Nakul P. Bende, UMass Amherst
Researchers made a cone out of Polyvinyl siloxane (dental rubber) with some weakened areas. When the cone is slapped, it collapses and holds the shape.
The art of origami as we know it today -- folding flat sheets of paper into intricate sculptures -- was first developed in Japan around 400 years ago. Similar paper folding techniques in China and Europe go back even further, but the Japanese turned what was usually a practical tradition into a vibrant art form. In the modern age, origami principles have inspired a surprisingly wide range of applications in science, mathematics and technology.
Entrepreneur Alastair Pryor has developed a line of portable compact shelters that fold out like origami tents, for use in emergencies and disasters. Weighing in at a slender 35 pounds each, the structures fold flat for easy transportation then open into 6.5 x 6.5 x 6.5 waterproof cubes.
Johns Hopkins University
Let's get small! In 2011, biomolecular engineers at Johns Hopkins began investigating ways to employ origami techniques for self-assembling nanotech machines. The team designed mathematically precise "nets" of tiny flat plates that, when heated to a specific temperature, fold themselves into complex geometric structures -- like 12-sided dodecahedrons the size of a dust speck.
FoldScope via Youtube
Earlier this year, scientists at Stanford University unveiled the remarkableFoldscope
-- an origami microscope that can be assembled from a flat sheet of paper in under 10 minutes. Pop in a tiny lens, light and battery, and the Foldscope can provide 2,000X magnification for less than $1 in materials.
Designed for use in small-scale indoor farming, the Microgarden is a kind of miniature origami greenhouse for "microgreens" -- tiny edible plants that require little water or light. The greens get their moisture from a thin layer of seaweed-based gel inside the transparent plastic paper, which can be folded into a variety of shapes.
Harvard Microrobotics Lab/Seoul National University's BioRobotics Laboratory via Youtube
At this year's IEEE International Conference on Robotics and Automation (ICRA), two separate research teams debuted origami-inspired wheel systems for robots. Because the folded wheel spokes can change their shape on the fly, the diameter of the wheel itself can be altered to increase speed or torque when needed.
Harvard Microrobotics Laboratory
Origami techniques are also useful, turns out, for mass producing coin-sized robotic insects. In 2012, engineers at Harvard developed a system for assembling microrobots inspired by origami and pop-up books. The technique uses 18 layers of material in an intricate, laser-cut design. Flexible hinges allow the microrobot to self-assemble in one movement, like a pop-up book.
University of Maryland
Researchers at the University of Maryland recently demonstrated a new method for hydrogen fuel cell storage using tiny origami-like containers. The process, dubbed HAGO (hydrogenation-assisted graphene origami), incorporates an electric field that causes the origami boxes to fold and unfold on their own. Researches hope the technique will improve fuel cell capacity in hydrogen-powered vehicles.
MIT Media Lab /Tangible Media Group
By way of a composite material technology dubbed PneUI, MIT's Tangible Media Group has developed a wearable smart phone template that folds itself into a bracelet. Pneumatically actuated hinges built into the material allow the device to fold and unfold, origami-style, with a top structural layer made from silicone, fabric, wood or even -- yes -- paper.
Origami techniques have even been applied to that most intractable of modern dilemmas -- getting the last of the toothpaste out of the tube. Arizona State University design student Nicole Pannuzzo has designed an origami-inspired toothpaste tube that collapses like an accordion, leaving a flat piece of paper when extrusion is complete.
Genuinely innovative and surprisingly pretty, NASA's prototype starshade project looks like a giant origami sunflower in space. The idea is to deploy the starshade along with space-based telescopes when studying potentially habitable exoplanets, which are necessarily close to their host sun. The starshade's "petals" -- 34 meters in diameter when unfolded-- are specifically designed to reduce glare and impede the bending of light around the edges. This allows the telescope, positioned in the shadow of the starshade, to get better images of the target plant.
A new mathematical rule explains how simple, 3-D curved surfaces — such as domes or saddles — can be folded and snapped into new positions or to form different structures.
