Abstract: A so-called geometric-analytical algorithm,which is a new efficient algorithm for the inverse kinematics of robot PUMA 560,is presented.It is based on a method that fully utilizcs the special geome-try of such a robot and takes advantage of analytical algorithm.Transcendental function calls requiringmuch computation time are greatly reduced.Computation results demonstrate that the computation timeis reduced by over 25 per cent,compared with that of geometric algorithm or analytical algorithm.It hasgreat value for on-line robot control and has actually been used for coordinated motion of two industrialrobots.