With the introduction of generalized function sets (GF set) to represent the characteristics of the end-effectors of parallel mechanisms, two classes of GF sets are proposed. The type synthesis of parallel mechanisms having the second class GF sets and two dimensional rotations, including 2-, 3-, and 4DOF parallel mechanisms, is investigated. First, the intersection algorithms for the GF 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 GF sets and two dimensional rotations have been illustrated to show the effectiveness of the proposed methodology.

SUMMARYA method is presented for the type synthesis of a class of parallel mechanisms having one-dimensional (1D) rotation based on the theory of Generalized Function sets (GF sets for short), which contain two classes. The type synthesis of parallel mechanisms having the first class GF sets and 1D rotation is investigated. The Law of one-dimensional rotation is given, which lays the theoretical foundation for the intersection operations of GF sets. Then the kinematic limbs with specific characteristics are designed according to the 2D and 3D axis movement theorems. Finally, several synthesized parallel mechanisms have been sketched to show the effectiveness of the proposed methodology.

The novel design of parallel mechanisms plays a key role in the potential application of parallel mechanisms. In this paper, the type synthesis of parallel mechanisms with the first class GF sets and two-dimensional rotations is studied. The rule of two-dimensional rotations is given, which lays the theoretical foundation for the intersection operations of specific GF sets. Next, kinematic limbs with specific characteristics are designed according to the 2-D and 3-D axes movement theorems. Finally, several synthesized parallel mechanisms with the first class GF sets and two-dimensional rotations are illustrated to show the effectiveness of the proposed methodology.

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