Abstract: 6-UPS Cross rod parallel machine tool is an improvement of the Stewart parallel mechanism. As two layers in the moving platform destroy the symmetry of generally Stewart platform, it is difficult to calculate the analytical solutions of the forward kinematics problem efficiently. Lodrigues parameters are used to describe the rotation matrix. Through the analysis of the coupling relationships among the position and orientation variables of the moving platform, and eliminated position vector parameters in the basic motion equations, the 4th order equations which have three parameters are obtained. Thus, with the use of Newton iterative method, the iterated function that solved the equations is constructed. The method is proved correct and effective through the analysis of the actual parallel machine tools.

Key words: Direct forward solution of the kinematics, Lodrigues parameters, Newton iteration, Parallel machine tool