Static of Parallel Manipulators and Closeness to Singularity

Singularity is a major problem for parallel robots as in these configurations the robot cannot be controlled, and there may be infinite forces/torques in its joints, possibly leading to a robot breakdown. In the recent years classification and detection of singularities have made large progress. However, the issue of closeness to a singularity is still open and we propose in this paper an approach that is based on a static analysis. Our measure of closeness to a singularity is based on the very practical issue of having the joint forces/torques lower than a given threshold. We consider a planar parallel robot whose end-effector has a constant orientation and is submitted to a known wrench and we show that it is possible to compute the border of the region that describes all possible end-effector location for which the joint forces are lower than the fixed threshold.

[1]  R. Bricard.  Mémoire sur la théorie de l'octaèdre articulé , 1897 .

[2]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[3]  Jean-Pierre Merlet.  Singular Configurations of Parallel Manipulators and Grassmann Geometry , 1989, Int. J. Robotics Res..

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

[5]  C. Gosselin,et al.  On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators , 1995 .

[6]  Masaru Uchiyama,et al.  Singularity-consistent path planning and control of parallel robot motion through instantaneous-self-motion type singularities , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[7]  S. Bhattacharya,et al.  Comparison of an exact and an approximate method of singularity avoidance in platform type parallel manipulators , 1998 .

[8]  G. Bögelsack,et al.  Twenty-five years IFToMM commission a “standardization of terminology”—History, methodology, results and future work , 1998 .

[9]  R. G. Fenton,et al.  Identification and classification of the singular configurations of mechanisms , 1998 .

[10]  Min Ki Lee,et al.  Kinematic and dynamic analysis of a double parallel manipulator for enlarging workspace and avoiding singularities , 1999, IEEE Trans. Robotics Autom..

[11]  Karl Wohlhart,et al.  Degrees of shakiness , 1999 .

[12]  Manfred Husty,et al.  Architecture Singular Parallel Manipulators and their Self-Motions , 2000 .

[13]  Boris Mayer St-Onge,et al.  Singularity Analysis and Representation of the General Gough-Stewart Platform , 2000, Int. J. Robotics Res..

[14]  John T. Wen,et al.  Kinematic control of parallel robots in the presence of unstable singularities , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[15]  Sven Soetebier,et al.  Connecting Assembly Modes for Workspace Enlargement , 2002 .

[16]  Alon Wolf,et al.  Investigation of Parallel Manipulators Using Linear Complex Approximation , 2003 .

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

[18]  Philip A. Voglewede,et al.  Measuring "closeness" to singularities for parallel manipulators , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[19]  C. K. Jui,et al.  Path Tracking of Parallel Manipulators in the Presence of Force Singularity , 2005 .

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

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

[22]  Damien Chablat,et al.  Singular curves and cusp points in the joint space of 3-RPR parallel manipulators , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[23]  Damien Chablat,et al.  Singular curves in the joint space and cusp points of 3-RPR parallel manipulators , 2007, Robotica.

[24]  Damien Chablat,et al.  Workspace and Assembly modes in Fully-Parallel Manipulators : A Descriptive Study , 2007, ArXiv.

[25]  Jean-Pierre Merlet.  A Formal-Numerical Approach for Robust In-Workspace Singularity Detection , 2007, IEEE Transactions on Robotics.