The novel synthesis of mechanisms for continuous origami based on the topological graph theory

Crease design is one of the most significant problems in continuous origami mechanisms. In this paper, a novel synthesis method is proposed to create creases. First, the basic operations of screw motion are described based on screw theory. Then, an innovative approach named loop splitting is demonstrated. This approach is then employed to analyse the motion output of single-loop and multiloop parallel mechanisms through the step-by-step disassembly of branches. According to the idea of loop splitting, two theorems used to design continuous origami mechanisms are proposed and proven. Furthermore, the categories of continuous origami mechanisms are described in this paper, and splicing design requirements for the initial origami units are proposed. In addition, three different categories of origami mechanisms based on the proposed design method are introduced: single-vertex with 4 creases, single-vertex with 6 creases, and combinations of single-vertex with 4 and 6 creases. Finally, the efficiency of the newly presented synthesis method is demonstrated via the construction of prototypes.