One-degree-of-freedom flat-foldable thick-panel origami-kirigami structures: modular arrays and closed polyhedra

Introduction

The emergence of origami geometry has led to remarkable advancements in rigid origami and thick-panel origami structures, garnering widespread attention from researchers. These structures hold vast potential for applications ranging from space deployable structures^{1, 2–3} to origami robots^4,5, scalable architectural designs^6,7, and origami metamaterials^{8, 9–10}. Origami structures, characterized by their high folding/unfolding ratio, flatness, and polyhedral closure, offer promising applications in space, including ultra-large-area solar arrays, solar sails, sunshades, large-caliber reflecting antennas and telescopes, air-space trans-domain morphing wings, deployable space stations, and extra-terrestrial modular foldable buildings^11,12. Thick-panel origami structures for space applications possess the following attributes: (1) one-degree-of-freedom (one-DOF) mechanisms with deterministic motion, facilitating ease of actuation and control; (2) flat-foldability, allowing compact stowage; (3) deployability, enabling unfolding upon reaching orbit; and (4) modularity and scalability, permitting design flexibility to meet mission requirements.

Rigid origami patterns consist of systematically arranged vertices and creases. Typical vertices include the four-crease vertex and the six-crease vertex. Variations derived from the four-crease vertex include the Miura pattern¹³, eggbox pattern¹⁴, helical pattern¹⁵, twist origami pattern¹⁶, and winding origami patterns^2,3,17,18. Examples of six-crease vertex arrangements include the Resch pattern^19,20, waterbomb pattern^21,22, diamond pattern^23,24, and Kresling pattern^25,26. Current origami patterns are typically designed based on a few standard multi-crease vertices, such as four-crease and six-crease vertices, lacking a comprehensive design theory for novel multi-crease, multi-vertex origami patterns. Modular origami, involving the integration of multiple origami units folded from a single sheet into two- or three-dimensional composite structures^9,27,28, presents new opportunities for designing multi-crease multi-vertex origami patterns. Thick-panel origami accounts for panel thickness, as directly applying zero-thickness origami models may cause physical interference. Therefore, thick-panel origami structures often adapt zero-thickness origami patterns through thick-panel methods^{12,24,29, 30, 31–32}. Combining kirigami with origami introduces novel approaches to constructing one-DOF thick-panel origami-kirigami structures^28,33.

Mathematicians have demonstrated that closed polyhedral structures cannot achieve rigid folding while remaining closed³⁴. Achieving rigid flat folding for closed polyhedral structures is a substantial challenge, with kirigami technologies offering potential solutions. Recent research has focused on the development of rigid foldable polyhedral structures by incorporating creases,...