Computing Cusps of 3R Robots Using Distance Geometry
نویسنده
چکیده
The singularities of a 3R robot are usually determined, in terms of its joint angles, from the determinant of its Jacobian which can then be mapped onto the robot’s workspace through its forward kinematics. The presence of cusps in these singularity plots permits to change robot’s posture without meeting a singularity and hence their relevance. This paper shows how, using Distance Geometry, the singularities in the workspace of a 3R robot can be represented as an octic curve of the form 4δ1δ3−δ 2 2 = 0, where δi, i = 1,2,3, are quartic polynomials and, what is more important, its cusps correspond to those points in which δ2 = δ3 = 0. This leads to important simplifications over previous approaches.
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