With the introduction of generalized function sets ( set) to represent the characteristics of the end-effectors of parallel mechanisms, two classes of sets are proposed. The type synthesis of parallel mechanisms having the second class sets and two dimensional rotations, including 2-, 3-, and 4DOF parallel mechanisms, is investigated. First, the intersection algorithms for the sets are established via the axiom of two dimensional rotations. Second, the kinematic limbs with specific characteristics are designed according to the axis movement theorem. Finally, several parallel mechanisms having the second class sets and two dimensional rotations have been illustrated to show the effectiveness of the proposed methodology.