Singular surfaces and cusps in symmetric planar 3-RPR manipulators

Details Singular surfaces and cusps in symmetric planar 3-RPR manipulators Singular surfaces and cusps in symmetric planar 3-RPR manipulators

2011-07-22

arxiv.org/abs/1107.4498v1

Computer Science

Robotics

IEEE/RSJ International Conference on Intelligent Robots and Systems, San Franisco : United States (2011)

Scientific paper

We study in this paper a class of 3-RPR manipulators for which the direct kinematic problem (DKP) is split into a cubic problem followed by a quadratic one. These manipulators are geometrically characterized by the fact that the moving triangle is the image of the base triangle by an indirect isometry. We introduce a specific coordinate system adapted to this geometric feature and which is also well adapted to the splitting of the DKP. This allows us to obtain easily precise descriptions of the singularities and of the cusp edges. These latter second order singularities are important for nonsingular assembly mode changing. We show how to sort assembly modes and use this sorting for motion planning in the joint space.

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