Skip to main content
SpringerLink
Log in

Parasitic rotation evaluation and avoidance of 3-UPU parallel mechanism

  • Research Article
  • Published:
Frontiers of Mechanical Engineering Aims and scope Submit manuscript

Abstract

Based on the prototype of 3-UPU (universal-prismatic-universal joint) parallel mechanism proposed by Tsai [1], the parasitic rotation evaluation is performed and calculated the bound of instability of SNU (Seoul National University) 3-UPU parallel mechanism. Through analysis of the terminal constraint system of the 3-UPU parallel mechanism, the equation about the parasitic rotation and limited clearance is presented. Then the norm of possible parasitic rotation is employed to evaluate the mechanism stability with limited clearance. The higher this number the worst is the pose, the lower it is the best it is. And the contour atlas of parasitic rotation is obtained, which can be used for further analysis and design. With the practice experiment result of SUN 3-UPU parallel mechanism, we find it’s bound of instability, which indicates there will appear the parasitic rotation when the number exceeds the bound. Finally, the method for avoidance of possible parasitic motions is presented by adding redundantly actuated limbs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Tsai LW. Kinematics of a three-DOF platform with three extensible limbs. In: Recent Advances in Robot Kinematics, Lenarčič J and Parenti-Castelli V eds. Boston: Kulwer Academic Publishers, 1996, 401–410

    Chapter  Google Scholar 

  2. Gregorio R D, Parenti-Castelli V. Mobility analysis of the 3-UPU parallel mechanism assembled for a pure translational motion. Journal of Mechanical Design, 2002, 124(2): 259–264

    Article  Google Scholar 

  3. Hervé J M, Sparacino F. Structural synthesis of parallel robots generating spatial translation. In: Proceedings of the Fifth International Conference on Advanced Robotics, 1991, 808–813

  4. Hervé J M. New translational parallel manipulators with extensible parallelograms. In: Proceedings of the 11th World Congress in Mechanism and Machine Science. Tianjin, China, 2004, 1599–1603

  5. Tsai L W. Systematic enumeration of parallel manipulator. In: Proceedings of the 1st European-American Forum on Parallel Kinematic Machines. Milan, Italy, 1998, 1–11

  6. Carricato M, Parenti-Castelli V. A family of 3-DOF translational parallel manipulators. Journal of Mechanical Design, 2003, 125(2): 302–307

    Article  Google Scholar 

  7. Carricato M, Parenti-Castelli V. Singularity-free fully-isotropic translational parallel mechanisms. International Journal of Robotics Research, 2002, 21(2): 161–174

    Article  Google Scholar 

  8. Kong X W, Gosselin C. Type synthesis of 3-DOF translational parallel manipulators based on screw theory. Journal of Mechanical Design, 2004, 126(1): 83–92

    Article  Google Scholar 

  9. Gogu G. Structure Synthesis of Parallel Robots. New York: Springer, 2008

    Book  Google Scholar 

  10. Gogu G. Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations. European Journal of Mechanics, A, Solids, 2004, 23(6): 1021–1039

    Article  MATH  Google Scholar 

  11. Huang Z, Li Q. Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method. International Journal of Robotics Research, 2003, 22(1): 59–79

    Google Scholar 

  12. Jin Q, Yang T L. Theory for topology synthesis of parallel manipulators and its application to three-dimension-translation parallel manipulators. Journal of Mechanical Design, 2004, 126(4): 625–639

    Article  Google Scholar 

  13. Joshi S A, Tsai L W. Jacobian analysis of limited-DOF parallel manipulator. Journal of Mechanical Design, 2002, 124(2): 254–258

    Article  Google Scholar 

  14. Tsai L W, Joshi S A. Kinematics and optimization of a spatial 3-UPU parallel manipulator. Journal of Mechanical Design, 2000, 122(4): 439–446

