The folding pattern, known as the Miura-ori, is a periodic way to tile the plane using the simplest mountain-valley fold in origami. A folded Miura can be packed into a flat, compact shape and unfolded in one continuous motion, making it suitable for packing rigid structures like solar panels.It also occurs in nature in a variety of situations, such as in insect wings and leaves.
“We found an incredible amount of flexibility hidden inside the geometry of the Miura-ori,” said researcher, Levi Dudte. “As it turns out, this fold is capable of creating many more shapes than we imagined.
“The collapsibility, transportability and deployability of Miura-ori folded objects makes it a potentially attractive design for everything from space-bound payloads to small-space living to laparoscopic surgery and soft robotics,” Dudte continued.
To explore the potential of the tessellation, the team developed an algorithm that can create certain shapes using the Miura-ori fold, repeated with small variations. Given the specifications of the target shape, the program lays out the folds needed to create the design, which can then be laser printed for folding.
The program takes into account several factors, including the stiffness of the folded material and the trade-off between the accuracy of the pattern and the effort associated with creating finer folds.
“Essentially, we would like to be able to tailor any shape by using an appropriate folding pattern,” said Professor of Applied Mathematics, Organismic and Evolutionary Biology, and Physics, L Mahadevan. “Starting with the basic mountain-valley fold, our algorithm determines how to vary it by gently tweaking it from one location to the other to make a vase, a hat, a saddle, or to stitch them together to make more and more complex structures.
Prof Mahadevan concluded: “The really exciting thing about this fold is it is completely scalable. You can do this with graphene, which is one atom thick, or you can do it on the architectural scale.”
