类Exechon并联机构模块可重构概念设计与运动学分析
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摘要
可重构与模块化设计是实现并联机构多功能、提升装备加工柔性的关键技术.受商用Exechon并联机构模块优异性能的设计启发,在其变异机构Exe-Variant的基础上,应用机构变异思想提出两种类Exechon并联机构模块——Exe-Ⅰ和Exe-Ⅱ.基于可锁定关节、模块化支链以及可重构并联机构的设计思路,依次开展Exechon、Exe-Variant、Exe-Ⅰ和Exe-Ⅱ等4种类Exechon并联机构的模块化、可重构概念设计.针对以上并联机构模块进行运动学分析:运用螺旋理论分析类Exechon并联机构的系统螺旋系,构建类Exechon并联机构的系统全雅克比矩阵,依次分析机构自由度和奇异性;通过矢量闭环方程推导其逆运动学模型和动平台连带运动;以"分层切片"的工作空间搜索方法预估其工作空间.运动学对比分析表明:对类Exechon并联机构模块开展的可重构设计,保留了并联机构的自由度类型和结构奇异性特征,并显著改善了部分类Exechon并联机构的逆运动学连带运动的复杂程度以及动平台可达工作空间的分布.最后,借助3D打印技术制作了Exe-Ⅰ并联机构模块的原理样机,运动学精度实验结果与理论分析结果吻合较好,数据的绝对误差在±0.4 mm以内,并且其相对误差不大于实验值的3.2%,验证了运动学分析的正确性.本文提出的可重构与模块化概念设计,可为类Exechon并联机构模块的高效可重构设计及其工程应用提供关键技术支撑.
Reconfigurable and modular designs can be a key technology to realize the versatility as well as improve the flexibility of parallel kinematic machines(PKMs). Inspired by the design of the high-performance Exechon PKM,two novel Exechon-like PKMs—Exe-Ⅰ and Exe-Ⅱ are proposed on the basis of the Exe-Variant PKM. Four types of reconfigurable Exechon-like PKM modules—Exechon,Exe-Variant,Exe-Ⅰ,and Exe-Ⅱ were conceptually designed by following the design flows of lockable joints,modular limbs,and reconfigurable PKMs. With regard to the kinematic analysis of Exechon-like PKMs,the degrees of freedom(DoF)and singularities were analyzed with the screw theory,wherein the screw systems of the Exechon-like PKMs were formulated and overfull Jacobian matrices of the PKMs were derived. Loop-closure equations were formulated to develop the inverse kinematic model and parasitic motions of the moving platform. The reachable workspaces of the proposed PKMs were predicted by a "sliced partition" algorithm. A comparative analysis of the kinematics shows that the reconfigurable design of the Exechonlike PKMs can keep the Do F of the PKMs and their architectural singularities unchanged. The analysis also shows that the reconfigurable design can significantly improve the complexity of the parasitic motions of inverse kinematics and the distributions of the moving platform's reachable workspaces for several Exechon-like PKMs. Finally,using the 3D printing technology,a laboratory prototype of Exe-Ⅰ PKM was built to conduct the kinematic experiment.The experimental values agree well with the theoretical values. The absolute error is less than ±0.4 mm and the relative error is within 3.2%,which verifies the effectiveness of the proposed kinematic analysis module. The conceptual designs of reconfigurable and modular PKMs in this study can prove to be key techniques to realize efficient reconfigurable designs and engineering applications of Exechon-like PKMs.
