Criterion for constant power transmission and the excellent motion/force transmission occurring within a class of translational parallel mechanisms is proposed. A host of configurations of the translational parallel mechanisms which meet the criterion are synthesized. The motion/force transmission performance of two translational mechanisms 3-CRU and 3-PRRU are analysed. The “original” input power is introduced and the angle between the axial directions of the TWS and MTS which exactly reflects the capacity of the “original” input to output transmission is presented.