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Dexterity characterization of the RPR parallel manipulator based on the local and global condition indices

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Abstract

In this paper, the kinematic performance of a planar parallel manipulator 3-RPR is investigated. Based on the constraint equations, robot geometric Jacobian matrix is calculated. Since the end-effector of the 3-RPR planar parallel manipulator performs both translational and rotational motions, robot geometric Jacobian matrix is transformed to a homogeneous form. This method defines a new Jacobian that transforms the linear velocities of two points on the end-effector to the actuator velocities. The velocity manipulability index is used for studying the ability of the manipulator to move. The manipulator distance singularity and kinematic accuracy is checked out by using the Local conditioning index (LCI) and Global conditioning index (GCI). The effect of Jacobian matrix homogenization on both the LCI and manipulability index is investigated in detail. Furthermore, the relation between LCI and the manipulability ellipsoids for certain moving platform orientations is studied. The paper is finally concluded by checking out the shapes of the manipulability ellipsoids for different moving platform orientations over the whole workspace.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Yazd University, Yazd, Iran

    Vahid Rezania & Saeed Ebrahimi

Authors
  1. Vahid Rezania
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  2. Saeed Ebrahimi
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Correspondence to Saeed Ebrahimi.

Additional information

Recommended by Associate Editor Kyoungchul Kong

Vahid Rezania received his B.S. degree from Razi University of Kermanshah, Iran (2012), M.S. degree from Yazd University, Iran (2014), all in Mechanical Engineering. His research interests include robotics, modal analysis, and robust control of systems with parameter uncertainty.

Saeed Ebrahimi is currently an Associate Professor of Mechanical Engineering at Yazd University, Iran. He has received his Ph.D. in Mechanical Engineering from Stuttgart University, Germany, in 2007. He has also completed his postdoctoral fellowship at the Center for Intelligent Machines (CIM), McGill University in 2008. His current research interest includes Dynamic Modelling of Multibody Systems, Robotics, Mechanisms Design and Vibration Analysis of Mechanical Systems.

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Rezania, V., Ebrahimi, S. Dexterity characterization of the RPR parallel manipulator based on the local and global condition indices. J Mech Sci Technol 31, 335–344 (2017). https://doi.org/10.1007/s12206-016-1237-8

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  • DOI: https://doi.org/10.1007/s12206-016-1237-8

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