam/ch/reader/view_abstract. aspx? flag=1&file_no=20181247&journal_id=jcsam. DOI:10. 6041/j. issn.1000-1298. 2018. 12. 047.(in Chinese)
[21]贺磊盈,涂叶凯,叶伟,等.一种可整周回转的新型3T1R并联机构运动学分析[J].机械工程学报,2018,54(11):151-160.HE Leiying,TU Yekai,YE Wei,et al. Kinematics analysis of a novel 3T1R parallel manipulator with full rotational capability[J]. Journal of Mechanical Engineering,2018,54(11):151-160.(in Chinese)
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