计及重力的3-RRS并联机构静刚度分析
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摘要
研究重力场作用下3-RRS并联机构半解析静刚度建模方法。建模中同时考虑运动部件重力和末端外载荷对关节反力的影响,以及支链分布重力和所有构件/铰链弹性对关节变形的影响,并基于各部件在关节空间中的刚度模型建立机构末端静刚度模型。通过算例得到3-RRS并联机构末端静刚度和重力引起的末端变形在工作空间的分布规律;通过研究各构件刚度和重力分别对末端静刚度和变形的影响,得出为实现轻质高刚的结构设计应从球副和转动副刚度相匹配、主动臂和从动臂的驱动和约束刚度相匹配以及动平台轻量化设计等方面入手。
Stiffness is one of the most important performance factors that should be considered for parallel mechanism. A semi-analytical approach for the stiffness analysis of a 3-RRS parallel mechanism was presented with consideration of gravity. The force analysis was carried out by taking both gravity of all moving components and the externally applied wrench imposed upon the platform into account. The deflection analysis that considered the distributed gravity of all limbs and joint/link compliances was investigated. On the basis of the formulation of component stiffness matrices in the joint space,the stiffness model of the parallel mechanism was achieved. Based on a numerical example,the stiffness distributions and deflection distributions induced by gravity throughout the entire task workspace were evaluated,and the contributions of the component stiffness to the global stiffness and the contributions of the components gravity to platform deflection were investigated. Meanwhile,the effectiveness of the proposed modeling approach was verified by the FEA software at a typical configuration. Numerical example showed that in order to make the parallel mechanism with lightweight yet rigid design,the rigidities of different components,as well as the actuated and constraint rigidities of each component should be matched each other. For the considered 3-RRS parallel mechanism,the rigidity of the spherical joint should be improved while the rigidity of the revolute joint should be reduced,the actuated rigidity of the limb should be enhanced while the constraint rigidities of that should be reduced.
Stiffness is one of the most important performance factors that should be considered for parallel mechanism. A semi-analytical approach for the stiffness analysis of a 3-RRS parallel mechanism was presented with consideration of gravity. The force analysis was carried out by taking both gravity of all moving components and the externally applied wrench imposed upon the platform into account. The deflection analysis that considered the distributed gravity of all limbs and joint/link compliances was investigated. On the basis of the formulation of component stiffness matrices in the joint space,the stiffness model of the parallel mechanism was achieved. Based on a numerical example,the stiffness distributions and deflection distributions induced by gravity throughout the entire task workspace were evaluated,and the contributions of the component stiffness to the global stiffness and the contributions of the components gravity to platform deflection were investigated. Meanwhile,the effectiveness of the proposed modeling approach was verified by the FEA software at a typical configuration. Numerical example showed that in order to make the parallel mechanism with lightweight yet rigid design,the rigidities of different components,as well as the actuated and constraint rigidities of each component should be matched each other. For the considered 3-RRS parallel mechanism,the rigidity of the spherical joint should be improved while the rigidity of the revolute joint should be reduced,the actuated rigidity of the limb should be enhanced while the constraint rigidities of that should be reduced.
引文
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9陶兆胜,彭澎,赵艳芹.Exe-Variant并联模块静刚度分析[J/OL].农业机械学报,2017,48(4):377-382.http:∥www.jcsam.org/jcsam/ch/reader/view_abstract.aspx?flag=1&file_no=20170450&journal_id=jcsam.DOI:10.6041/j.issn.1000-1298.2017.04.050.TAO Zhaosheng,PENG Peng,ZHAO Yanqin.Stiffness analysis for Exe-Variant parallel kinematic machine[J/OL].Transactions of the Chinese Society for Agricultural Machinery,2017,48(4):377-382.(in Chinese)
10 ZHANG J,ZHAO Y,DAI J.Compliance modeling and analysis of a 3-RPS parallel kinematic machine module[J].Chinese Journal of Mechanical Engineering,2014,27(4):703-713.
11 CAO W A,DING H,YANG D.A method for compliance modeling of 5-DOF over-constrained parallel robotic mechanisms with3T2R output motion[J].Journal of Mechanisms&Robotics,2016,9(1):941-954.
12 GOSSELIN C.Stiffness mapping for parallel manipulator[J].IEEE Transactions on Robotics and Automation,1990,6(3):377-382.
13 PASHKEVICH A,KLIMCHIK A,CHABLAT D.Enhanced stiffness modeling of manipulators with passive joints[J].Mechanism&Machine Theory,2011,46(5):662-679.
14 KLIMCHIK A,CHABLAT D,PASHKEVICH A.Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings[J].Mechanism&Machine Theory,2014,79:1-28.
