The Miura fold: art and mathematics of origami
July 19, 2014 7:53 PM   Subscribe

Computational geometrist Erik Demaine also does some pretty cool origami sculptures.
posted by gemutlichkeit at 8:16 PM on July 19, 2014 [5 favorites]

gemutlichkeit, those are amazing! Thanks! Demaine has written about the history of curved origami scupture, and here's a review with some information on "elephant hide" paper, a favorite medium for the more complex curved shapes seen in Demaine's portfolio.
posted by filthy light thief at 9:00 PM on July 19, 2014

Between the Folds is a wonderful documentary about what I guess you could call "Advanced Origami".
posted by Rumple at 9:05 PM on July 19, 2014 [6 favorites]

Hah! The hotlinked schematic in the OP is from my blog; here's a picture of my partner opening and closing a miura-folded panel of tyvek:

Dr. Miura never attempted to pursue a patent on the fold, because he felt that as a type of origami fold it belonged to that ancient tradition and was in some way not appropriate for one person to control the rights to it. IIRC he did patent a form of the Miura fold where its rotated around a cylinder like so: which makes the can very easy to crush.

Shameless plug: a Miura-folded map of San Francisco that I designed is for sale here:
posted by wheatpond_ at 9:12 PM on July 19, 2014 [12 favorites]

Keen, thanks for the info, wheatpond_! Sorry for nicking the pic - it was in an unimpressive Lifehacker post (which linked to a non-Muira fold YouTube video, among other things). Here's the blog post on your site with the diagram embedded.
posted by filthy light thief at 9:40 PM on July 19, 2014 [1 favorite]

I really liked Lang's page about this, the origami-folded Eyeglass Telescope.
posted by Joe in Australia at 9:40 PM on July 19, 2014 [1 favorite]

Here's the original paper by Koryo Miura detailing the miura fold and some applications. The figures are really beautiful:
posted by wheatpond_ at 10:29 PM on July 19, 2014 [1 favorite]

"here's a picture of my partner opening and closing a miura-folded panel of tyvek:"

That is so hypnotic! I could watch the paper opening and closing for ages. Also, I am now in your power.

Amazing that this is used for both Solar Panels and Maps. I have wondered before about how a map is folded: it always seemed a really neat and clever piece of, well, maybe topology but I am not sure if that is the right word.
posted by marienbad at 2:49 AM on July 20, 2014

That's neat---I'd not seen that fold before.

On the other hand, using a fold like that with only two states (open and closed) for something like a big city map seems like it might be impractical in, say, the cramped environment of a passenger seat.
posted by leahwrenn at 7:45 AM on July 20, 2014

A conventional accordian map fold also has the advantage of making the legend available irregardless of fold state.
posted by Mitheral at 7:56 AM on July 20, 2014

The Miura fold ("Miura-ori") has a long history in the field of spaceflight, where by that I mean "a lot of people have talked about using it in spaceflight for a long time."

The example I am familiar with is for stowing and deploying thin membranes for solar sails and other applications. You'll recall that the Japanese IKAROS spacecraft, the first to demonstrate solar sailing by doing a Venus flyby, was propelled by a sail stowed in a compact volume. IKAROS is an amazing and sophisticated spacecraft for several reasons, but it doesn't use the Miura fold.

The problem arises in reversing some of the creases in the later steps - something paper does very well, because the fibrous structure partially fails along the crease and encourages the reverse crease to follow the same path. However, solid polymers aren't made of fibres; instead, they have a different microstructure that takes a stiff permanent set when it is deformed by a crease, making the reverse crease harder to form and much uglier than the first. That means large Miura-folded polymer membranes must use a different folding technique than the one used for small paper ones. The process is much more laborious, and the results are much more finicky to re-stow once deployed. Which matters, because these things take so long to fold that you really don't want to have to throw them away each time. Unlike the paper versions, which smoothly transition between the deployed state to the stowed state, the intersections between creases in the polymer versions pop back and forth exactly as they "should not do." (Maybe this isn't the fold's fault. Maybe we're just doing it wrong.)

In my own lab, where I am part of a team building a deployable sail for an upcoming space mission, one of the engineers experimented extensively with Miura-folded membranes and produced a fair number of prototypes. They work, but as the size of sail grows the number of individual creases to manually reverse goes up as the square of the side length. Takes hours to fold a sail measuring just metre on a side. Plus, they want to be stowed in a particular shape in order to deploy properly; they're harder to pack in an arbitrarily-shaped volume. These things matter. We still can't see a way to make it work. In the end we just fold the fucking things back and forth in two directions, like a regular shitty old road map. Works fine.

