Using Maple to Analyse Parallel Robots

We present the SIROPA Maple Library which has been designed to study serial and parallel manipulators at the conception level. We show how modern algorithms in Computer Algebra can be used to study the workspace, the joint space but also the existence of some physical capabilities w.r.t. to some design parameters left as degree of freedom for the designer of the robot.

[1]  Marc Moreno Maza,et al.  On Solving Parametric Polynomial Systems , 2012, Mathematics in Computer Science.

[2]  Fabrice Rouillier,et al.  Workspace, joint space and singularities of a family of delta-like robot , 2018, Mechanism and Machine Theory.

[3]  Damien Chablat,et al.  Kinetostatic analysis and solution classification of a class of planar tensegrity mechanisms , 2019, Robotica.

[4]  Fabrice Rouillier,et al.  Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators , 2012, ArXiv.

[5]  Damien Chablat,et al.  A Six Degree of Freedom Epicyclic-Parallel Manipulator , 2012 .

[6]  Damien Chablat,et al.  Working modes and aspects in fully parallel manipulators , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[7]  M. Husty.  An algorithm for solving the direct kinematics of general Stewart-Gough platforms , 1996 .

[8]  Solen Corvez,et al.  Using Computer Algebra Tools to Classify Serial Manipulators , 2002, Automated Deduction in Geometry.

[9]  Fabrice Rouillier,et al.  On the determination of cusp points of 3-R\underline{P}R parallel manipulators , 2010, ArXiv.

[10]  Jeha Ryu,et al.  Orientation workspace analysis of 6-DOF parallel manipulators , 1999 .

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

[12]  Wisama Khalil,et al.  Modeling, Identification and Control of Robots , 2003 .

[13]  Chao Chen,et al.  A new 6-dof 3-legged parallel mechanism for force-feedback interface , 2010, Proceedings of 2010 IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications.

[14]  George E. Collins,et al.  Cylindrical Algebraic Decomposition I: The Basic Algorithm , 1984, SIAM J. Comput..