Reconfigurable and modular designs can be a key technology to realize the versatility as well as improve the flexibility of parallel kinematic machines(PKMs). Inspired by the design of the high-performance Exechon PKM,two novel Exechon-like PKMs—Exe-Ⅰ and Exe-Ⅱ are proposed on the basis of the Exe-Variant PKM. Four types of reconfigurable Exechon-like PKM modules—Exechon,Exe-Variant,Exe-Ⅰ,and Exe-Ⅱ were conceptually designed by following the design flows of lockable joints,modular limbs,and reconfigurable PKMs. With regard to the kinematic analysis of Exechon-like PKMs,the degrees of freedom(DoF)and singularities were analyzed with the screw theory,wherein the screw systems of the Exechon-like PKMs were formulated and overfull Jacobian matrices of the PKMs were derived. Loop-closure equations were formulated to develop the inverse kinematic model and parasitic motions of the moving platform. The reachable workspaces of the proposed PKMs were predicted by a "sliced partition" algorithm. A comparative analysis of the kinematics shows that the reconfigurable design of the Exechonlike PKMs can keep the Do F of the PKMs and their architectural singularities unchanged. The analysis also shows that the reconfigurable design can significantly improve the complexity of the parasitic motions of inverse kinematics and the distributions of the moving platform's reachable workspaces for several Exechon-like PKMs. Finally,using the 3D printing technology,a laboratory prototype of Exe-Ⅰ PKM was built to conduct the kinematic experiment.The experimental values agree well with the theoretical values. The absolute error is less than ±0.4 mm and the relative error is within 3.2%,which verifies the effectiveness of the proposed kinematic analysis module. The conceptual designs of reconfigurable and modular PKMs in this study can prove to be key techniques to realize efficient reconfigurable designs and engineering applications of Exechon-like PKMs.
引文
[1]Chen Xiang,Liu Xinjun,Xie Fugui,et al.A comparison study on motion/force transmissibility of two typical 3-DoF parallel manipulators:The sprint Z3 and A3 tool heads[J].International Journal of Advanced Robotic Systems,2014,11(1):1-10.
[2]赵庆,王攀峰,黄田.考虑链间耦合的高速并联机器人惯性参数预估方法[J].天津大学学报:自然科学与工程技术版,2017,50(8):868-876.Zhao Qing,Wang Panfeng,Huang Tian.An inertial parameter estimation method for high-speed parallel robots by considering inter-chain coupling[J].Journal of Tianjin University:Science and Technology,2017,50(8):868-876(in Chinese).
[3]刘海涛,熊坤,贾昕胤,等.3自由度冗余驱动下肢康复并联机构的运动学优化设计[J].天津大学学报:自然科学与工程技术版,2018,51(4):357-366.Liu Haitao,Xiong Kun,Jia Xinyin,et al.Kinematic optimization of a redundantly actuated 3-DOFparallel mechanism for lower-limb rehabilitation[J].Journal of Tianjin University:Science and Technology,2018,51(4):357-366(in Chinese).
[4]Bi Z M,Jin Yan.Kinematic modeling of Exechon parallel kinematic machine[J].Robotics and Computer Integrated Manufacturing,2011,27(1):186-193.
[5]张俊,赵艳芹.Exechon并联模块的静刚度建模与分析[J].机械工程学报,2016,52(19):34-41.Zhang Jun,Zhao Yanqin.Stiffness modeling and evaluation for Exechon parallel kinematic machine module[J].Journal of Mechanical Engineering,2016,52(19):34-41(in Chinese).
[6]Jin Yan,Mctoal P,Higgins C,et al.Parallel kinematic assisted automated aircraft assembly[J].International Journal of Robotics and Mechatronics,2014,1(3):89-95.
[7]Tang Tengfei,Zhao Yanqin,Zhang Jun,et al.Conceptual Design and Workspace Analysis of an ExechonInspired Parallel Kinematic Machine[M]//Advances in Reconfigurable Mechanisms and Robots II.Cham,Switzerland:Springer Publishing Company,2016:445-453.
[8]Jin Yan,Bi Z M,Liu Haitao,et al.Kinematic analysis and dimensional synthesis of exechon parallel kinematic machine for large volume machining[J].ASME Journal of Mechanisms and Robotics,2015,7(4):041004-01-041004-8.
[9]Jin Yan,Bi Z M,Higgins C,et al.Optimal design of a new parallel kinematic machine for large volume machining[M]//Advances in Reconfigurable Mechanisms and Robots I.London,UK:Springer Publishing Company,2012:343-354.
[10]Zlatanov D,Zoppi M,Molfino R.Constraint and singularity analysis of the Exechon tripod[C]//ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.USA:ASME,2012:679-688.
