Motion coupling is one of the typical characters of parallel robots. This makes it complicated to control the parallel robots. Therefore, the design of parallel mechanisms with decoupled motions is an important and challenging issue in the parallel robotic field. However, research in this field, including the definition and type synthesis theory, is weak or lacking. In this paper, the reducible correlation between the input and the output of 3-DOF translational mechanisms with decoupled motions is investigated and the definition of this topic is presented. A new parameter named Gf coordinate is propsed for the synthesis of 3-DOF reducible translational mechanisms. The type synthesis theory for this kind of mechanisms is obtained and some reducible mechanisms are synthesized.