Type synthesis of serial kinematic chains with screw type terminal constraints based on an adding joint method

Serial kinematic chains(SKCs) with screw type terminal constraints are ubiquitous. However, the type synthesis of such mechanisms has not been systematically studied. Unlike the SKCs which only have pure constraint forces and torques, these kinds of SKCs contain independent screw type terminal constraints with non-zero pitch. This paper develops a systematic work for the type synthesis of general SKCs with terminal screw type constraints. In this paper, combined with the screw theory and the atlas method, the principle and steps for synthesizing SKCs based on an adding joint method are proposed. To derive feasible SKCs with terminal screw type constraints, the concept of constraint-kinematic identification graph(CKIG) is proposed and used to identify the screw type constraints in SKCs. Based on the proposed approach, varied 4R, 3R1P and 2R2P SKCs with 1F1H and 1C1H type terminal constraints and numerous 5R, 4R1P and 3R2P SKCs with 1H type terminal constraint are obtained. In addition, some examples for constructing novel parallel mechanisms(PMs) using the derived SKC with screw type terminal constraints are given. This paper provides an effective method for the type synthesis of SKCs with screw type terminal constraints.