Planar Parallel Robotic Machine Design

  • Dan ZhangEmail author


Parallel kinematic machines with their unique characteristics of high stiffness (their actuators bear no moment loads but act in a simple tension or compression) and high speeds and feeds (high stiffness allows higher machining speeds and feeds while providing the desired precision, surface finish, and tool life), combined with versatile contouring capabilities have made parallel mechanisms the best candidates for the machine tool industry to advance machining performance. It is noted that the stiffness is the most important factor in machine tool design since it affects the precision of machining. Therefore, to build and study a general stiffness model is a very important task for machine tool design. In this chapter, we will build a general stiffness model through the approach of kinematic and static equations. The objective of this model is to provide an understanding of how the stiffness of the mechanism changes as a function of its position and as a function of the characteristics of its components. This can be accomplished using stiffness mapping.

There are two methods to build mechanism stiffness models [170]. Among them, the method which relies on the calculation of the parallel mechanism’s Jacobian matrix is adopted in this book.


Parallel Mechanism Flexible Beam Torsional Spring Parallel Kinematic Machine Actuate Joint 
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  1. 14.
    Asada H, Cro Granito JA (1985) Kinematics and statics characterization of wrist joints and their optimal design. In: Proceedings of the IEEE international conference on robotics and automation, pp 244–250Google Scholar
  2. 36.
    Cléroux L, Gosselin CM (1996) Modeling and identification of non-geometric parameters in semi-flexible serial robotic mechanisms. In: Proceedings of the ASME mechanisms conference, Irvine, CAGoogle Scholar
  3. 56.
    Gosselin CM (1988) Kinematic analysis,optimization and programming of parallel robotic manipulators. PhD thesis, McGill UniversityGoogle Scholar
  4. 57.
    Gosselin CM (1990) Stiffness mapping for parallel manipulators. IEEE Trans Robot Autom 6(3):377–382CrossRefGoogle Scholar
  5. 58.
    Gosselin CM, Angeles J (1988) The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator. ASME J Mech Transm Autom Des 110(1):35–41Google Scholar
  6. 59.
    Gosselin CM, Angeles J (1990) Singularity analysis of closed-loop kinematic chains. IEEE Trans Robot Autom 6(3):281–290CrossRefGoogle Scholar
  7. 61.
    Gosselin CM, Wang JG (1997) Singularity loci of planar parallel manipulators with revolute actuators. J Robot Auton Syst 21:377–398CrossRefGoogle Scholar
  8. 62.
    Gosselin CM, Zhang D (1999) Stiffness analysis of parallel mechanisms using a lumped model. Technical report, Département de Génie Mécanique, Université LavalGoogle Scholar
  9. 83.
    Klein CA, Blaho BE (1987) Dexterity measures for the design and control of kinematically redundant manipulators. Int J Robot Res 6(2):72–83CrossRefGoogle Scholar
  10. 133.
    Sefrioui J, Gosselin CM (1993) Singularity analysis of representation of planar parallel manipulators. J Robot Auton Syst 10:209–224CrossRefGoogle Scholar
  11. 143.
    Timoshenko SP, Gere JM (1972) Mechanics of materials. PWS Publication, Boston, MAGoogle Scholar
  12. 165.
    Yoshikawa T (1984) Analysis and control of robot manipulators with redundancy. In: Proceedings of first international symposium on robotics research, pp 735–747Google Scholar
  13. 170.
    Zhang D (2000) Kinetostatic analysis and optimization of parallel and hybrid architectures for machine tools. Laval University, CanadaGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Faculty of Engineering and Applied ScienceUniversity of Ontario Institute of Technology (UOIT)OshawaCanada

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