一种仿人肩关节的运动学和工作空间分析
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摘要
针对人体肩关节的结构特点,提出了一种以球面5R并联机构为原型的仿人肩关节。通过Paden-Kahan子问题思路,推导出了该并联机构的位置反解。基于螺旋理论和指数积公式,并结合直接法和虚拟机构法,给出了少自由度非对称型并联机构的运动学分析方法,得到了该并联机构的速度雅可比矩阵。应用多参数的迭代抽样优化方法,分析了工作空间评价指标与结构参数之间的关系,同时考虑加工装配工艺,最终选取了一组较合理的结构参数。研究结果表明:所提仿人肩关节结构紧凑、工作空间大,且符合人体肩关节活动特点。
A humanoid shoulder joint based on spherical 5 R parallel mechanism is proposed according to the structural characteristics of human shoulder joint. The inverse position solution of parallel mechanism is derived through the idea of the Paden-Kahan sub-problem. A kinematics analysis method of the asymmetric parallel mechanism with few degrees of freedom is given based on the screw theory and the product of exponentials formula in combination with the direct method and the imaginary mechanism method,and the velocity jacobian matrix of parallel mechanism is obtained. The iterative sampling optimization method for multi-parameter is used to analyze the relationship between the evaluation index of working space and the structural parameter of the mechanism. A reasonable set of structural parameters is selected in considering the processing assembly process. The research results show that the humanoid shoulder joint is compact,and has a large working space and conforms to the kinematical characteristics of human shoulder joint.
A humanoid shoulder joint based on spherical 5 R parallel mechanism is proposed according to the structural characteristics of human shoulder joint. The inverse position solution of parallel mechanism is derived through the idea of the Paden-Kahan sub-problem. A kinematics analysis method of the asymmetric parallel mechanism with few degrees of freedom is given based on the screw theory and the product of exponentials formula in combination with the direct method and the imaginary mechanism method,and the velocity jacobian matrix of parallel mechanism is obtained. The iterative sampling optimization method for multi-parameter is used to analyze the relationship between the evaluation index of working space and the structural parameter of the mechanism. A reasonable set of structural parameters is selected in considering the processing assembly process. The research results show that the humanoid shoulder joint is compact,and has a large working space and conforms to the kinematical characteristics of human shoulder joint.
引文
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[2] SHYAM R B A,ACHARYA M,GHOSAL A. A heliostat basedon a three degree-of-freedom parallel manipulator[J]. Solar Ener-gy,2017,157:672-686.
[3] CERVANTES-SNCHEZ J J,RICO-MARTNEZ J M,OROZCO-MUˇNIZ J D. A natural extension of the 4R linkage to the 3-RRRspherical parallel manipulator[J]. Journal of the Brazilian Societyof Mechanical Sciences&Engineering,2015,18(7):1-13.
[4]杨龙,褚宏鹏,孙通帅,等. 3-RRR+(S-P)人形机器人仿生肩关节主参数设计及其工作空间分析[J].中国机械工程,2017,28(2):199-205.YANG L,CHU H P,SUN T S,et al. Main parameter design andworkspace analysis of a novel 3-RRR+(S-P)humanoid roboticbionic shoulder[J]. China Mechanical Engineering, 2017,28(2):199-205.(in Chinese)
[5]王跃灵,金振林,李研彪.球面3-RRR并联机构动力学建模与鲁棒-自适应迭代学习控制[J].机械工程学报,2010,46(1):68-73.WANG Y L,JIN Z L,LI Y B. Dynamic modeling and robust-adaptive iterative learning control of 3-RRR spherical parallelmechanism[J]. Journal of Mechanical Engineering,2010,46(1):68-73.(in Chinese)
[6]张亮.仿人机器人肩肘腕关节及臂的设计[D].秦皇岛:燕山大学,2016:9-44.ZHANG L. Design for shoulder elbow wrist joint and arm of hu-manoid robot[D]. Qinhuangdao:Yanshan University,2016:9-44.(in Chinese)
[7]侯雨雷,汪毅,范建凯,等. 3-PCSS/S球面并联肩关节机构优化与仿生设计[J].机械工程学报,2015,51(11):16-23.HOU Y L,WANG Y,FAN J K,et al. Optimization and bionicdesign of 3-PCSS/S spherical parallel mechanism for the shoulderjoint[J]. Journal of Mechanical Engineering,2015,51(11):16-23.(in Chinese)
[8] SAKAGAMI Y,WATANABE R,AOYAMA C,et al. The inltelli-gent ASIMO:system overview and integration[C]∥Proceedings ofInternational Conference on Intelligent Robots and Systems. Lau-sanne,Switzerland:IEEE,2002:2478-2483.