15 LI Y,XU Q.Stiffness analysis for a 3-PUU parallel kinematic machine[J].Mechanism&Machine Theory,2008,43(2):186-200.
16胡波,路懿.求解3-RPS并联机构刚度的新方法[J].机械工程学报,2010,46(1):24-29.HU Bo,LU Yi.New approach for analyzing the stiffness of 3-RPS parallel manipulator[J].Journal of Mechanical Engineering,2010,46(1):24-29.(in Chinese)
17落海伟,张俊,王辉,等.3-RPS并联机构静刚度建模方法[J].天津大学学报(自然科学与工程技术版),2015,48(9):797-803.LUO Haiwei,ZHANG Jun,WANG Hui,et al.Static stiffness modeling method of 3-RPS PKM[J].Journal of Tianjin University(Science and Technology),2015,48(9):797-803.(in Chinese)
18赵铁石,赵延治,边辉,等.空间并联机构连续刚度非线性映射[J].机械工程学报,2008,44(8):20-25.ZHAO Tieshi,ZHAO Yanzhi,BIAN Hui,et al.Continuous stiffness non-linear mapping of spatial parallel mechanism[J].Chinese Journal of Mechanical Engineering,2008,44(8):20-25.(in Chinese)
19 QUENNOUELLE C,GOSSELIN C.Kinematostatic modeling of compliant parallel mechanisms[J].Meccanica,2011,46(1):155-169.
20郭萌萌.重力作用下被动过约束并联机构受力与虚拟仿真分析[D].秦皇岛:燕山大学,2015.GUO Mengmeng.The force and virtual simulation analysis of passive over-constrained parallel mechanism with gravity[D].Qinhuangdao:Yanshan University,2015.(in Chinese)
21刘文兰,许允斗,闫文楠,等.重力对超静定结构受力的影响[J].中国机械工程,2017,28(6):648-655.LIU Wenlan,XU Yundou,YAN Wennan,et al.Influences of limbs'gravity on force analyses of statically indeterminate structures[J].China Mechanical Engineering,2017,28(6):648-655.(in Chinese)
22 WANG M,LIU H,HUANG T,et al.Compliance analysis of a 3-SPR parallel mechanism with consideration of gravity[J].Mechanism&Machine Theory,2015,84:99-112.
23 LI Q,WANG M,HUANG T,et al.Compliance analysis of a 3-DOF spindle head by considering gravitational effects[J].Chinese Journal of Mechanical Engineering,2015,28(1):1-10.
24 HUANG T,LIU H T,CHETWYND D G.Generalized Jacobian analysis of lower mobility manipulators[J].Mechanism and Machine Theory,2011,46(6):831-844.
2毛冰滟,谢志江,吴小勇,等.基于引导人工蜂群算法的3-RPS并联机构正解优化[J/OL].农业机械学报,2017,48(1):339-345.http:∥www.j-csam.org/jcsam/ch/reader/view_abstract.aspx?flag=1&file_no=20170145&journal_id=jcsam.DOI:10.6041/j.issn.1000-1298.2017.01.045.MAO Bingyan,XIE Zhijiang,WU Xiaoyong,et al.Forward kinematics optimization of 3-RPS parallel manipulator based on globalbest artificial bee colony algorithm[J].Transactions of the Chinese Society for Agricultural Machinery,2017,48(1):339-345.(in Chinese)
3 HENNES N,STAIMER D.Application of PKM in aerospace manufacturing high performance machining centers ECOSPEED,ECOSPEED-F and ECOLINER[C]∥Proceedings of the 4th Chemnitz Parallel Kinematics Seminar,Chemnitz:Verlag Wissenschaftliche Scripten,2004:557-568.
4 OLAZAGOITIA J L,WYATT S.New PKM tricept T9000 and its application to flexible manufacturing at aerospace industry[J].SAE Technical Papers,2007,2142:37-48.
5 BI Z M.Kinetostatic modeling of Exechon parallel kinematic machine for stiffness analysis[J].International Journal of Advanced Manufacturing Technology,2014,71(1-4):325-335.
6 HUANG T,LI M,ZHAO X M,et al.Conceptual design and dimensional synthesis for a 3-DOF module of the Tri Variant-a novel5-DOF reconfigurable hybrid robot[J].IEEE Transactions on Robotics,2005,21(3):449-456.
