A new method has been proposed for the solution of the inverse kinematics of 6R robots. Firstly, the forward kinematics model of robots is established by adopting the screw theory, and then by suing the transformation of the exponential product formula, the separability of the n-degree-of-freedom robots and the general geometric constraints of the reconfigurable connection thus can be verified. Taking PUMA-560 robots as an example, the geometric constraints for its separation and reconnection are given. On the premise of satisfying the constraint conditions, the solution formula of each joint angle can be derived, thus consequently obtaining the inverse kinematics solution of the robots, with the error of calculating pose restricted within 10-13 degree of magnitude. Compared with the D-H coordinate method, the speed of the proposed algorithm is increased by 12%, thus avoiding the influence of singular points.