Singular Planes and Dexterous Robot Mechanisms
When the Jacobian matrix connecting the joint displacements with the displacements in the task coordinates degenerates into a singular matrix, the mechanism cannot move in certain directions and the task cannot be performed. These are the kinematic singularities of the mechanism. This chapter deals with describing the kinematic singularities in industrial robots in the form of the singular planes. They represent the loci of singular points on the terminal link of a robotic system. We calculate the singular planes for serial mechanisms that are normally used in industrial robots, such as the articulated arm, the spherical arm, the cylindrical arm and the Scara arm. At the end, the singularities of a spherical wrist are discussed and a singularity-free pointing system is presented.