, Volume 46, Issue 1, pp 221–237 | Cite as

Kinematic analysis of a 5-R SP parallel mechanism with centralized motion

  • Ernesto Rodriguez-Leal
  • Jian S. Dai
  • Gordon R. Pennock
Parallel Manipulators


The paper presents a kinematic analysis of a parallel mechanism, referred to here as a mechanism with centralized motion. The paper includes a proof, based on the geometry of the mechanism, that the platform exhibits centralized motion. An interesting feature of this parallel mechanism is that it is partially collapsible which may be beneficial in practical applications where storage space is limited. The platform is connected to a base, regarded as fixed in this paper, by five identical legs where each leg is a three-link chain connected by a revolute joint, a spherical joint, and a prismatic joint. The result is that the platform has a screw motion about an axis which is perpendicular to the base and passes through the centroids of the base and the platform, for all positions of the platform. The pitch of the instantaneous screw depends on the platform assembly configuration and is a function of the platform position and orientation. To complete the kinematic study, the paper includes closed-form solutions to the inverse and forward position and velocity problems. Finally, the paper includes several numerical examples to illustrate some of the key features of this novel parallel mechanism.


Parallel mechanism RSP architecture Centralized-motion Forward kinematics Inverse kinematics Instantaneous screw axis Jacobian matrix 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Ernesto Rodriguez-Leal
    • 1
  • Jian S. Dai
    • 2
  • Gordon R. Pennock
    • 3
  1. 1.Department of Mechatronics and AutomationTecnológico de MonterreyMonterreyMexico
  2. 2.Department of Mechanical Engineering, King’s College LondonUniversity of LondonLondonUK
  3. 3.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA

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