Multibody System Dynamics

, Volume 21, Issue 2, pp 167–192 | Cite as

Coupling characteristics of rigid body motion and elastic deformation of a 3-PRR parallel manipulator with flexible links

  • Xuping Zhang
  • James K. Mills
  • William L. Cleghorn


Modeling of multibody dynamics with flexible links is a challenging task, which not only involves the effect of rigid body motion on elastic deformations, but also includes the influence of elastic deformations on rigid body motion. This paper presents coupling characteristics of rigid body motions and elastic motions of a 3-PRR parallel manipulator with three flexible intermediate links. The intermediate links are modeled as Euler–Bernoulli beams with pinned-pinned boundary conditions based on the assumed mode method (AMM). Using Lagrange multipliers, the fully coupled equations of motions of the flexible parallel manipulator are developed by incorporating the rigid body motions with elastic motions. The mutual dependence of elastic deformations and rigid body motions are investigated from the analysis of the derived equations of motion. Open-loop simulation without joint motion controls and closed-loop simulation with joint motion controls are performed to illustrate the effect of elastic motion on rigid body motions and the coupling effect amongst flexible links. These analyses and results provide valuable insight to the design and control of the parallel manipulator with flexible intermediate links.


Flexible manipulators Parallel manipulators Assumed mode method Coupling effect 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Xuping Zhang
    • 1
  • James K. Mills
    • 1
  • William L. Cleghorn
    • 1
  1. 1.Department of Mechanical and Industrial EngineeringUniversity of TorontoTorontoCanada

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