Analysis of the Topology of the Singularity Set of Planar 3-RPR Parallel Robots with Linear Platforms

Jose Capco (1) , Christoforos Spartalis (1)

1 Leopold Franzens Universität Innsbruck - University of Innsbruck

In [4] most of the results for a general 3-RPR planar robot with linear platforms are proven, i.e. there is a singularity-free path between two symmetrical direct kinematics solutions and there are no singularity-free paths between non-symmetrical direct kinematics solutions. We provide alternative and easy theoretical proofs of these results. We describe the topology of the kinematic singularities of these robots. We prove that the singularityfree set of the domain of the kinematic map for such robots consists of three components. One of our main results is the detailed analysis of the special case, i.e. when the anchor points of the moving platform and the fixed platform have the same cross-ratios. For this case we show that, the singularity-free set consists of four connected components, no direct kinematics solutions can be connected without crossing the singularity and that the absolute value of the determinant of the Jacobian evaluates to the same number for any of the direct kinematics solutions. We provide some nice geometric properties of the direct kinematics solutions for this special case.

Mots clés: direct kinematics; parallel planar robots; singularities

Domaines: Géométrie algébrique [math.AG]; Robotique [cs.RO]

Jose Capco, Christoforos Spartalis. Analysis of the Topology of the Singularity Set of Planar 3-RPR Parallel Robots with Linear Platforms. 2nd IMA Conference on Mathematics of Robotics, Sep 2021, (online, Manchester), United Kingdom. ⟨hal-03275882v1⟩