Comparison of 3-PP̲R parallel planar manipulators based on their sensitivity to joint clearances

In this paper, 3-PP̲R planar parallel manipulators with D- or U-shape base are compared with respect to their workspace size and kinematic sensitivity to joint clearances. First, the singularities and workspace of a general 3-PP̲R planar parallel manipulator are analyzed. Then, an error prediction model applicable to both serial and parallel manipulators is developed. As a result, two nonconvex quadratically constrained quadratic programs are formulated in order to find the maximum reference-point position error and the maximum orientation error of the moving-platform for given joint clearances. Finally, the contributions of the paper are highlighted by means of a comparative study of two manipulators.

[1]  Jean-Pierre Merlet,et al.  Direct kinematics of planar parallel manipulators , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[2]  Jian Meng,et al.  Accuracy Analysis of Parallel Manipulators With Joint Clearance , 2009 .

[3]  Stéphane Caro,et al.  Design and analysis of a 3-PPR planar robot with U-shape base , 2009, 2009 International Conference on Advanced Robotics.

[4]  Hanqi Zhuang,et al.  Self-calibration of parallel mechanisms with a case study on Stewart platforms , 1997, IEEE Trans. Robotics Autom..

[5]  Ferdinand Freudenstein,et al.  Kinematic Synthesis of Linkages , 1965 .

[6]  C. Gosselin,et al.  The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator , 1988 .

[7]  Damien Chablat,et al.  Multiobjective Design Optimization of 3–PRR Planar Parallel Manipulators , 2011 .

[8]  C. Gosselin,et al.  Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory , 2003 .

[9]  Jadran Lenarčič,et al.  Advances in robot kinematics : analysis and design , 2008 .

[10]  Karla L. Hoffman,et al.  A method for globally minimizing concave functions over convex sets , 1981, Math. Program..

[11]  Hui Wang,et al.  Position Errors Due to Clearances in Journal Bearings , 1989 .

[12]  Philippe Cardou,et al.  Finding the Maximal Pose Error in Robotic Mechanical Systems Using Constraint Programming , 2010, IEA/AIE.

[13]  V. Parenti-Castelli,et al.  A New Technique for Clearance Influence Analysis in Spatial Mechanisms , 2005 .

[14]  Juan A. Carretero,et al.  A Comparison between Two Motion Planning Strategies for Kinematically Redundant Parallel Manipulators , 2008 .

[15]  Gabriele M. T. D'Eleuterio,et al.  Tracking control for end-effector position and orientation of structurally flexible manipulators , 1993, J. Field Robotics.