Computation of the safe working zones of Planar and Spatial Parallel Manipulators

This paper presents the computation of the safe working zone (SWZ) of a parallel manipulator having three degrees of freedom. The SWZ is defined as a continuous subset of the workspace, wherein the manipulator does not suffer any singularity, and is also free from the issues of link interference and physical limits on its joints. The proposed theory is illustrated via application to two parallel manipulators: a planar 3-RRR manipulator and a spatial manipulator, namely, MaPaMan-I. It is also shown how the analyses can be applied to any parallel manipulator having three degrees of freedom, planar or spatial.

[1]  John F. O'Brien,et al.  A geometric approach for the design of singularity-free parallel robots , 2009, 2009 IEEE International Conference on Robotics and Automation.

[2]  Nilanjan Chakraborty,et al.  Proximity Queries Between Convex Objects: An Interior Point Approach for Implicit Surfaces , 2008, IEEE Trans. Robotics.

[3]  Tatsuo Arai,et al.  Planning link-interference-free trajectories for a parallel link manipulator , 1993, Proceedings of IECON '93 - 19th Annual Conference of IEEE Industrial Electronics.

[4]  S. Sathiya Keerthi,et al.  A fast procedure for computing the distance between complex objects in three-dimensional space , 1988, IEEE J. Robotics Autom..

[5]  Ashitava Ghosal,et al.  Analysis of the degrees-of-freedom of spatial parallel manipulators in regular and singular configurations , 2013 .

[6]  Saurav Agarwal,et al.  Analytical Determination of the Proximity of Two Right-Circular Cylinders in Space , 2016 .

[7]  Dimiter Zlatanov,et al.  A General Method for the Numerical Computation of Manipulator Singularity Sets , 2014, IEEE Transactions on Robotics.

[8]  Andreas Pott.  Efficient Computation of the Workspace Boundary, Its Properties and Derivatives for Cable-Driven Parallel Robots , 2018 .

[9]  Jean-Pierre Merlet,et al.  Parallel Robots , 2000 .

[10]  Saurav Agarwal,et al.  Identifying Singularity-Free Spheres in the Position Workspace of Semi-regular Stewart Platform Manipulators , 2016, ARK.

[11]  Jean-Pierre Merlet,et al.  Designing a Parallel Manipulator for a Specific Workspace , 1997, Int. J. Robotics Res..

[12]  Charles Pinto,et al.  Workspaces associated to assembly modes of the 5R planar parallel manipulator , 2008, Robotica.

[13]  A. Ghosal,et al.  Analysis of configuration space singularities of closed-loop mechanisms and parallel manipulators , 2004 .

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

[15]  L. W. Tsai,et al.  Robot Analysis: The Mechanics of Serial and Parallel Ma-nipulators , 1999 .

[16]  Bahram Ravani,et al.  A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators , 2001 .

[17]  Claude Reboulet,et al.  Optimal design of a redundant spherical parallel manipulator , 1997, Robotica.

[18]  Oscar Altuzarra,et al.  Maximal Operational Workspace of Parallel Manipulators , 2010 .

[19]  Sandipan Bandyopadhyay,et al.  Dynamic singularity avoidance for parallel manipulators using a task-priority based control scheme , 2016 .

[20]  Clément Gosselin,et al.  The Maximal Singularity-Free Workspace of the Gough–Stewart Platform for a Given Orientation , 2008 .

[21]  Guilin Yang,et al.  Workspace generation and planning singularity-free path for parallel manipulators , 2005 .

[22]  Anirban Nag,et al.  Analytical Determination of a Sphere Inside Which the Stewart Platform Translates Without Suffering Any Leg Interference , 2018, ARK.

[23]  Ashitava Ghosal,et al.  Optimum design of multi-degree-of-freedom closed-loop mechanisms and parallel manipulators for a prescribed workspace using Monte Carlo method , 2017 .

[24]  Sandipan Bandyopadhyay,et al.  Determination of the Safe Working Zone of a Parallel Manipulator , 2014 .

[25]  Josep M. Porta,et al.  Planning Singularity-Free Paths on Closed-Chain Manipulators , 2013, IEEE Transactions on Robotics.

[26]  C. Gosselin,et al.  Determination of maximal singularity-free zones in the workspace of planar three-degree-of-freedom parallel mechanisms , 2006 .

[27]  Manfred Husty,et al.  Workspace Analysis of Stewart-Gough-Type Parallel Manipulators , 2006 .

[28]  Manfred Husty,et al.  Workspace and Singularity Analysis of a 3-RUU Parallel Manipulator , 2018 .

[29]  Hamid M. Daniali,et al.  A new approach to determine the maximal singularity-free zone of 3-RPR planar parallel manipulator , 2012, Robotica.

[30]  Stéphane Caro,et al.  Determination of the Maximal Singularity-Free Workspace of 3-DOF Parallel Mechanisms with a Constructive Geometric Approach , 2015 .

[31]  K. Y. Tsai,et al.  A general method to determine compatible orientation workspaces for different types of 6-DOF parallel manipulators , 2015 .

[32]  Ashitava Ghosal,et al.  Robotics: Fundamental Concepts and Analysis , 2006 .

[33]  Sandipan Bandyopadhyay,et al.  On the position kinematic analysis of MaPaMan: a reconfigurable three-degrees-of-freedom spatial parallel manipulator , 2013 .

[34]  A. Mallik,et al.  Variational approach for singularity-free path-planning of parallel manipulators , 2003 .