线矢力各向同性分析与其在机构构型综合中的应用
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摘要
鉴于线矢力与机构的承载能力密切相关,对线矢力的各向同性条件进行了研究,得到了线矢力满足各向同性的一般条件,提出了一种事先考虑驱动副布置的冗余驱动移动三自由度并联机构构型综合方法。该方法首先综合与支链约束力螺旋和驱动力螺旋均互易的运动链;然后再构造与支链约束力螺旋互易而与驱动力螺旋不互易的驱动副,从而得到了数种典型的满足驱动线矢力各向同性的冗余驱动三自由度移动并联机构构型;最后,对其中的一种典型机构4-PRRR进行了分析,结果表明,该机构在运动过程中始终满足承载能力各向同性,验证了前述线矢力各向同性分析与构型综合理论的正确性。
The carrying capacity of a mechanism is closely related to its line vector force. A thorough isotropic analysis of line vector forces was presented. The results showed that the isotropic condition can be satisfied when the line vector forces were evenly distributed on a conical surface with a cone-top angle of 109. 472°. In addition,since few three degrees-of-freedom( DOFs) translational redundantly actuated parallel manipulators were reported,by combining the isotropic line vector forces,a method for the type synthesis of 3-DOF,redundantly actuated translational parallel mechanisms( PMs) was proposed,in which the arrangement of the active joints was taken into account in advance. Using this method,firstly a kinematic chain with a twist system reciprocal to both the constraint and actuation wrenches was constructed,and then the active joint reciprocal to the constraint wrenches but not to the actuation wrench was constructed. Thus,a series of typical redundantly actuated PMs with isotropic actuation forces were obtained. Finally,the 4-PRRR PM was analyzed as an example,and the results showed that the isotropy of the load-carrying capacity can always be satisfied during its movement,because the condition of force Jacobian matrix was always equal to one,which to some extent verified the correctness of the isotropic analysis and the synthesis method proposed in this research. For this method,it not only satisfied the expected requirements,but also meant that the active joints no longer needed to be selected,and the rationality of the selection did not need to be considered,which provided a new method for the type synthesis of parallel manipulators.
The carrying capacity of a mechanism is closely related to its line vector force. A thorough isotropic analysis of line vector forces was presented. The results showed that the isotropic condition can be satisfied when the line vector forces were evenly distributed on a conical surface with a cone-top angle of 109. 472°. In addition,since few three degrees-of-freedom( DOFs) translational redundantly actuated parallel manipulators were reported,by combining the isotropic line vector forces,a method for the type synthesis of 3-DOF,redundantly actuated translational parallel mechanisms( PMs) was proposed,in which the arrangement of the active joints was taken into account in advance. Using this method,firstly a kinematic chain with a twist system reciprocal to both the constraint and actuation wrenches was constructed,and then the active joint reciprocal to the constraint wrenches but not to the actuation wrench was constructed. Thus,a series of typical redundantly actuated PMs with isotropic actuation forces were obtained. Finally,the 4-PRRR PM was analyzed as an example,and the results showed that the isotropy of the load-carrying capacity can always be satisfied during its movement,because the condition of force Jacobian matrix was always equal to one,which to some extent verified the correctness of the isotropic analysis and the synthesis method proposed in this research. For this method,it not only satisfied the expected requirements,but also meant that the active joints no longer needed to be selected,and the rationality of the selection did not need to be considered,which provided a new method for the type synthesis of parallel manipulators.
引文
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[3] ZHAO J S,ZHOU K,FENG Z J. A theory of degrees of freedom for mechanisms[J]. Mechanism and Machine Theory,2004,39(6):621-643.
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[7] HUANG Z,CHEN L H,LI Y W. The singularity principle and property of Stewart parallel manipulator[J]. Journal of Robotic Systems,2003,20(4):163-176.
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[17] CARRICATO M,PARENTI-CASTELLI V. Singularity-free fully-isotropic translational parallel mechanisms[J]. International Journal of Robotics Research,2002,21(2):161-174.
[18] YU J J,DAI J S,BI S S,et al. Numeration and type synthesis of 3-DOF orthogonal translational parallel manipulators[J].Progress in Natural Science,2008,18(5):563-574.
[19] ZHAO Y J,GAO F. Dynamic performance comparison of the 8PSS redundant parallel manipulator and its non-redundant counterpart—the 6PSS parallel manipulator[J]. Mechanism and Machine Theory,2009,44(5):991-1008.