Other researchers building deployable sails at this scale seem to have reached the same conclusion. Many people do a single accordion fold and wrap them around a spinning hub. Some people go with two orthogonal sets of accordion-folds like we do, and pull the fucker out haphazardly, which by the classical understanding of paper folding mechanics (I'm told) "should not work." Even randomly folding the membranes, just shoving them the fuck in there, is more workable than some more structured alternatives. It seems to be a counter-intuitive quirk of some flexible materials (certain ropes, for instance) that if you carefully roll or fold them into a compact volume and then pull them out they tend to get knotted and tangled; but if you just let them pack together as they seem to "want" to do, then they unpack just fine. Takes more volume, yes; but at least it's not going to fuck up when you're thousands of kilometres away and can't go tug on it in just the right spot.

I guess what I'm saying here is that the Miura fold is cool, but that in my experience it's proven to be much more complicated that it first appears. Ironic that something superficially flexible can be somewhat rigid.

(Obviously, "citation needed" for just about every thing I've said. Maybe I'll come back and add them in another comment, but technically I should be writing my thesis about this exact same topic at this very moment so basically I'm just procrastinating here.)
posted by Verg at 8:41 AM on July 20, 2014 [13 favorites]

Do you know if adding hinges would alleviate the problem or is that nixed for other reasons?
posted by Mitheral at 9:52 AM on July 20, 2014

I love MetaFilter for threads like this: someone finds something neat and shares it, and other members who have personally worked on the topic join the discussion.

More on the diverse applications for origami: Know How to Fold 'Em: How Origami Changed Science, From Heart Stents to Airbags (LA Times, Apr 26, 2012) -- an article on origami, and specifically the Japanese American National Museum exhibit, Folding Paper.
posted by filthy light thief at 8:00 AM on July 21, 2014 [1 favorite]

20 minutes later I now have 3 shitty attempts at a Miura fold, and one halfway decent Miura fold sitting on my desk. Great post!
posted by DynamiteToast at 1:36 PM on July 21, 2014 [2 favorites]

Mitheral: Short answer; yes. But that's better suited to rigid solar panels rather than flexible membranes. There's one example of a Japanese spacecraft that did just that; but good pictures are hard to find.

While we're on the topic of hinges, remind me to tell you some day about another innovative space mechanism that can be made using everyday materials.

Promise I'll come back soon with citations.

...20 minutes later I now have 3 shitty attempts at a Miura fold, and one halfway decent Miura fold...

SEE?? SEE!!?
posted by Verg at 7:06 PM on July 21, 2014

While we're on the topic of hinges, remind me to tell you some day about another innovative space mechanism that can be made using everyday materials.

Today. Today would be a good day...
posted by leahwrenn at 6:51 AM on July 27, 2014 [1 favorite]

As promised! (Forgive me while I am a bit lazy in terms of creating in-text hyperlinks.)

The evidence suggests that IKAROS does not use Miura folds. This image appears to show a two-stage deployment process, with the second stage consisting of something like an accordion fold:
The Planetary Society published a blog post with links to primary sources pertaining to the IKAROS deployment. There is no Miura fold in sight. The folks at the university of Surrey (and one of their spinoff companies, apparently) have been kind enough to publish an overview of folding methods:
Both these sites state that the IKAROS sail is called a "folded hyperbolic paraboloid"... which, if you look closely, is similar to a Miura fold but not the same. They reference a paper that talks about the fold in question:
"Deployable membranes designed from folding tree leaves"
If you can access it, it is a fairly clear paper that has some good illustrations.

The Space Flier Unit (SFU) mission included the 2D Solar Array experiment (2DSA), which appears to consist of a Miura-folded composed of rigid panels.
This site shows the only picture I can find of the array:
This page has an illustration of a "sun paddle Test Satellite," which may or may not be the same spacecraft.

The sail on the SPROUT spacecraft appears to use a Miura fold, but it might also be one of the leaf folds...
It was launched recently, but I don't think any results have been published yet:

Finally, on the subject of space mechanisms made from everyday materials; some hinges can be made using "tape springs," which are simply carpenter tapes or tape measures. Here is one paper that describes a rolling hinge made using tape-springs:
They do not need bearings or lubrication, which makes them useful in space.

Tape springs have other applications as deployable booms and antennas, but I think I will leave that for another comment or post.
posted by Verg at 12:41 PM on August 12, 2014

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