Engineering with Origami

Engineers are turning to origami for inspiration for all types of applications, from medical devices to space applications, and even stopping bullets. But why is it that this ancient art of paper folding is so useful for modern engineering? Origami, literally folding paper, dates back at least 400 years in Japan, but the number of designs was limited. There were only a handful of patterns, maybe 100 or 200 total in Japan. Nowadays, there are tens of thousands that have been documented, and most of that change happened in the 20th century.

There were a handful of Japanese origami masters, and by far, the most successful of them was a man named Akira Yoshizawa, who created thousands of new designs, wrote many, many books of his works, and his work inspired a worldwide renaissance of origami creativity. Well, I wanted to fold a cactus. The first thing one needed to do is figure out how do I get spines on a cactus. So you can imagine if I can make two spines here, I could do the same thing to make a whole row. Then I can go back and do a complete design. That's what this is. [Laughter] And this is actually the cactus, and the pot are from a single sheet of paper. The paper's green on one side, red on the other. That whole thing is this thing. So this is one uncut square of paper.

How big was that piece of paper? This is about a one-meter square, so there is a huge amount of size reduction to go from a meter down to here. But you need that to get all of the spines. And how long did that take to make? That took about seven years from start to finish. Wow! Why is origami this thing that was created for aesthetics mainly? Why is it so useful? I guess is the question for, like, you know, structural things that were for mechanical engineering or for space applications. Like, why does it find itself in so many of these applications? Why is it so useful?

Well, the thing that makes origami useful is it is a way of transforming a flat sheet into some other shape with relatively little processing. This is a folded pattern; it's called a triangulated cylinder. It is bi-stable, meaning it's stable in two positions. This is one, and then if I give it a twist, this is the other. This really has a bunch of bi-stable mechanisms in it because I can, you can see how it sort of pops into place. But if you combine the two mechanisms going in different directions, then you get the sort of magical color change effect.

Yeah, that's impressive! So you look at this and you say, okay, that is a cute paper toy. Is it anything more than that? And the answer is yes. Does that turn into that? It turns into that. Yep! We're working with a company called Two Against Surgical that does the Da Vinci surgical robot, where they wanted to be able to insert a flexible catheter with the robot. But the flexible catheters tend to buckle and stuff. So we had developed these origami bellows that, if you look down there, there's a hole that no matter how far we move this, that stays the same size on the inside. And what that means is we can put the catheter in there, and as the catheter moves and it's getting inserted into the body, it still has supports along the way.

Or for another example, here I have a foldable bulletproof collapsible wall. It's based on the Yoshimura crease pattern, meaning it might make this out of a bulletproof material. It can be very compact, being a police officer's car, and deploy out and be bulletproof. But would it actually work? Well, they've put it to the test. Using 12 layers of Kevlar, it can stop bullets from a handgun, and a new design featuring interchangeable panels should be able to stop rifle rounds. Those, and that vial, that is, those are actually bullets that have been stopped by origami.

An intrinsic benefit of origami is that the simple act of folding a material can make it more rigid. I was going to ask you about this, yeah, more origami. But I was going to say it's a way of making the can stronger without actually like thinner metal, right? But for engineering applications, the more common challenge is how to fold thick rigid materials. This is polypropylene; okay, very rigid. There's no way that I'm going to be able to fold that into this vertex. So this is an example; it shows a couple of surrogate folds we can use to replace the creases, and then also that piece of polypropylene folds up, and it also accommodates the thickness by cutting or scoring materials and adding hinges as necessary. Thick rigid materials can, in effect, be folded.

This is useful, for example, in deploying solar panels. This pattern is perhaps the granddaddy of deployable structures; it's called the Miura Ori. It's been used for solar arrays. In fact, it was one of the first patterns that flew on a space mission back in 1995. It was called the Space Flyer Mission. As you see here, it all opens and closes in a single motion, and when it flattens, it's very thin and compact.

It's a fun pattern called the origami flasher, and you get this kind of interesting flasher motion. This has been proposed as a design for satellite solar arrays, increasing compactness for launch and reliability in deployment. [Music] A new area for origami research is in improving the aerodynamics of freight locomotives. The thing with freight locomotives is, you know, they're just like bricks going down the tracks, so their aerodynamics are horrible. Ideally, I'd like to have a nose cone on the front of a freight locomotive to improve the aerodynamics, but you can't because they're like Lego blocks. They're hooked up anywhere along the train; you don't know if it's the first one or the second one or the third one.

Here's a scaled prototype showing a pattern that we demonstrated on a freight locomotive. It folds up to be very flat, but then deploys out, and it turns out our computer models and wind tunnel testing show that this will save this one company multiple millions of dollars a year in diesel. [Music] This is a violinist; it was one of my favorite mechanism designs because he fiddles. If you pull his head, fantastic functional motions of origami are inspiring new designs for devices like compliant mechanisms that can complete full 360-degree rotations. Unlike a traditional mechanism with, you know, bearings or hinges, I can hook on a motor, and I can get continuous revolution. I couldn't do that with a compliant mechanism, but it turns out no one bothered to tell the paper folders that and created a continuously revolving compliant mechanism, which is called a Kalita cycle.

