In this paper we present a new formulation method to solve kinematic problem of serial robot manipulators. In this method our major aims are to formulize inverse kinematic problem in a compact closed form and to avoid singularity problem. This formulation is based on screw theory with dual - quaternion. Compared with other methods, screw theory methods just establish two coordinates, and its geometrical meaning is obvious. We used dual-quaternion in plücker coordinates as a screw operator for compactness. 6R-DOF industrial robot manipulators forward and inverse kinematic equations are derived using this new formulation and simulation results are given.