New interval-based approach to determine the guaranteed singularity-free workspace of parallel robots

In the present paper we introduce an improved method to obtain the guaranteed singularity-free workspace of planar parallel kinematic machines. A geometric condition for the existence of singularities is extended to be used in interval analysis. Therefore, we eliminate the need of calculating the inconvenient interval form of the Jacobian's determinant. Hence, an appropriate description of the singularity-free workspace is obtained and the computational effort is reduced significantly. With the interval-based approach error sources, like manufacturing tolerances, can be considered. Consequently, regions that do not satisfy the proposed condition can be guaranteed not to have any type-two singularities. Several analysis examples demonstrate the efficiency of the proposed geometrical-based solver in comparison to existing solvers, i.e. based on the Jacobian's determinant.

[1]  M. Hiller,et al.  A framework for the analysis, synthesis and optimization of parallel kinematic machines , 2006, ARK.

[2]  John T. Wen,et al.  Singularities in three-legged platform-type parallel mechanisms , 2003, IEEE Trans. Robotics Autom..

[3]  Weihai Chen,et al.  A geometrical method for the singularity analysis of 3-RRR planar parallel robots with different actuation schemes , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[4]  Jens Kotlarski,et al.  On singularity avoidance and workspace enlargement of planar parallel manipulators using kinematic redundancy , 2007 .

[5]  Jean-Pierre Merlet.  The necessity of optimal design for parallel machines and a possible certified methodology , 2005 .

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

[7]  Xianwen Kong,et al.  Type Synthesis of Parallel Mechanisms , 2010, Springer Tracts in Advanced Robotics.

[8]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

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

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

[11]  Clément Gosselin,et al.  Singularity loci of planar parallel manipulators with revolute actuators , 1997, Robotics Auton. Syst..

[12]  Jadran Lenarčič,et al.  Advances in robot kinematics : mechanisms and motion , 2006 .

[13]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[14]  M.L. Husty,et al.  Self-motions of Griffis-Duffy type parallel manipulators , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[15]  Computing the worst case accuracy of a PKM over a workspace or a trajectory , 2008 .

[16]  Tatsuo Arai,et al.  A prototype parallel manipulator: kinematics, construction, software, workspace results, and singularity analysis , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[17]  Roger Boudreau,et al.  The Synthesis of Three-Degree-of-Freedom Planar Parallel Mechanisms with Revolute Joints (3-ṞRR) for an Optimal Singularity-Free Workspace , 2004 .

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

[19]  Bijan Shirinzadeh,et al.  Certified workspace analysis of 3RRR planar parallel flexure mechanism , 2008, 2008 IEEE International Conference on Robotics and Automation.

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

[21]  A. Neumaier.  Interval methods for systems of equations , 1990 .

[22]  J. P. Merlet,et al.  Parallel Robots (Solid Mechanics and Its Applications) , 2006 .