    Article  Google Scholar 

  15. Joshi S A, Tsai L W. A comparison study of two 3-DOF parallel manipulators one with three and the other with four supporting legs. IEEE Transactions on Robotics and Automation, 2003, 19(2): 200–209

    Article  Google Scholar 

  16. Guan L W, Wang J S, Wang L P. Mobility analysis of the 3-UPU parallel mechanism based on screw theory. In: Proceedings of the 2004 International Conference on Intelligent Mechatronics and Automation. Chengdu, China, 2004, 309–314

  17. Han C, Kim J, Kim J, Park F C. Kinematic sensitivity analysis of the 3-UPU parallel mechanism. Mechanism and Machine Theory, 2002, 37(8): 787–798

    Article  MATH  Google Scholar 

  18. Zlatanov D, Bonev I. Constraint singularity of parallel mechanism. In: Proceedings of the IEEE International Conference on Robotics and Automation. Washington DC, USA, 2002, 496–502

  19. Bonev I, Zlatanov D. The mystery of the singular SNU translational parallel robot. http://www.parallemic.org/Reviews/Review004.html

  20. Zlatanov D, Bonev I, Gosselin C. Constraint singularities as configuration space singularities. In: Advances in Robot Kinematics: Theory and Applications, Lenarčič J and Thomas F eds. Boston: Kluwer Academic Publishers, 2002, 183–192

    Google Scholar 

  21. Wolf A, Shoham M. Investigation of parallel manipulators using linear complex approximation. Journal of Mechanical Design, 2003, 125(3): 564–572

    Article  Google Scholar 

  22. Wolf A, Shoham M. Investigation of singularities and self-motions of the 3-UPU robot. In: Advances in Robot Kinematics: Theory and Applications, Lenarčič J and Thomas F eds. Boston: Kluwer Academic Publishers, 2002, 165–174

    Google Scholar 

  23. Conconi M, Carricato M. A new assessment of singularities of parallel kinematic chains. IEEE Transactions on Robotics and Automation, 2009, 25(4): 757–770

    Google Scholar 

  24. Gogu G. Constraint singularities and the structural parameters of parallel robots. In: Advances in Robot Kinematics: Analysis and Design, Lenarčič J and Wenger P eds. New York: Springer, 2008, 3–12

    Google Scholar 

  25. Chebbi A H, Parenti-Castelli V. Geometric and manufacturing issues of the 3-UPU pure translational manipulator. In: New Trends in Mechanism Science: Analysis and Design, Mechanisms and Machine Science 5. 2010, 595–603

    Google Scholar 

  26. Chebbi A H, Affi Z, Romdhane L. Kinetostatic and singularity analyses of the 3-UPU translational parallel robot. In: Computational Kinematics: Proceedings of the 5th International Workshop on Computational Kinematics. New York: Springer, 2009, 61–68

    Google Scholar 

  27. Merlet J P. Parallel Robot. New York: Springer, 2006

    Google Scholar 

  28. Tsai L W. Robot Analysis: The Mechanics of Serial and Parallel Manipulators. New York: Wiley, 1999

    Google Scholar 

  29. Fang Y F, Tsai L W. Structure synthesis of a class of 4-DoF and 5-DoF parallel manipulators with identical limb structures. International Journal of Robotics Research, 2002, 21(9): 799–810

    Article  Google Scholar 

  30. Kong X W, Gosselin C. Type Synthesis of Parallel Mechanisms. New York: Springer, 2007 219–230

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Robotics Research Lab, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Haibo Qu, Yuefa Fang & Sheng Guo

Authors
  1. Haibo Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuefa Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sheng Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haibo Qu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qu, H., Fang, Y. & Guo, S. Parasitic rotation evaluation and avoidance of 3-UPU parallel mechanism. Front. Mech. Eng. 7, 210–218 (2012). https://doi.org/10.1007/s11465-012-0317-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11465-012-0317-4

Keywords

Search

Navigation