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Genericity And Singularities Of Robot Manipulators, Ming-Chuan Leu, D. K. Pai

Mechanical and Aerospace Engineering Faculty Research & Creative Works

The kinematic singularities of robot manipulators are studied from the point of view of the theory of singularities. The notion of a "generic'' kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator, is examined. For three-joint robots, an equivalent algebraic condition for genericity using the Jacobian determinants is derived. This condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators. Orientation and translation singularities of manipulators are studied in detail. A complete characterization of orientation singularities of robots with any number of joints is given. The translation …