A new analytic scheme for solving the inverse kinematics equations of PUMA robot manipulator is presented in this paper.The formulas of calculating the sine and cosine of all rotate angle variables were given to obtain each variable directly without judging the range of each variable.This method is simple and significant to optimize the robot motion.The simulation results on AutoCAD show that the algorithm is correct.The method changes the triangulated equations to polynomial equations which could be solved by using Wu wenjun’s method.