American Scientist

Leonardo da Vinci’s Mona Lisa is one of the most recognizable paintings in the world. For hundreds of years, artists and historians have commented on everything from her subtle gaze and smile to her smooth skin and graceful hands. If one looks closer, however, the crease patterns of her sleeves also reveal da Vinci’s genius as an engineer: The sleeves accurately display the process that happens when metal pipes buckle under stress. This compression is now known as a Yoshimura pattern, because it is one of the origami patterns that Japanese engineer Yoshimaru Yoshimura identified in the 1950s.

A research group at Brigham Young University in Provo, Utah, has built upon the foundational work of Yoshimura and others using advanced mathematical and computer models. Mechanical engineer Larry Howell and his team specialize in what are called compliant mechanisms, which get their motion from bending, and deployable structures, which fold small in packaging and then expand once released. The team had already been exploring paper folding techniques, which provided the backdrop for Howell’s student Kelvin Wang—who has a long personal history with origami—to do something extraordinary. Wang discovered a new class of origami that he named bloom patterns, because they resemble flowers opening as they unfold. As the team recently reported in the Proceedings of the Royal Society A, these innovative patterns could be used to deploy solar arrays, satellites, or telescopes in space, and for medical devices implanted inside the human body.

“At first, I wasn’t confident the origami was novel, so we had to search the literature and contact experts,” Howell says. “One of those people we consulted is origami expert Robert Lang, who became a coauthor on the paper.” Lang confirmed that the patterns were new.

Bloom patterns can be made by joining wedge-shaped segments of crease patterns around a central polygon, such as a pentagon or hexagon. Howell says that what really makes Wang’s discovery special is that bloom patterns incorporate three properties that have never been combined in a class of origami before. The first is flat foldability: The pattern starts out flat like a sheet of paper, and when folded, the second position is also flat. That property is important for potential space applications because structures can be stowed efficiently in a compact state for launch. The second property is that the patterns are developable, which refers to the capability of the three-dimensional structure to be collapsed without stretching its material. The third property is that the structure is rotationally symmetrical, so it always looks the same when viewed from the central point, regardless of the angle. It can also be unfolded in all directions at once to become a large, flat sheet.

Although patterns such as Yoshimura and others that are similar, such as one called Miura-Wire-Crimp, were established in origami, the new research used their crease patterns to tessellate, meaning that identical shapes were used to generate a consistent motif.

“We did something different by tessellating the Yoshimura and repeating it in ways no one realized you could do before,” Howell adds. “We theorized we could apply the same method to other linear tessellations and put them together in a way that could also be rotational.”

Origami crease patterns were used to tessellate, repeating identical shapes to create a consistent motif.

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During their work, Howell and his team encountered a few challenges that they are continuing to research. One issue dealt with creases in the kind of material used in the bloom pattern. If the shape is made of paper, the creases in its plant-based cellulose fibers look broken under a microscope and are flexible. But creases in aluminum, plastic, Tyvek, or many other materials don’t behave the same way. These surrogate creases or surrogate folds, as the team called them, prompted the researchers to explore how to get these materials to behave like paper.

Another concern is that these other materials have more thickness than paper, which can become problematic. If one layer of a solar panel is trapped between other layers, it could make the equipment inoperable. Thus, the fold patterns have to be able to accommodate the thicknesses of different materials.

Collaborations are the key to successfully resolving these research issues, according to Howell. “The art led us to look at things in a way we would not have discovered using our traditional engineering approaches,” he says, “and then we used mathematical modeling to try to describe how things work.” Howell’s lab is now working with NASA and other universities and private companies to demonstrate the feasibility of a deployable outer-space telescope that uses the bloom patterns. The group is also teaming up with the University of Notre Dame on a lower-limb prosthetic that uses a compliant mechanism for the ankle.

“In collaborations with the telescope, we can do the origami, but we can’t do the optics,” Howell says. “When we started doing medical devices, we were working with physicians, surgeons, and other medical professionals. For the lower limb prosthetics, we needed to work with people in that community to help us understand what the needs are. Scientific collaboration is essential and valuable."