Kinematic solutions of robots with continuous three-roll wrists using the zero reference position method

Robot manipulators have a variety of wrist arrangements. In commonly found wrist arrangements, the wrist axes are either cointersecting or nearly cointersecting, but rotations at some wrist joints must be restricted to avoid mechanical interference. Closed-form algebraic solutions for many simple robots with such wrists have been developed over the years. This paper deals specifically with robots with continuous 3-roll wrists. In a continuous 3- roll wrist, all wrist joints have unrestricted spin freedom without any mechanical inference. Although several manipulators now exist with such wrists, hardly any literature exists which deals with them. We present explicit closed-form solutions for robots with two types of continuous 3-roll wrists. The zero reference position method has been used to derive these solutions. The results presented in this paper should be useful in developing computer control for these robots with continuous 3-roll wrists.