This work bridges the gap between theory and practice. The development of general inverse kinematic solution techniques is new, hence few detailed applications of these methods exist. Before methods such as these were available, most commercial manipulators were designed to be geometrically simple, yielding 4th or lower degree governing equations. With the further development and application of these techniques, industry will be capable of implementing more complex manipulators for highly specialized tasks. A general inverse kinematic analysis technique is applied to an industrial manipulator designed for the inspection of nuclear reactor vessels. The analysis is performed by solving the 16th degree univariate displacement polynomial of the general six-degree-of-freedom arm using an equivalent seven-degree-of-freedom closed-loop spatial chain. All possible combinations of joint angles for a given hand position and orientation are obtained. A region in which the manipulator has the maximum number of solutions is used as a numerical example. The inverse kinematic analysis was programmed in C, which is included in Appendix D. / Master of Science