Force optimization of kinematically-redundant planar parallel manipulators following a desired trajectory

Abstract In this work, an optimization-based methodology for resolving the generalized forces for kinematically-redundant planar parallel manipulators following a desired trajectory is presented. The proposed methodology assumes that the manipulator is performing a task that is slow enough to allow kinetostatic analysis to be used. Two test trajectories were used to show the effectiveness of the proposed methodology. The results for a kinematically-redundant 3- P R P R manipulator were compared against the results for a non-redundant 3-R P R manipulator. The results show that the redundant manipulator has improved force capabilities compared to the non-redundant manipulator. In particular, the redundant manipulator is able to pass through singular configurations with feasible generalized forces, something the non-redundant manipulator cannot do.

[1]  Ty A. Lasky,et al.  Kinematically-Redundant Variations of the 3-RRR Mechanism and Local Optimization-Based Singularity Avoidance , 2007 .

[2]  Jean-Pierre Merlet.  Redundant parallel manipulators , 1996 .

[3]  Juan A. Carretero,et al.  Kinematic analysis and path planning of a new kinematically redundant planar parallel manipulator , 2008, Robotica.

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

[5]  S. Nokleby,et al.  Force capabilities of redundantly-actuated parallel manipulators , 2005 .

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

[7]  Roger Boudreau,et al.  Synthesis of Planar Parallel Mechanisms While Considering Workspace, Dexterity, Stiffness and Singularity Avoidance , 2006 .

[8]  Clément Gosselin,et al.  Design and analysis of kinematically redundant parallel manipulators with configurable platforms , 2005, IEEE Transactions on Robotics.

[9]  C. Gosselin,et al.  Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms , 2004 .

[10]  P. Zsombor-Murray,et al.  Singularity analysis of planar parallel manipulators , 1995 .

[11]  Steven A. Velinsky,et al.  Determination of the kinematically redundant active prismatic joint variable ranges of a planar parallel mechanism for singularity-free trajectories , 2009 .

[12]  Roger Boudreau,et al.  The synthesis of planar parallel manipulators with prismatic joints for an optimal, singularity-free workspace , 2002, J. Field Robotics.

[13]  Jorge Angeles,et al.  Instantaneous kinematics and design of a novel redundant parallel manipulator , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[14]  Daniel Martins,et al.  Force Capabilities of Kinematically Redundant Planar Parallel Manipulators , 2011 .

[15]  Optimization strategies for additional actuators of kinematically redundant parallel kinematic machines , 2010, 2010 IEEE International Conference on Robotics and Automation.

[16]  Feng Gao,et al.  Performance atlases of the workspace for planar 3-DOF parallel manipulators , 2000, Robotica.

[17]  Clément Gosselin,et al.  GEOMETRIC SYNTHESIS OF PLANAR 3-RPR PARALLEL MECHANISMS FOR SINGULARITY-FREE WORKSPACE , 2009 .

[18]  Clément Gosselin,et al.  Singularity analysis and representation of planar parallel manipulators , 1992, Robotics Auton. Syst..

[19]  Walter Schumacher,et al.  A parallel x-y manipulator with actuation redundancy for high-speed and active-stiffness applications , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[20]  Clément Gosselin,et al.  Singularity analysis of closed-loop kinematic chains , 1990, IEEE Trans. Robotics Autom..

[21]  Juan A. Carretero,et al.  3-PRRR redundant planar parallel manipulator: Inverse displacement, workspace and singularity analyses , 2007 .