[11]柴馨雪,项济南,李秦川.2-UPR-RPU并联机构奇异分析[J].机械工程学报,2015,51(13):144-151.Chai Xinxue,Xiang Jinan,Li Qinchuan.Singularity analysis of a 2-UPR-RPU parallel mechanism[J].Journal of Mechanical Engineering,2015,51(13):144-151(in Chinese).
[12]Jin Yan,Lian Binbin,Price M,et al.QrPara:A new reconfigurable parallel manipulator with 5 axis capability[M]//Advances in Reconfigurable Mechanisms and RobotsⅡ.Cham,Switzerland:Springer Publishing Company,2016:247-258.
[13]Zhang Jun,Zhao Yanqin,Jin Y.Kinetostatic model based stiffness analysis of Exechon PKM[J].Robotics and Computer Integrated Manufacturing,2016,37:208-220.
[14]Bi Z M.Kinetostatic modeling of Exechon parallel kinematic machine for stiffness analysis[J].The International Journal of Advanced Manufacturing Technology,2014,71(1/2/3/4):325-335.
[15]Bonnemains T,Chanal H,Bouzgarrou B C,et al.Dynamic model of an overconstrained PKM with compliances:The Tripteor X7[J].Robotics and Computer Integrated Manufacturing,2013,29(1):180-191.
[16]Zhang Jun,Zhao Yanqin,Jin Yan.Elastodynamic modeling and analysis for an Exechon parallel kinematic machine[J].ASME Journal of Manufacturing Science and Engineering,2016,138(3):031011-1-031011-14.
[17]Bi Z M,Lang S Y T,Verner M,et al.Development of reconfigurable machines[J].The International Journal of Advanced Manufacturing Technology,2008,39(11/12):1227-1251.
[18]黄田,李曚,吴孟丽,等.可重构PKM模块的选型原则--理论与实践[J].机械工程学报,2005,41(8):36-41.Huang Tian,Li Meng,Wu Mengli,et al.Criteria for conceptual design of reconfigurable PKM modulestheory and application[J].Journal of Mechanical Engineering,2005,41(8):36-41(in Chinese).
[19]Song Chaoyang,Feng Huijuan,Chen Yan,et al.Reconfigurable mechanism generated from the network of Bennett linkages[J].Mechanism and Machine Theory,2015,88:49-62.
[20]Zhang Ketao,Dai Jian S,Fang Yuefa.Geometric constraint and mobility variation of two 3SvPSv metamorphic parallel mechanisms[J].ASME Journal of Mechanical Design,2013,135(1):011001-1-011001-8.
[21]Gan Dongming,Dai Jian S,Dias J,et al.Unified kinematics and singularity analysis of a metamorphic parallel mechanism with bifurcated motion[J].ASME Journal of Mechanisms and Robotics,2013,5(3):031004-1-031004-11.
[22]Gan Dongming,Dias J,Seneviratne L.Unified kinematics and optimal design of a 3rRPS metamorphic parallel mechanism with a reconfigurable revolute joint[J].Mechanism and Machine Theory,2016,96:239-254.
[23]Gan Dongming,Dai Jian S,Dias J,et al.Variable motion/force transmissibility of a metamorphic parallel mechanism with reconfigurable 3T and 3R motion[J].ASME Journal of Mechanisms and Robotics,2016,8(5):051001-1-051001-9.
[24]Kong Xianwen,Jin Yan.Type synthesis of 3-DOF multimode translational/spherical parallel mechanisms with lockable joints[J].Mechanism and Machine Theory,2016,96:323-333.
[25]Palpacelli M C,Carbonari L,Palmieri G,et al.Analysis and design of a reconfigurable 3-DoF parallel manipulator for multimodal tasks[J].IEEE/ASME Transactions on Mechatronics,2015,20(4):1975-1985.
[26]Carbonari L,Callegari M,Palmieri G,et al.A new class of reconfigurable parallel kinematic machines[J].Mechanism and Machine Theory,2014,79:173-183.
[27]Kong Xianwen,Huang Chintien.Type synthesis of single-DOF single-loop mechanisms with two operation modes[C]//International Conference on Reconfigurable Mechanisms and Robots.London,UK,2009:136-141.