7栾玉亮,荣伟彬,孙立宁.基于有限元方法3-PPSR大长径比柔性并联机器人刚度模型分析[J].机器人,2014,36(6):730-736.LUAN Yuliang,RONG Weibin,SUN Lining.Analysis on stiffness model of 3-PPSR flexible parallel robot with high aspect ratio based on finite element method[J].Robot,2014,36(6):730-736.(in Chinese)
8陈落根.数字化设计平台中的CAD与CAE集成技术研究[D].天津:天津大学,2013.CHEN Luogen.Research on CAD-CAE integrated technology for a digital design platform[D].Tianjin:Tianjin University,2013.(in Chinese)
9陶兆胜,彭澎,赵艳芹.Exe-Variant并联模块静刚度分析[J/OL].农业机械学报,2017,48(4):377-382.http:∥www.jcsam.org/jcsam/ch/reader/view_abstract.aspx?flag=1&file_no=20170450&journal_id=jcsam.DOI:10.6041/j.issn.1000-1298.2017.04.050.TAO Zhaosheng,PENG Peng,ZHAO Yanqin.Stiffness analysis for Exe-Variant parallel kinematic machine[J/OL].Transactions of the Chinese Society for Agricultural Machinery,2017,48(4):377-382.(in Chinese)
10 ZHANG J,ZHAO Y,DAI J.Compliance modeling and analysis of a 3-RPS parallel kinematic machine module[J].Chinese Journal of Mechanical Engineering,2014,27(4):703-713.
11 CAO W A,DING H,YANG D.A method for compliance modeling of 5-DOF over-constrained parallel robotic mechanisms with3T2R output motion[J].Journal of Mechanisms&Robotics,2016,9(1):941-954.
12 GOSSELIN C.Stiffness mapping for parallel manipulator[J].IEEE Transactions on Robotics and Automation,1990,6(3):377-382.
13 PASHKEVICH A,KLIMCHIK A,CHABLAT D.Enhanced stiffness modeling of manipulators with passive joints[J].Mechanism&Machine Theory,2011,46(5):662-679.
14 KLIMCHIK A,CHABLAT D,PASHKEVICH A.Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings[J].Mechanism&Machine Theory,2014,79:1-28.
15 LI Y,XU Q.Stiffness analysis for a 3-PUU parallel kinematic machine[J].Mechanism&Machine Theory,2008,43(2):186-200.
16胡波,路懿.求解3-RPS并联机构刚度的新方法[J].机械工程学报,2010,46(1):24-29.HU Bo,LU Yi.New approach for analyzing the stiffness of 3-RPS parallel manipulator[J].Journal of Mechanical Engineering,2010,46(1):24-29.(in Chinese)
17落海伟,张俊,王辉,等.3-RPS并联机构静刚度建模方法[J].天津大学学报(自然科学与工程技术版),2015,48(9):797-803.LUO Haiwei,ZHANG Jun,WANG Hui,et al.Static stiffness modeling method of 3-RPS PKM[J].Journal of Tianjin University(Science and Technology),2015,48(9):797-803.(in Chinese)
18赵铁石,赵延治,边辉,等.空间并联机构连续刚度非线性映射[J].机械工程学报,2008,44(8):20-25.ZHAO Tieshi,ZHAO Yanzhi,BIAN Hui,et al.Continuous stiffness non-linear mapping of spatial parallel mechanism[J].Chinese Journal of Mechanical Engineering,2008,44(8):20-25.(in Chinese)
19 QUENNOUELLE C,GOSSELIN C.Kinematostatic modeling of compliant parallel mechanisms[J].Meccanica,2011,46(1):155-169.
20郭萌萌.重力作用下被动过约束并联机构受力与虚拟仿真分析[D].秦皇岛:燕山大学,2015.GUO Mengmeng.The force and virtual simulation analysis of passive over-constrained parallel mechanism with gravity[D].Qinhuangdao:Yanshan University,2015.(in Chinese)
21刘文兰,许允斗,闫文楠,等.重力对超静定结构受力的影响[J].中国机械工程,2017,28(6):648-655.LIU Wenlan,XU Yundou,YAN Wennan,et al.Influences of limbs'gravity on force analyses of statically indeterminate structures[J].China Mechanical Engineering,2017,28(6):648-655.(in Chinese)
22 WANG M,LIU H,HUANG T,et al.Compliance analysis of a 3-SPR parallel mechanism with consideration of gravity[J].Mechanism&Machine Theory,2015,84:99-112.
23 LI Q,WANG M,HUANG T,et al.Compliance analysis of a 3-DOF spindle head by considering gravitational effects[J].Chinese Journal of Mechanical Engineering,2015,28(1):1-10.
24 HUANG T,LIU H T,CHETWYND D G.Generalized Jacobian analysis of lower mobility manipulators[J].Mechanism and Machine Theory,2011,46(6):831-844.