Abstract: A method to describe a numeral value with a special numeration system is introduced in this paper, and the applied rules are defined, and then expression of the special numeration system is derived. This method is used to define the steps of the optimal algorithm, and then this algorithm is applied to computing an inverse solution of the redundant manipulator kinematics. A likelihood solution can be found quickly in the infinitude groups of likelihood solutions within the limited search times. In this algorithm, anti trigonometric function and the inverse matrix are not needed. The derivation and simulation show that the algorithm has many good qualities such as concise arithmetic, tiny calculation, fast convergence velocity, well stability and extensive adaptability.