[28]叶伟,方跃法,郭盛,等.基于运动限定机构的可重构并联机构设计[J].机械工程学报,2015,51(13):137-143.Ye Wei,Fang Yuefa,Guo Sheng,et al.Design of reconfigurable parallel mechanisms with discontinuously movable mechanism[J].Journal of Mechanical Engineering,2015,51(13):137-143(in Chinese).
[29]Tang Tengfei,Zhang Jun.Conceptual design and comparative stiffness analysis of an Exechon-like parallel kinematic machine with lockable spherical joints[J].International Journal of Advanced Robotic Systems,2017,14(4):1-13.
[30]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,2006.Huang Zhen,Zhao Yongsheng,Zhao Tieshi.Advanced spatial Mechanism[M].Beijing:Higher Education Press,2006(in Chinese).
[2]赵庆,王攀峰,黄田.考虑链间耦合的高速并联机器人惯性参数预估方法[J].天津大学学报:自然科学与工程技术版,2017,50(8):868-876.Zhao Qing,Wang Panfeng,Huang Tian.An inertial parameter estimation method for high-speed parallel robots by considering inter-chain coupling[J].Journal of Tianjin University:Science and Technology,2017,50(8):868-876(in Chinese).
[3]刘海涛,熊坤,贾昕胤,等.3自由度冗余驱动下肢康复并联机构的运动学优化设计[J].天津大学学报:自然科学与工程技术版,2018,51(4):357-366.Liu Haitao,Xiong Kun,Jia Xinyin,et al.Kinematic optimization of a redundantly actuated 3-DOFparallel mechanism for lower-limb rehabilitation[J].Journal of Tianjin University:Science and Technology,2018,51(4):357-366(in Chinese).
[4]Bi Z M,Jin Yan.Kinematic modeling of Exechon parallel kinematic machine[J].Robotics and Computer Integrated Manufacturing,2011,27(1):186-193.
[5]张俊,赵艳芹.Exechon并联模块的静刚度建模与分析[J].机械工程学报,2016,52(19):34-41.Zhang Jun,Zhao Yanqin.Stiffness modeling and evaluation for Exechon parallel kinematic machine module[J].Journal of Mechanical Engineering,2016,52(19):34-41(in Chinese).
[6]Jin Yan,Mctoal P,Higgins C,et al.Parallel kinematic assisted automated aircraft assembly[J].International Journal of Robotics and Mechatronics,2014,1(3):89-95.
[7]Tang Tengfei,Zhao Yanqin,Zhang Jun,et al.Conceptual Design and Workspace Analysis of an ExechonInspired Parallel Kinematic Machine[M]//Advances in Reconfigurable Mechanisms and Robots II.Cham,Switzerland:Springer Publishing Company,2016:445-453.
[8]Jin Yan,Bi Z M,Liu Haitao,et al.Kinematic analysis and dimensional synthesis of exechon parallel kinematic machine for large volume machining[J].ASME Journal of Mechanisms and Robotics,2015,7(4):041004-01-041004-8.
[9]Jin Yan,Bi Z M,Higgins C,et al.Optimal design of a new parallel kinematic machine for large volume machining[M]//Advances in Reconfigurable Mechanisms and Robots I.London,UK:Springer Publishing Company,2012:343-354.
[10]Zlatanov D,Zoppi M,Molfino R.Constraint and singularity analysis of the Exechon tripod[C]//ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.USA:ASME,2012:679-688.
[11]柴馨雪,项济南,李秦川.2-UPR-RPU并联机构奇异分析[J].机械工程学报,2015,51(13):144-151.Chai Xinxue,Xiang Jinan,Li Qinchuan.Singularity analysis of a 2-UPR-RPU parallel mechanism[J].Journal of Mechanical Engineering,2015,51(13):144-151(in Chinese).
[12]Jin Yan,Lian Binbin,Price M,et al.QrPara:A new reconfigurable parallel manipulator with 5 axis capability[M]//Advances in Reconfigurable Mechanisms and RobotsⅡ.Cham,Switzerland:Springer Publishing Company,2016:247-258.
[13]Zhang Jun,Zhao Yanqin,Jin Y.Kinetostatic model based stiffness analysis of Exechon PKM[J].Robotics and Computer Integrated Manufacturing,2016,37:208-220.
