Application of line geometry and linear complex approximation to singularity analysis of the 3-DOF CaPaMan parallel manipulator

This paper analyzes the singularities of a three degree of freedom (DOF) spatial parallel manipulators utilizing line geometry and linear complex approximation. First, the 6 × 6 matrix, mapping external wrenches acting on the moving platform to internal forces/moments at the manipulator’s joints, is derived as a set of six governing lines. By analyzing the dependencies of these lines, all singular configurations of the manipulator are obtained. Then, the closest linear complex to these six governing lines is derived. The closest linear complex’s axis and pitch provides information and understanding of the robot’s self-motion when in a singular configuration. Moreover, in the neighborhood of a singular configuration the instantaneous motions arising from manufacturing tolerances and low rigidity are determined. The proposed analysis has been applied to the 3-DOF parallel robots CaPaMan (Cassino Parallel Manipulator) and CaPaMan2.