Origami engineering: An unfolding story

Brain stent designed by CSE professor and grad student draw global interest

By Joel Hoekstra

The Weisman Art Museum is just a short walk away from Richard James’s office on the University of Minnesota’s Twin Cities campus. Designed by the award-winning architect Frank Gehry and completed in the early 1990s, the building is clad in shiny metal panels joined together at surprising angles. To some, its crinkled surface recalls nothing so much as a sheet of reused aluminum foil.

James, however, sees something in the structure akin to origami, the ancient art of paper-folding. The museum’s exterior was cobbled together from multiple pieces of prefabricated metal, of course, but James, a Distinguished McKnight University professor in the College of Science and Engineering, observes that something similar could’ve been produced from a singular sheet. Even curved, convex, and concave forms can be coaxed from flat materials if the right approach is applied. 

“Buildings designed by Gehry often use isometric deformations,” James said, citing as an example the architect’s Walt Disney Concert Hall in Los Angeles.

Aerospace applications and more

James’s interest in the mathematics that underlie origami recently led him to offer a course on the topic. Origami originated more than a thousand years ago in east Asia, where paper was first produced, and over the last century it has become a popular pastime around the world. But U.S. scientists became especially interested in the geometries of origami in the 1950s and ’60s as the global space race began to heat up. 

“The classic application of origami design is in space structures,” said James, a faculty member in the Department of Aerospace Engineering and Mechanics. “You have structures, like solar cells, that you want to deploy into space. You have to fit them inside a rocket so they take up the least amount of space. One solution? You fold them.”

Today, origami has attracted attention for its potential value in such diverse fields as architecture, therapeutics, antenna design, and robotics. American physicist Robert Lang, who pioneered “origami engineering,” has demonstrated its versatility across a range of fields, but it’s still the unexpected results that draw attention. 

“He can tell you how to make the fold lines on a piece of paper so that when you fold it up, it's a rhinoceros,” James said. “I mean, it's really, impressive.

None of the students who enrolled in James’s 2023 origami class created a rhino, but students did take the topic seriously—immersing themselves in both the complex mathematical calculations and actual paper-folding. 

“The students had very creative ideas,” James says. “They showed how origami could be used in a variety of applications, from understanding how insect wings are shaped to designing clothing that drapes across the body in an attractive way.”

Creased and curved

James is particularly interested in origami as it relates to phase change materials—i.e., materials that change in shape or structure based on physical conditions. Funded by a multi-university research initiative grant from the U.S. Department of Defense, he and graduate student Huan Liu, have conducted basic research in the area of curved-tile origami.

Traditionally, origami requires strict, crisp folding techniques. 

“It’s very restrictive” James said. “You start with a flat sheet, and you, you draw some lines on the sheet, and you try to fold it on those lines. There's always a straight line that travels through a point that goes to the boundaries of the material. You can only deform it in so many ways.”

Curved-tile origami, on the other hand, can produce curved and even spherical forms.

“We depart from rigid folding by allowing the tiles to deform isometrically; that is, they are allowed to bend but not stretch,” James and Liu wrote in a recent presentation on the topic. “This is the way a piece of paper or sheet metal deforms.”

Liu, who began a postdoctoral fellowship at Caltech in fall 2024, experimented with curved origami folding techniques to create numerous spiral and cylindrical designs. 

“Folding [paper] on some Sunday afternoons has been one of my most enjoyable moments,” she said.

The work ultimately led her and James to consider potential applications of their research, including ways to incorporate curved origami into the design of high-performance vertical-axis wind turbines, long dismissed as an inefficient technology. In 2023, James and Huan launched a company, Whirrlenergy, to further the endeavor.

James and Liu are also collaborating with a German researcher on the use of curved origami in brain stent design. 

In 2022, Eckhard Quandt, vice president of research at Kiel University, asked the pair to explore methods for designing origami stents that could be fed into the brain through a catheter and then unfolded to block an aneurysm. 

Prototypes are currently being developed based on designs produced by James’s lab at the University of Minnesota Twin Cities campus.

The potential benefits of mingling origami engineering seem to be endless, James noted. But even when it’s applied to research, origami remains beautiful and fascinating. 

“It’s a mixture of math, science, and art,” he said.