Abstract: Structural synthesis for 4-DOF non-overconstrained parallel manipulators,an open problem in the field of mechanism,is solved.Current structural synthesis methods of 4-DOF parallel manipulators are summarized,and the conflict between the number of constraints and limbs is technically solved using the concept of kinematics group and screw theory.A new method is presented for designing 4-DOF non-overconstrained symmetrical parallel manipulators through an analytical process.Some concepts are defined to make the structural synthesis efficient and convenient.Topological structures necessary for this kind of mechanism are analyzed,and two parallel mechanisms of such kind are obtained.The configurations and spatial assembly conditions of all possible kinematic pairs are provided.Finally,some typical mechanisms are given as design examples.