A new inverse kinematic solution for serial robot manipulators is represented in this paper. Major aims of this paper are to obtain singularity avoiding inverse kinematic solutions and formulize kinematic problems in a compact closed form. Our solution method is based on screw theory and it uses quaternions as a screw motion operator. Screw theory methods based on line transformation. All screw motions are represented as a rotation about a line together with a translation along the line with respect to base frame. Thus screw theory methods do not suffer from singularities. Two quaterninos are used to represent screw motion. First one is for orientation and second one is for translation. Thus we formulize kinematic problems in a compact closed form. 6R-DOF industrial robot manipulators forward and inverse kinematic equations are derived using this new formulation and also it compared with D-H convention that is the most common method in robot kinematic.