Type synthesis of parallel mechanisms having the first class G_F sets and one-dimensional rotation

A 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 (G_F sets for short), which contain two classes. The type synthesis of parallel mechanisms having the first class G_F sets and 1D rotation is investigated. The Law of one-dimensional rotation is given, which lays the theoretical foundation for the intersection operations of G_F 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.