[20] NOKLEBY S B,FISHER R,PODHORODESKI R P,et al. Force capabilities of redundantly-actuated parallel manipulators[J]. Mechanism and Machine Theory,2005,40(5):578-599.
[21]刘晓飞,姚建涛,赵永生.基于模型的冗余驱动并联机构神经网络同步协调控制[J/OL].农业机械学报,2018,49(2):367-375. http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? file_no=20180248&flag=1. DOI:10.6041/j. issn. 1000-1298. 2018. 02. 048.LIU Xiaofei,YAO Jiantao,ZHAO Yongsheng. Model-based synchronous control of redundantly actuated parallel manipulator with neural network[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2018,49(2):367-375.(in Chinese)
[22] TOKIDA K. Estimating reliability for redundant agricultural machinery systems[J]. Ama Agricultural Mechanization in Asia Africa&Latin America,2010,41(1):72-76.
[23]孟庆宽,张漫,杨耿煌,等.自然光照下基于粒子群算法的农业机械导航路径识别[J/OL].农业机械学报,2016,47(6):11-20. http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? file_no=20160602&flag=1. DOI:10. 6041/j. issn. 1000-1298. 2016. 06. 002.MENG Qingkuan,ZHANG Man,YANG Genghuang,et al. Guidance line recognition of agricultural machinery based on particle swarm optimization under natural illumination[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2016,47(6):11-20.(in Chinese)
[24] HUANG Z,LI Q C. Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method[J]. International Journal of Robotics Research,2003,22(1):59-79.
[25]赵铁石,黄真.欠秩并联机器人输入选取的理论和应用[J].机械工程学报,2000,36(10):81-85.ZHAO Tieshi,HUANG Zhen. Theory and application of selecting actuating components of spatial parallel mechanisms[J].Chinese Journal of Mechanical Engineering,2000,36(10):81-85.(in Chinese)
[26]杨廷力.平面复链的结构特征及其运动分析和力分析的状态变量法[J].西安理工大学学报,1987,3(2):4-19.YANG Tingli. Structural character of planar mechanisms and the state variables method of kinematic and kinetostatic analysis[J]. Journal of Xi'an University of Technology,1987,3(2):4-19.(in Chinese)
[27] BARUH H. Analytical dynamics[M]. Boston:WCB/McGraw-Hill,1999.
[28] FIRMANI F,ZIBIL A,NOKLEBY S B,et al. Wrench capabilities of planar parallel manipulators. Part I:wrench polytopes and performance indices[J]. Robotica,2008,26(6):791-802.
[2] HUANG Z,LIU J F,ZENG D X. A general methodology for mobility analysis of mechanisms based on constraint screw theory[J]. Science in China Series E:Technological Sciences,2009,52(5):1337-1347.
[3] ZHAO J S,ZHOU K,FENG Z J. A theory of degrees of freedom for mechanisms[J]. Mechanism and Machine Theory,2004,39(6):621-643.
[4] FANG Y F,TSAI L W. Structure synthesis of a class of 4-DOF and 5-DOF parallel manipulators with identical limb structures[J]. International Journal of Robotics Research,2002,21(9):799-810.
[5] KONG X W,GOSSELIN C M. Type synthesis of 4-DOF SP-equivalent parallel manipulators:a virtual chain approach[J].Mechanism and Machine Theory,2006,41(11):1306-1319.
[6] GLAZUNOV V. Design of decoupled parallel manipulators by means of the theory of screws[J]. Mechanism and Machine Theory,2010,45(2):239-250.
[7] HUANG Z,CHEN L H,LI Y W. The singularity principle and property of Stewart parallel manipulator[J]. Journal of Robotic Systems,2003,20(4):163-176.
[8] MONSARRAT B,GOSSELIN C M. Singularity analysis of a three-leg six-degree-of-freedom parallel platform mechanism based on Grassmann line geometry[J]. The International Journal of Robotics Research,2001,20(4):312-328.
[9] WOLF A,SHOHAM M. Investigation of parallel manipulators using linear complex approximation[J]. Journal of Mechanical Design,2003,125(3):564-572.
[10] TSAK Y I,HUANG K D. The design of isotropic 6-DOF parallel manipulators using isotropy generators[J]. Mechanism and Machine Theory,2003,38(11):1199-1214.
