Type synthesis of parallel mechanisms having the second class G_F sets and two dimensional rotations

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