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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.
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An additive algorithm for origami design
Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable fourfold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight, and curved-folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based metastructure design.
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- Award ID(s):
- 1922321
- PAR ID:
- 10228910
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 21
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- Article No. e2019241118
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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