[14]Bi Z M.Kinetostatic modeling of Exechon parallel kinematic machine for stiffness analysis[J].The International Journal of Advanced Manufacturing Technology,2014,71(1/2/3/4):325-335.
[15]Bonnemains T,Chanal H,Bouzgarrou B C,et al.Dynamic model of an overconstrained PKM with compliances:The Tripteor X7[J].Robotics and Computer Integrated Manufacturing,2013,29(1):180-191.
[16]Zhang Jun,Zhao Yanqin,Jin Yan.Elastodynamic modeling and analysis for an Exechon parallel kinematic machine[J].ASME Journal of Manufacturing Science and Engineering,2016,138(3):031011-1-031011-14.
[17]Bi Z M,Lang S Y T,Verner M,et al.Development of reconfigurable machines[J].The International Journal of Advanced Manufacturing Technology,2008,39(11/12):1227-1251.
[18]黄田,李曚,吴孟丽,等.可重构PKM模块的选型原则--理论与实践[J].机械工程学报,2005,41(8):36-41.Huang Tian,Li Meng,Wu Mengli,et al.Criteria for conceptual design of reconfigurable PKM modulestheory and application[J].Journal of Mechanical Engineering,2005,41(8):36-41(in Chinese).
[19]Song Chaoyang,Feng Huijuan,Chen Yan,et al.Reconfigurable mechanism generated from the network of Bennett linkages[J].Mechanism and Machine Theory,2015,88:49-62.
[20]Zhang Ketao,Dai Jian S,Fang Yuefa.Geometric constraint and mobility variation of two 3SvPSv metamorphic parallel mechanisms[J].ASME Journal of Mechanical Design,2013,135(1):011001-1-011001-8.
[21]Gan Dongming,Dai Jian S,Dias J,et al.Unified kinematics and singularity analysis of a metamorphic parallel mechanism with bifurcated motion[J].ASME Journal of Mechanisms and Robotics,2013,5(3):031004-1-031004-11.
[22]Gan Dongming,Dias J,Seneviratne L.Unified kinematics and optimal design of a 3rRPS metamorphic parallel mechanism with a reconfigurable revolute joint[J].Mechanism and Machine Theory,2016,96:239-254.
[23]Gan Dongming,Dai Jian S,Dias J,et al.Variable motion/force transmissibility of a metamorphic parallel mechanism with reconfigurable 3T and 3R motion[J].ASME Journal of Mechanisms and Robotics,2016,8(5):051001-1-051001-9.
[24]Kong Xianwen,Jin Yan.Type synthesis of 3-DOF multimode translational/spherical parallel mechanisms with lockable joints[J].Mechanism and Machine Theory,2016,96:323-333.
[25]Palpacelli M C,Carbonari L,Palmieri G,et al.Analysis and design of a reconfigurable 3-DoF parallel manipulator for multimodal tasks[J].IEEE/ASME Transactions on Mechatronics,2015,20(4):1975-1985.
[26]Carbonari L,Callegari M,Palmieri G,et al.A new class of reconfigurable parallel kinematic machines[J].Mechanism and Machine Theory,2014,79:173-183.
[27]Kong Xianwen,Huang Chintien.Type synthesis of single-DOF single-loop mechanisms with two operation modes[C]//International Conference on Reconfigurable Mechanisms and Robots.London,UK,2009:136-141.
[28]叶伟,方跃法,郭盛,等.基于运动限定机构的可重构并联机构设计[J].机械工程学报,2015,51(13):137-143.Ye Wei,Fang Yuefa,Guo Sheng,et al.Design of reconfigurable parallel mechanisms with discontinuously movable mechanism[J].Journal of Mechanical Engineering,2015,51(13):137-143(in Chinese).
[29]Tang Tengfei,Zhang Jun.Conceptual design and comparative stiffness analysis of an Exechon-like parallel kinematic machine with lockable spherical joints[J].International Journal of Advanced Robotic Systems,2017,14(4):1-13.
[30]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,2006.Huang Zhen,Zhao Yongsheng,Zhao Tieshi.Advanced spatial Mechanism[M].Beijing:Higher Education Press,2006(in Chinese).
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