Typically, snapping metal in half isn't a useful operation, but some objects could benefit from such innovative folding techniques. For instance, parts of a satellite need to collapse down for storage during launch but then quickly expand in space.
Future robots could be more practical if they are able to reconfigure their arms without the need of moving parts. As such, understanding how to bend materials smoothly or snap them quickly could enable more efficient mechanical designs, said Arthur Evans, a postdoctoral researcher in the Department of Mathematics at the University of Wisconsin-Madison.
"There's a lot of math behind how you can fold flat things," Evans told Live Science. "There's a whole lot less about how you can fold nonflat things."
Origami artists usually fold flat sheets of paper to create shapes or structures. But folding materials with curves (such as dome- or saddle-shaped objects) usually means the finished product will be stiffer and stronger. This is similar to how folding a flat pizza slice into a cylinder-type shape helps keep the slice rigid.
The Venus flytrap is a domelike plant with leaves that are shaped like clamshells. When a fly brushes past the plant's sensitive hairs, it quickly folds the dome back together, snapping shut (like a spring mechanism without springs).
Engineers have used this snapping technique to build satellite airfoils that can collapse and expand, and to design tiny spherical particles that lock together. But researchers don't yet have theories to explain when or why it happens, Evans said.
Robert Lang, a physicist-turned-origami artist, published one of the earliest studies on folding nonflat surfaces in the journal The Mathematical Intelligencer in 2012. The research showed how to take paper curved in the 3-D shape of a saddle (akin to a Pringles chip) and fold it into a crane.
In their new study, Evans and his colleagues found a general mathematical rule that explains whether a curved surface will either snap or bend smoothly when folded. The rule takes into account only the geometric shape of an object, not its material or size.
"It looks like we can get a lot of information just by looking at the geometry," Evans said.
To understand the mathematical rule, imagine a cylinder and a straight piece of wire. If the wire can wrap along the cylinder and doesn't deform it in any way, then you can fold the cylinder along that curve without snapping it.
Researchers made a cone out of Polyvinyl siloxane (dental rubber) with some weakened areas. When the cone is slapped, it collapses and holds the shape.Nakul P. Bende, UMass Amherst
If instead the wire bends tightly around the cylinder so that it strains to straighten out, then it will pull the cylinder and expand it slightly. If a curve pulls on any curved surface like this, the curve will snap when folded.
"The equations cover any kind of surface you could possibly think of," Evans said.
To experimentally test this rule, the team looked at three so-called shell shapes that mathematically represent all the different cases of curvature: the cylinder, the sphere and the spiral-staircase-shaped helicoid. The researchers found that, in general, the sphere always snaps while the helicoid bends along two special paths and snaps everywhere else.
Evans and his colleagues created 3D-printed models made out of dental rubber and plastic and strategically poked the models to examine how they deformed from different forces at different distances.
The researchers have not yet demonstrated any applications for the theory, but since the rule depends only on the shape of the surface, it can be applied to any material of any size, they said.
For example, at the microscopic scale, Evans speculated that knowing which curves snap quickly could someday help researchers create tiny snapping cells or capsules that could mix together liquids, such as drugs going into the human body, faster than mixing methods available today.
"They put together an elegant theory," Ashkan Vaziri, an engineering researcher at Northeastern University in Boston, who was not involved in the study but has studied such shapes, told Live Science.
Now, Evans and his colleagues said they are thinking about how to use their findings to design structures that can collapse down and lock into place, such as new, collapsible satellite airfoils.
Engineers have been making locking structures that take advantage of bending or snapping for a while, but knowing a rule for such structures before they are designed would be more efficient, Evans said. Engineers could then pre-crease any curved object in just the right spots so that when it's pushed or slapped, it snaps or slowly bends into a different, predesigned configuration.
But for now, researchers only know for sure what happens to a single fold.
"It gets pretty complicated pretty fast," Evans said.
One of the next steps might be to investigate how to connect multiple folds together to create more-complicated structures, the researchers said. In the future, scientists might also investigate how to get structures to automatically bend or snap without being pushed or slapped.
The study is available on arXiv, a preprint server for science research, and was published online in the journal Proceedings of the National Academy of Sciences.
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