LAUSR

Abstract This paper proposes a new-kind three-translational and two-rotational (3T2R) motion with one fixed and one variable rotation directions. The serial kinematic chains (SKCs) that generate the proposed motions are synthesized. They are quite different from the SKCs generating 3T2R motion with two fixed rotation directions. Firstly, according to the relationships between the two rotations in a motion, the classification of 3T2R motions is discussed. By using finite screw as mathematical tool, the expressions of the two different kinds of 3T2R motions are formulated as algebraic sets. Secondly, serial motion generators of the 3T2R motions are investigated. The SKCs that generate the first-kind 3T2R motion are briefly reviewed; the twenty-eight types of SKCs that generate the second-kind 3T2R motion are synthesized by analytical derivations. Finally, the SKCs with the second-kind 3T2R motion are used to synthesize new parallel mechanisms. Two five-degree-of-freedom (five-DoF) systematical parallel mechanisms are taken as examples to show the applications of these SKCs. This paper provides theoretical foundations for the research on motions generated by complex SKCs and on motion patterns with variable rotation directions and centers.