Origami motions are also being used in medical devices. These would be, you know, the creases in the paper. And we have here now forceps, and so what's nice about this is we could put this at a smaller scale right on the medical instrument to go into the body, but then can morph and become the gripper. So it'll be a very small incision but then go in and do some more complex tasks inside the body. A variant of this mini gripper is now being used in robotic surgeries, replacing the previous mechanism and reducing the number of parts by 75 percent. The origami-inspired device is smaller but with a wider range of motion.

Functional origami can be miniaturized even further. This is the world's smallest origami flapping bird. That sounds cool! This one was devoted to developing techniques to make microscopic self-folding origami, and what you see here is a microscope photo of the finished bird. But what the bird actually looks like? Well, I'll need my micro lens. You'll probably need not just your macro lens; you’ll need your microscope because it's smaller than a grain of salt. So it started out; it was a bit less than a millimeter square, but when it's folded, it's much, much smaller.

Wow! Now you might ask yourself, what would anyone ever use a microscopic flapping bird for? And the answer is, well, nothing for a flapping bird. But there are medical devices, medical applications, implants that are microscopic where you might want a little machine. This is a nano injector used in gene therapy to deliver DNA to cells. It's only four micrometers thick, so 400 of them can fit onto a one-centimeter-wide computer chip.

There are some things down there that kind of look about Star Wars to me. Yes, this art is called elliptic infinity, and we wanted to do that in a material other than paper. You see this from flat into that elliptic infinity shape. This is actually a lamp that's made from a single sheet. So it comes in an envelope like this. Put its cable in, fold it, add a clip. Now this relies on a lot of math; the curvature of these lines affects links. The bending and curvature here to here to here, all of these are coupled, and pretty much the only way to design them and get all the folds to play together is by following mathematical methods.

My professional background is mathematics and physics. I did laser physics for 15 years as a profession. I got my PhD in applied physics, and my kind of my job in many cases was to figure out how to describe lasers mathematically. If I could put my problem in the mathematical language, then I could rely on the tools of mathematics to solve those problems and to accomplish the goals. But I also felt like origami would be amenable to that same approach. So I started trying to figure out how to describe origami using the tools of mathematics, and that worked.

I'm sort of fascinated about the math here; like, it's hard for me to conceive of, like, what does that math look like? The math comes down to a way of representing a design called a crease pattern. Let me grab a couple of crease patterns. Okay, so this is an origami crease pattern. It's a plan for how to fold, in this case, how to fold a scorpion. A really good way of designing something like this is to represent every feature—claw, leg, tail—by a circular region, a circular shape. It's not circular folds; it's an abstract concept that you represent the pattern by a circle, but then you find an arrangement of those circles on the square, like packing balls into a box.

So for the scorpion, you've got a long tail; imagine a big circle like a big tin can, and the legs are smaller circles, or circles of different sizes. So you've got different smaller cans and the claws are a couple more circles, and you're going to put them into a square box in such a way that they all fit. So you pack the circles into the box, and the arrangement of those circles tells you the skeleton of the crease pattern. From that, you can geometrically construct all the crease patterns you follow rules, put a line between the center of every pair of circles, and then whenever any two lines meet in a V, you add a fold halfway in between. It's called a ridge fold.

And there's similar, more complicated rules for adding more and more lines, but the thing is, it's all step by step. It says, if you find this geometric pattern that tells you where to add the next line, and you go through that process until you've constructed all the lines. When you're done, you can take away the circles; they were the scaffolding for your pattern, and the pattern of lines that's left is the folds you need to create the shape. And that's what's shown here. This was probably the biggest revolution in the world of origami design: if you followed that systematic process, the fold pattern would give you the exact shape that you set out to fold to begin with.

The circle packing method that I described works for anything that can be represented as a stick figure, like a scorpion. You could draw this as a stick figure with a line for the body and tail, lines for each of the legs, lines for the claws. And from that stick figure, from any stick figure, you can use circle packing and get a shape that folds. But suppose the thing you're folding is not a stick figure? Suppose it's something that's more like a surface, like a sphere or, you know, or a cloud or, or just, in animal terms, a big blobby body like an elephant. A stick figure algorithm is not going to work.

But there are other algorithms for that. About 10 years ago, a Japanese mathematician named Tomohiro Tachi developed an algorithm that works for any surface. You give it a triangulated surface as a mathematical description, and he will give you—or his algorithm will give you—the folding pattern that folds into that surface. It's now quite famous, and it's called Origamizer. And that is a way you could make a sheet of anything and take on any three-dimensional shape.

So origami is useful in engineering because it provides a method of taking a flat sheet of material and forming it into virtually any shape by folding. Or if the end product is flat, origami offers a way to reduce its dimensions while still deploying easily. The simple act of folding can increase rigidity, or origami can take advantage of the flexibility of materials to create specific motions. And its principles are scalable, enabling the miniaturization of devices.

Perhaps most of all, origami allows engineers to piggyback on the bright ideas people have had over the centuries while experimenting with folding paper. But translating these ideas into practical solutions requires a lot of math modeling and experimentation.

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