Advertisement

Generalized Mobility and Decoupling Conditions of Closed-Loop Mechanism

  • Fan ZhangEmail author
  • Guohua Cui
  • Dan Zhang
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

This paper purposes a new kinematic analysis approach of closed-loop mechanisms based on the linear dependence of twists. First, the generalized velocity equation of closed-loop mechanisms is established by means of the exponential product form of rigid body motion. Second, the condition of the decoupling of closed-loop mechanism is obtained. Third, a simple analysis approach for decoupling analysis of the mechanism is proposed. Next, the approach is proven by the analysis of the decoupling mechanism and partial decoupling mechanisms and the synthesis of a decoupling spherical mechanism. The examples indicate that the actuation wrench is related with the linear dependence of the kinematic joints of the close-loop mechanism. This broadens the traditional knowledge about the actuation wrenches based on the reciprocal screw theory.

Keywords

Closed-loop mechanism Decoupling Motion Linear dependence Mobility analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The research work is supported by the Science and Technology Commission of Shanghai Municipality under Grant No. 17441901200.

References

  1. [1].
    Gosselin, C. M., Jean, M. J. R., and Systems, A.: Determination of the workspace of planar parallel manipulators with joint limits, 17(3), 129-138 (1996).Google Scholar
  2. [2].
    Huo, X., Sun, T., and Song, Y.: A geometric algebra approach to determine motion/constraint, mobility and singularity of parallel mechanism, Mechanism & Machine Theory, 116, 273-293 (2017).Google Scholar
  3. [3].
    Xu, Y., Zhang, D., Yao, J., Zhao, Y. J. M., and Theory, M.: Type synthesis of the 2R1T parallel mechanism with two continuous rotational axes and study on the principle of its motion decoupling, 108, 27-40 (2017).Google Scholar
  4. [4].
    Joshi, S. A., and Tsai, L.-W., Jacobian analysis of limited-DOF parallel manipulators, in ASME 2002 International design engineering technical conferences and computers and information in engineering conference, 2002, pp. 341-348: American Society of Mechanical Engineers.Google Scholar
  5. [5].
    Jin, X., Fang, Y., Qu, H., and Guo, S.: A class of novel 2T2R and 3T2R parallel mechanisms with large decoupled output rotational angles, Mechanism & Machine Theory, 114, 156-169 (2017).Google Scholar
  6. [6].
    Kong, X., and Gosselin, C. M., Type Synthesis of Linear Translational Parallel Manipulators, Springer Netherlands, (2002).Google Scholar
  7. [7].
    Gosselin, C. M., Kong, X., Foucault, S., and Bonev, I. A.: A fully-decoupled 3-dof translational parallel mechanism, In 2002 Parallel Kinematic Machines International Conference, (Chemnitz, Germany, Apr. 20-21, 2004), , 595-610 (2004).Google Scholar
  8. [8].
    Zeng, D., Wang, H., Fan, M., Wang, J., and HOU, Y.: Type Synthesis of Three Degrees of Freedom Rotational Generalized Decoupling Parallel Mechanism, Advances in Mechanical Engineering, 3, p. 003 (2017).Google Scholar
  9. [9].
    Gogu, G., Fully-isotropic Three-degree-of-freedom Parallel Wrists, in IEEE International Conference on Robotics and Automation, 2007, pp. 895-900.Google Scholar
  10. [10].
    Zhang, F., and Dan, Z.: Structural Synthesis of Decoupled Spherical Parallel Mechanism Based on Driven-chain Principle, Transactions of the Chinese Society for Agricultural Machinery 42(11), 195-199 (2011).Google Scholar
  11. [11].
    Zhang Yanbin, J. X., Han Jianhai, GUO Bingjing, ZHAO Yifu. : Type Synthesis of Uncoupled Rotational Parallel Mechanisms with Two Degrees of Freedom, Journal of Mechanical Engineering, 54(15), 21-30 (2018).CrossRefGoogle Scholar
  12. [12].
    Murray, R. M., A mathematical introduction to robotic manipulation, CRC press, (2017).Google Scholar
  13. [13].
    Leon, S. J., Linear algebra with applications, Collier Macmillam Publishers, (1986).Google Scholar
  14. [14].
    Merlet, J. P.: Singular configurations of parallel manipulators and grassmann geometry, International Journal of Robotics Research, 8(5), 194-212 (1989).Google Scholar
  15. [15].
    Gosselin Clement, M. e. a.: Two degree-of-freedom spherical orienting device, (1999).Google Scholar
  16. [16].
    Zhang, F., Zhang, D., and Yang, J.: Kinematics Analysis of RRR-UPRR-RPUR Spherical Parallel Manipulator, Transactions of the Chinese Society for Agricultural Machinery, 42(9), 202-202 (2011).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Intelligent Robot Research CenterShanghai University of Engineering ScienceShanghaiChina
  2. 2.Kaneff Department in Advanced Robotics and MechatronicsYork UniversityTorontoTaiwan

Personalised recommendations