Based on principal screw theory and imaginary mechanism method

the kinematic characters of a three degree-of-freedom spatial parallel manipulator with three UCR limbs were analyzed. According to the topologic structure of limbs

the screw coordinate system was set-up and the kinematics of limbs was analyzed. By the relation of the matrices of influence coefficient between limbs and moving platform

the kinematic model with the screw coordinates was established. It is showed that the matrices of influence coefficient is only dependent on the inputs and kinematic parameters and the method to analyze instantaneous motion is fit for others kinds of lower-DOF parallel manipulators. The instantaneous pitches of the principal screws gained decide that the kind of manipulator have always three DOFs with one translation and two rotations. By the numerical example when the moving platform is parallel to the base

the results of the pitches of principal screws validate the kinematic characters of the parallel manipulator.