Abstract: This paper presents a new method of the determination of singular position surfaces of the reference point on the hand,the boundary surfaces of workspace of anarbitrary n D.O.F manipulator,which may be plane,spherical,or spatial,withlimited revolute and prismatic joints.For illustration,5R,6R and 5R-P manipulatorsare taken as examples.Comparing with all other methods previously used in this subject,our method possesses higher precision and takes shorter CPU time.