Configuration Synthesis and Analysis of Capture Origami Mechanism Based on Graph Theory

Abstract Origami mechanisms are extensively employed in various engineering applications due to their exceptional folding performance and deformability. The key to designing origami mechanisms lies in the design of the creases. The crease design is often derived from experience and inspiration, so it is crucial to have a systematic approach to crease design. In this paper, a novel synthesis approach based on graph theory is proposed, which effectively addresses the challenge of designing the creases in origami mechanisms. The essence of this method lies in the acquisition of the double symmetrical crease pattern through the directed graph product operation of two subgraphs. The crease pattern can be simplified by employing a technique that eliminates certain creases while preserving the non-isomorphism and symmetry of the pattern. An improved mixed-integer linear programming model is developed to achieve an automatic distribution of the peak_valley creases of the origami. The proposed method ultimately generates 12 unique double symmetrical crease patterns. The new method proposed in this paper, through systematic design, significantly improves the efficiency of mechanism design while opening up broad prospects for exploring new mechanism structures, thereby greatly expanding its application potential in cutting-edge fields such as aerospace engineering and intelligent robots.