Stealing Design Secrets from the Unexpected Master of Origami

 According to folklore, earwigs like to crawl through the ears of sleeping humans, burrow into their brains, and lay eggs. Perhaps for this reason, or maybe because of their large rear-end pinchers, these insects tend to fall in the “creepy” category. Don’t be fooled through, earwigs are more sophisticated than they look: they're record-holders in the ancient art of origami.

Earwig wings, 2008. 
Image Credit: © Stephen Luk.

Earwigs spend a lot of time crawling, tunneling, and chilling out in moist, dark places like under tree bark, in basements, and in compost piles—but they can fly too, and the need to both navigate tight crevices and take to the air has made them masters of origami. Open earwig wings are at least 10 times as large as closed wings, the best folding ratio in the entire known animal kingdom. In addition, the wings fold up without using muscles, and lock into place when open to remain stable during flight.

But none of this makes sense from the perspective of classical origami, the art and mathematical theory that describes folding. So how do these crawlers achieve the seemingly impossible? Using computer simulations, a team of scientists at ETH Zurich and Purdue University recently studied the complex folding behavior of earwig wings. Their results, published in a recent issue of Science, expand the possibilities of synthetic origami systems like solar sails, bendable electronic displays, and even some biomedical devices.

As often happens in research, the project began with a chance conversation. Purdue University’s Andres Arrieta studies mechanical systems that are stable in two different states, or bistable—think of the way a push-button umbrella remains open or closed. One day, a biology colleague mentioned that earwig wings were bistable. After looking through old biology papers, Arrieta realized that the curious, unexplained mechanisms behind earwig wings could have widespread applications for origami systems. To explore this, he teamed up with André Studart and Jakob Faber, experts in materials and bio-inspired structures at ETH Zurich.

The team started by analyzing the structure and formation of earwig wings. Using a computer simulation, they tried to recreate the folded wing according to the rules of classic origami. It didn’t work. They could fold a wing down to one-third of its open size, but nowhere near one-tenth. They also couldn’t replicate the wing’s bistability, or its preprogrammed ability to fold.

It turns out that nature accomplishes these clever capabilities with resilin, an elastic material that composes the wing joints. Depending on its arrangement, a resilin joint can elongate, rotate, or both—and in doing so, open up more folding possibilities. When the team modified the rules of classic origami to treat the joints like springs that could elongate or rotate, they were finally able to recreate the folding process. Not only that, they were able to recreate the bistability and preprogrammed folding too.

The 3-D-printed imitation of the earwig wing can be folded as compact as its natural counterpart. However, the automatic folding function so far only works in the simplified prototypes. 
Image Credit: ETH Zurich.

From this, the team created a set of mathematical models that show how design parameters (such as spring stiffness) impact the shape and mechanical properties of the thing you’re folding. The models lay out the features that control the direction and order of folds, the possible geometries, and the strength of the self-locking mechanism. Their work shows that you can create structures that rapidly switch from one stable state into another when they are trigged by something in the environment.

Next, the team designed structures with the core features of an earwig wing—bistability and the ability to self-fold. They put this information into a multi-material 3D printer and printed fully folded prototypes that acted just as expected. These principles work across length scales—you can print small pre-folded structures, print large arrays for assembly, and even use springs in combination with conventional folds. 

If you think only of cranes when you hear origami, it’s time to expand your thinking. From the amazingly complex James Webb Space Telescope to origami-inspired robots that could someday travel through the body and deliver medical treatments, origami is at the forefront of many cutting edge technologies. With this new research, scientists and engineers have even more design freedoms at their disposal—including the potential to create designs that are preprogrammed, requiring less energy and fewer materials to fold or unfold. 

From bat ears to butterfly wings and dog noses, living things have developed countless smart designs to acquire unique advantages for themselves. Combining these designs with the wide range of materials available today, including many designed by humans and not found in nature, the possibilities are powerful. “We believe that if we can translate these arrangements and these designs from nature and recreate them with the synthetic materials we have now,” says Faber, “we might even be able to surpass these natural examples.” 

—Kendra Redmond