[9]张文增.拟人机器人的上肢的研制[D].北京:清华大学,2004:11-49.ZHANG W Z. Development of arm motion of humanoid robot[D].Beijing:Tsinghua University,2004:11-49.(in Chinese)
[10] AN H S,JIE H L,CHAN L,et al. Geometrical kinematic solu-tion of serial spatial manipulators using screw theory[J]. Mecha-nism&Machine Theory,2017,116:404-418.
[11] DENAVIT J,HARTENBERG R S. A kinematic notation for low-er-pair mechanisms based on matrices[J]. Applied Mechanics,1955,22:215-221.
[12] HE R B,ZHAO Y J,YANG S N,et al. Kinematic-parameteridentification for serial-robot calibration based on POE formula[J]. IEEE Transactions on Robotics,2010,26(3):411-423.
[13]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,2006:10-276.HUANG Z,ZHAO Y S,ZHAO T S. Advanced space mechanics[M]. Beijing:China Higher Education Press,2006:10-276.(in Chinese)
[14]艾青林,祖顺江,胥芳.并联机构运动学与奇异性研究进展[J].浙江大学学报(工学版),2012,46(8):1345-1359.AI Q L,ZU S J,XU F. Review of kinematics and singularity ofparallel manipulator[J]. Journal of Zhejiang University(Engi-neering Science). 2012,46(8):1345-1359.(in Chinese)
[15] GOUTTEFARDE M,GOSSELIN C M. Analysis of the wrench-closure workspace of planar parallel cable-driven mechanisms[J]. IEEE Transactions on Robotics,2006,22(3):434-445.
[16]冯海兵.并联宏/微驱动操作手工作的空间分析[J].光学精密工程,2013,21(3):717-723.FENG H B. Workspace of macro/micro actuated parallel mecha-nism[J]. Optics and Precision Engineering,2013,21(3):717-723.(in Chinese)
[17]李浩,张玉茹,王党校. 6-RSS并联机构工作空间优化算法对比分析[J].机械工程学报,2010,46(13):61-67.LI H,ZHANG Y R,WANG D X. Comparative analysis of opti-mization algorithms in workspace optimization of parallel mecha-nisms[J]. Journal of Mechanical Engineering,2010,46(13):61-67.(in Chinese)
[18] YUE Y,GAO F,ZHAO X C,et al. Relationship among input-force,payload,stiffness,and displacement of a 6-DOF perpen-dicular parallel micromanipulator[J]. Journal of Mechanisms&Robotics,2010,45(5):756-771.
[19]李研彪,刘毅,赵章风,等.基于空间模型技术的拟人机械腿的运动学传递性能分析[J].农业工程学报,2013,29(2):17-23.LI Y B,LIU Y,ZHAO Z F,et al. Kinematics transmission ana-lysis on anthropopathic mechanical leg based on spatial modeltechnique[J]. Transactions of the Chinese Society of AgriculturalEngineering,2013,29(2):17-23.(in Chinese)
[20] BOUDREAU R,GOSSELIN C M. The synthesis of planar paral-lel manipulators with a genetic algorithm[J]. Journal of Mecha-nical Design,1999,121(4):533-537.
[21]黄真,曾达幸.机构自由度计算:原理和方法[M].北京:高等教育出版社,2016:10-200.HUANG Z,ZENG D X. Mechanism degree of freedom:princi-ple and method[M]. Beijing:China Higher Education Press,2016:10-200.(in Chinese)
[22]牟德君,张一同,张兴.机构自由度和构件自由度的关系及本质区别[J].机械工程学报,2018,54(5):74-83.MOU D J,ZHANG Y T,ZHANG X. Relations between DOF ofmechanism and DOF of links and their essential differences[J].Journal of Mechanical Engineering,2018,54(5):74-83.(inChinese)
[23] MURRAY R M,SASTRY S S,LI Z X. A mathematical introduc-tion to robotic manipulation[M]. FL,US:CRC Press,1994:11-101.
[24]季晔,刘宏昭,原大宁. 4-SPS/PPU型并联机构工作空间与尺度分析[J].农业机械学报,2013,44(11):322-328.JI Y,LIU H Z,YUAN D N. Workspace and scale analysis of 4-SPS/PPU parallel mechanism[J]. Transactions of the ChineseSociety for Agricultural Machinery,2013,44(11):322-328.(in Chinese)
[25] ARAKELIAN V,BRIOT S,GLAZUNOV V. Increase of singu-larity-free zones in the workspace of parallel manipulators usingmechanisms of variable structure[J]. Mechanism&MachineTheory,2008,43(9):1129-1140.