[11] KIM H S. Design optimization of a Cartesian parallel manipulator[J]. Journal of Mechanical Design,2003,125(1):865-872.
[12] SALISBURY J K,CRAIG J J. Articulated hands:force control and kinematic issues[J]. International Journal of Robotics Research,1982,1(1):4-17.
[13] ZANGANEH K E,ANGELES J. Kinematic isotropy and the optimum design of parallel manipulators[J]. International Journal of Robotics Research,1997,16(2):185-197.
[14] BANDYOPADHYAY S,GHOSAL A. An algebraic formulation of kinematic isotropy and design[J]. Mechanism and Machine Theory,2008,43:591-616.
[15] YAO J T,HOU Y L,WANG H,et al. Spatially isotropic configuration of Stewart platform-based force sensor[J]. Mechanism and Machine Theory,2011,46(2):142-155.
[16] TSAI L W,JOSHI S. Kinematics and optimization of a spatial 3-UPU parallel manipulator[J]. ASME Journal of Mechanical Design,2000,122(4):439-446.
[17] CARRICATO M,PARENTI-CASTELLI V. Singularity-free fully-isotropic translational parallel mechanisms[J]. International Journal of Robotics Research,2002,21(2):161-174.
[18] YU J J,DAI J S,BI S S,et al. Numeration and type synthesis of 3-DOF orthogonal translational parallel manipulators[J].Progress in Natural Science,2008,18(5):563-574.
[19] ZHAO Y J,GAO F. Dynamic performance comparison of the 8PSS redundant parallel manipulator and its non-redundant counterpart—the 6PSS parallel manipulator[J]. Mechanism and Machine Theory,2009,44(5):991-1008.
[20] NOKLEBY S B,FISHER R,PODHORODESKI R P,et al. Force capabilities of redundantly-actuated parallel manipulators[J]. Mechanism and Machine Theory,2005,40(5):578-599.
[21]刘晓飞,姚建涛,赵永生.基于模型的冗余驱动并联机构神经网络同步协调控制[J/OL].农业机械学报,2018,49(2):367-375. http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? file_no=20180248&flag=1. DOI:10.6041/j. issn. 1000-1298. 2018. 02. 048.LIU Xiaofei,YAO Jiantao,ZHAO Yongsheng. Model-based synchronous control of redundantly actuated parallel manipulator with neural network[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2018,49(2):367-375.(in Chinese)
[22] TOKIDA K. Estimating reliability for redundant agricultural machinery systems[J]. Ama Agricultural Mechanization in Asia Africa&Latin America,2010,41(1):72-76.
[23]孟庆宽,张漫,杨耿煌,等.自然光照下基于粒子群算法的农业机械导航路径识别[J/OL].农业机械学报,2016,47(6):11-20. http:∥www. j-csam. org/jcsam/ch/reader/view_abstract. aspx? file_no=20160602&flag=1. DOI:10. 6041/j. issn. 1000-1298. 2016. 06. 002.MENG Qingkuan,ZHANG Man,YANG Genghuang,et al. Guidance line recognition of agricultural machinery based on particle swarm optimization under natural illumination[J/OL]. Transactions of the Chinese Society for Agricultural Machinery,2016,47(6):11-20.(in Chinese)
[24] HUANG Z,LI Q C. Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method[J]. International Journal of Robotics Research,2003,22(1):59-79.
[25]赵铁石,黄真.欠秩并联机器人输入选取的理论和应用[J].机械工程学报,2000,36(10):81-85.ZHAO Tieshi,HUANG Zhen. Theory and application of selecting actuating components of spatial parallel mechanisms[J].Chinese Journal of Mechanical Engineering,2000,36(10):81-85.(in Chinese)
[26]杨廷力.平面复链的结构特征及其运动分析和力分析的状态变量法[J].西安理工大学学报,1987,3(2):4-19.YANG Tingli. Structural character of planar mechanisms and the state variables method of kinematic and kinetostatic analysis[J]. Journal of Xi'an University of Technology,1987,3(2):4-19.(in Chinese)
[27] BARUH H. Analytical dynamics[M]. Boston:WCB/McGraw-Hill,1999.
[28] FIRMANI F,ZIBIL A,NOKLEBY S B,et al. Wrench capabilities of planar parallel manipulators. Part I:wrench polytopes and performance indices[J]. Robotica,2008,26(6):791-802.
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