Analysis of kinematic singularities for robot manipulators in Cartesian coordinate parameters

The authors analyze the singularity states of robot manipulators; only the manipulator inverse kinematic relationships are considered. In such relationships, three types of triangular equations arise for the kinematically general manipulator with the nominal decoupling conditions as found in conventional robots. These equations reveal the manipulator structural properties and the Cartesian configurations of the end effector in which the manipulator is singular; they may be used to determine the singularity states of a given trajectory. The method of singularity analysis presented is applicable to robots with six or less degrees of freedom