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.

1. Introduction

As space exploration endeavors continue to expand, the concomitant increase in space debris presents substantial challenges to orbital resource utilization and the operational safety of spacecraft [1]. Consequently, the development of efficient debris removal methods [2, 3] has become an urgent priority. Various methods for capturing and eliminating space debris have been proposed, including flying nets [4], harpoon systems [5], and microsatellite grippers [6]. Although these approaches exhibit some potential, their applicability remains constrained due to limited adaptability and operational flexibility. In this context, origami mechanisms, characterized by their distinctive folding capabilities and continuous deformation potential, present a promising and innovative solution. Origami structures have found successful applications in diverse fields such as deployable space mechanisms [7–11], architecture [12–14], and robotics [15–18], offering novel solutions to complex engineering problems. As depicted in Figure 1, the origami mechanism can function as foundational modules for a space capture manipulator. This manipulator can be compactly folded for efficient transport and subsequently deployed into variable configurations upon reaching the target orbit, enabling them to capture non-cooperative objects in space. The critical aspect of designing a space capture manipulator lies in the development of a suitable origami mechanism module.

The design process of origami mechanisms typically commences with the creation of crease patterns, followed by a detailed structural design. However, most existing crease pattern designs are still predominantly based on empirical knowledge and intuitive reasoning [19], thereby underscoring the need for a more systematic and standardized design methodology. To address this issue, Zhou et al. [20] introduced a numerical approach for generating three-dimensional origami structures, utilizing a set of vertices within the Cartesian coordinate framework. Lang et al. [21] contributed a series of mathematical and geometric techniques to systematically design crease patterns. Tachi et al. [22] proposed methodologies for rigid-folding and flat-folding origami, grounded in the fundamental constraints of a single degree-4 vertex. Belcastro et al. [23] developed a methodology for designing crease patterns by employing affine transformations and closure equations. Despite the existence of various crease pattern design methodologies, significant computational and analytical challenges persist, particularly in the design of novel