The double universal joint wrist on a manipulator: Solution of inverse position kinematics and singularity analysis

This paper presents three methods to solve the inverse position kinematics position problem of the double universal joint attached to a manipulator: (1) an analytical solution for two specific cases; (2) an approximate closed form solution based on ignoring the wrist offset; and (3) an iterative method which repeats closed form position and orientation calculations until the solution is achieved. Several manipulators are used to demonstrate the solution methods: cartesian, cylindrical, spherical, and an anthropomorphic articulated arm, based on the Flight Telerobotic Servicer (FTS) arm. A singularity analysis is presented for the double universal joint wrist attached to the above manipulator arms. While the double universal joint wrist standing alone is singularity-free in orientation, the singularity analysis indicates the presence of coupled position/orientation singularities of the spherical and articulated manipulators with the wrist. The cartesian and cylindrical manipulators with the double universal joint wrist were found to be singularity-free. The methods of this paper can be implemented in a real-time controller for manipulators with the double universal joint wrist. Such mechanically dextrous systems could be used in telerobotic and industrial applications, but further work is required to avoid the singularities.