Type synthesis of non-overconstrained and overconstrained two rotation and three translation (2R3T) parallel mechanisms with three branched chains

Abstract. In this paper, a new synthesis method of 2R3T (R denotes rotation and T denotes translation) overconstrained and non-overconstrained parallel mechanisms (PMs) with three branched chains based on the displacement sub-manifold method is presented. Firstly, the displacement sub-manifolds of mechanisms were determined based on 2R3T motions. Subsequently, the displacement sub-manifolds of the branched chains were derived using the displacement sub-manifold theory, and their corresponding motion diagrams were provided. Additionally, a comprehensive analysis of non-overconstrained 2R3T PMs with a single-constraint branched chain was conducted, and the type synthesis of overconstrained 2R3T PMs with two or three identical constraints was also performed, accompanied by the presentation of partial mechanism diagrams. Finally, the number of DOF (degrees of freedom) of the mechanism was calculated using the modified Kutzbach–Grübler equation for a new PMs,and the screw theory was used to verify the kinematic characteristics, proving this new method's correctness.