Kinematic and Stiffness Analysis of Lower-mobility Parallel Mechanisms Based on QR Decomposition

  • WANG Chang ,
  • ZHAO Tieshi ,
  • ZHAO Yanzhi ,
  • GENG Mingchao ,
  • LI Erwei
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  • 1. Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System, Yanshan University, Qinhuangdao 066004;
    2. Key Laboratory of Advanced Forging & Stamping Technology and Science (Yanshan University), Ministry of Education of China, Qinhuangdao 066004

Received date: 2014-12-20

  Revised date: 2015-08-10

  Online published: 2015-12-05

Abstract

A method to build the kinematic of lower-mobility parallel mechanism is mentioned based on the matrix QR decomposition. The forward and inverse kinematic model is built based on the first and second order influence matrix. The velocity and acceleration constraint matrix are also built. Based on the principle of virtual work, the flexibility matrix and directional stiffness are built. The coupling kinematic of the 3RPS mechanism is analyzed. The directional stiffness of 3RPS is analyzed to verify the structural constraint, and the directional stiffness is visually describes by the distribution of spherical coordinates.

Cite this article

WANG Chang , ZHAO Tieshi , ZHAO Yanzhi , GENG Mingchao , LI Erwei . Kinematic and Stiffness Analysis of Lower-mobility Parallel Mechanisms Based on QR Decomposition[J]. Journal of Mechanical Engineering, 2015 , 51(23) : 28 -35 . DOI: 10.3901/JME.2015.23.028

References

[1] CLAVEL R. Delta a fast robot with parallel geometry [C]// Proceedings of International Symposium on Industrial Robot,Apr. 26-28,1988,Lausanne. Switzerland:ISIR,1988:91-100.
 [2] 路懿,胡波. 少自由度并联机构研究进展[J]. 燕山大学学报,2011,35(5):377-384.LU Yi,HU Bo. Development evaluation of limited-DOF parallel manipulators[J]. Journal of Yanshan University,2011,35(5):377-384.
 [3] KIM S G,RYU J. New dimensionally homogeneous Jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators[J]. IEEE Transactions on Robotics and Automation,2003,19(4):731-736.
 [4] KONG X W,JAIME G A,RICO J M,et al. Kinematics and singularity analyses of a 4-dof parallel manipulator using screw theory[J]. Mechanism and Machine Theory,2006,41(9):1048-1061
 [5] HUANG Zhen,FANG Yuefa. Kinematic characteristics analysis of 3-DOF in-parallel actuated pyramid mechanisms[J]. Mechanism and Machine Theory,1996,31(8):1009-1018.
 [6] 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.
 [7] HUANG Z,ZHU S J. Kinematic analyses of 5-DOF 3-RCRR parallel mechanism[C]// ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers,2005:993-999.
 [8] JOSHI S,TSAI L W. Jacobian analysis of limited-DOF parallel manipulators[J]. ASME Journal of Mechanical Design,2002,124(2):254-258.
 [9] 胡波,路懿. 基于几何约束的两种少自由度机构雅可比矩阵的求解方法[C]// 中国机构与机器科学国际会议暨海峡两岸第四届机构学研讨会论文集,2008:204-206.HU Bo,LU Yi. Solving two forms of Jacobian matrix for lower mobility parallel manipulators based on geometrical constraint[C]// Proceedings of CCMMS,2008:204-206.
[10] RICO J M,GALLARDO J,DUFFY J. Screw theory and higher order analysis of open serial and closed chains[J]. Mechanism and Machine Theory,1999,34(4):559-586.
[11] RICO J M,DUFFY J. Forward and inverse acceleration analyses of in-parallel manipulators[J]. ASME Journal of Mechanical Design,2000,122(3):299-303.
[12] 李永刚,宋轶民,冯志友,等. 4 自由度非全对称并联机构的完整雅可比矩阵[J]. 机械工程学报,2007,43(6):37-40.LI Yonggang,SONG Yimin,FENG Zhiyou,et al. Complete Jacobian matrix of a class of incompletely symmetrical parallel mechanisms with 4-DOF[J]. Chinese Journal of Mechanical Engineering,2007,43(6):37-40.
[13] GOSSELIN C M. Stiffness mapping for parallel manipulators[J]. IEEE Translations on Robotics and Automation,1990,6(3):377-382.
[14] JOSHI S,TSAI L W. A comparison study of two 3-DOF parallel manipulators:One with three and the other with four supporting legs[J]. IEEE Transactions on Robotics and Automation,2003,19(2):200-209.
[15] DAI Jianshen,ZHAO Tieshi. Stiffness characteristics and kinematics analysis of two-link elastic underactuated manipulators[J]. Journal of Robotic Systems,2002,19(4):169-176.
[16] 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. Countinous stiffness nonlinear mapping of spatial parallel mechanism[J]. Chinese Journal of Mechanical Engineering,2008,44(8):20-25
[17] ZHAO T S,ZHAO Y Z,SHI L,et al. Stiffness characteristics and kinematics analysis of parallel 3-DOF mechanism with flexible joints[C]// Proceedings of Mechatronics and Automation,2007. IEEE,2007:1822-1827.
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