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In recent decades, origami has been explored to aid in the design of engineering structures. These structures span multiple scales and have been demonstrated to be used toward various areas such as aerospace, metamaterial, biomedical, robotics, and architectural applications. Conventionally, origami or deployable structures have been actuated by hands, motors, or pneumatic actuators, which can result in heavy or bulky structures. On the other hand, active materials, which reconfigure in response to external stimulus, eliminate the need for external mechanical loads and bulky actuation systems. Thus, in recent years, active materials incorporated with deployable structures have shown promise for remote actuation of light weight, programmable origami. In this review, active materials such as shape memory polymers (SMPs) and alloys (SMAs), hydrogels, liquid crystal elastomers (LCEs), magnetic soft materials (MSMs), and covalent adaptable network (CAN) polymers, their actuation mechanisms, as well as how they have been utilized for active origami and where these structures are applicable is discussed. Additionally, the state‐of‐the‐art fabrication methods to construct active origami are highlighted. The existing structural modeling strategies for origami, the constitutive models used to describe active materials, and the largest challenges and future directions for active origami research are summarized.

 

Abstract Origami has emerged as a powerful mechanism for designing functional foldable and deployable structures. Among various origami patterns, a large class of origami exhibits rotational symmetry, which possesses the advantages of elegant geometric shapes, axisymmetric contraction/expansion, and omnidirectional deployability, etc. Due to these merits, origami with rotational symmetry has found widespread applications in various engineering fields such as foldable emergency shelters, deformable wheels, deployable medical stents, and deployable solar panels. To guide the rational design of origami-based deployable structures and functional devices, numerous works in recent years have been devoted to understanding the geometric designs and mechanical behaviors of rotationally symmetric origami. In this review, we classify origami structures with rotational symmetry into three categories according to the dimensional transitions between their deployed and folded states as three-dimensional to three-dimensional, three-dimensional to two-dimensional, and two-dimensional to two-dimensional. Based on these three categories, we systematically review the geometric designs of their origami patterns and the mechanical behaviors during their folding motions. We summarize the existing theories and numerical methods for analyzing and designing these origami structures. Also, potential directions and future challenges of rotationally symmetric origami mechanics and applications are discussed. This review can provide guidelines for origami with rotational symmetry to achieve more functional applications across a wide range of length scales. 

Abstract Ring origami has emerged as a robust strategy for designing foldable and deployable structures due to its impressive packing abilities achieved from the snap-folding mechanism. In general, polygonal rings with rationally designed geometric parameters can fold into compacted three-loop configurations with curved segments, which result from the internal bending moment in the folded state. Inspired by the internal bending moment-induced curvature in the folded state, we explore how this curvature can be tuned by introducing initial natural curvature to the segments of the polygonal rings in their deployed stress-free state, and study how this initial curvature affects their folded configurations. Taking a clue from straight-segmented polygonal rings that fold into overlapping curved loops, we find it is possible to reverse the process by introducing curvature into the ring segments in the stress-free initial state such that the rings fold into a straight-line looped pattern with “zero” area. This realizes extreme packing. In this work, by a combination of experimental observation, finite element analysis, and theoretical modeling, we systematically study the effect of segment curvature on folding behavior, folded configurations, and packing of curved ring origami with different geometries. It is anticipated that curved ring origami can open a new avenue for the design of foldable and deployable structures with simple folded configurations and high packing efficiency.