：A method solving the output twist screw and the transmission wrench under the motion of a single limb is proposed based on the screw theory. Some conditions that a mechanism requires to realize the constant power transmission and reach the best motion/force transmissibility in different poses are presented. By taking the 3-CPU translational parallel mechanism as an example,the motion/force transmissibility performance of the mechanism is analyzed. In the meanwhile,the allocation pattern of the actuated joint when a limb can transmit all its input power to the moving platform is presented. The motion/force transmissibility performance of the 3-PRPU translational parallel mechanism is analyzed,and some effects of configurations to the transmission power of a single limb are summarized. The work can make a contribution to analyzing and synthesizing parallel mechanism with good motion/force transmissibility.