Fold a 2x1 rectangle to a line, locked, with a fixed edge

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Cadix
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Fold a 2x1 rectangle to a line, locked, with a fixed edge

Post by Cadix »

I'm not sure this is the right forum, but...

I'm trying to figure out if there's a good way to fold a 2x1 rectangle into a line where one of the short sides of the rectangle is fixed in place.

Image

So in this case, the red edge is the edge that is fixed in place and can't move. The rest of the paper, colored green, wants to get as small as possible and be locked that way. The more uniform the thickness and shape, the better.

It seems like this shouldn't be particularly difficult, but I'm drawing a blank.

Thanks :-)
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Gerardo
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Re: Fold a 2x1 rectangle to a line, locked, with a fixed edge

Post by Gerardo »

And must it keep the same width?
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Re: Fold a 2x1 rectangle to a line, locked, with a fixed edge

Post by Cadix »

Gerardo wrote: March 7th, 2022, 6:54 am And must it keep the same width?
It's probably important that the width doesn't change. Ideally, it'd stay a straight line as well. So think of the red line as a steel bar glued to the green paper along the short edge. I'd still be interested in ideas that caused it to bend, but probably not shorten.
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Re: Fold a 2x1 rectangle to a line, locked, with a fixed edge

Post by Cadix »

So I've got a prototype for one idea...

Image

Image

The raw edges seems to be correct, but I need to test it "in production" and make sure :-)

It's also not exactly perfect. An outer layer is not locked down. But, in theory, at the limit, the whole thing goes to a line. So that's pretty good :-)
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Re: Fold a 2x1 rectangle to a line, locked, with a fixed edge

Post by Gerardo »

You might also be able to create a type of tab from the middle of the paper if you use pleats. Then, maybe you might be able to roll the strip–or fold it in zigzag manner, to pack it down–and use the tab somehow to lock it together. It's just a very rough idea... not sure if it could work.

So what's all this for, Cadix :)?
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Re: Fold a 2x1 rectangle to a line, locked, with a fixed edge

Post by Cadix »

So... here's the short version (hopefully it's enough to make sense) :-)

So I've developed a split. Kinda like the Elias stretch in function, but it distributes paper differently, and locks. I can use it to make things like:

Image

More generally, I can create as many squares as I want, all connected at a point (the connections can be elsewhere on the squares).

So if I can take the first image and turn it into:

Image

I now have squares connected by "threads" (at the limit).

From these I can fold any model as usual. If the connection to the neighboring square is inside the model, the thread can, in theory, wind its way out. So... mathematically, at the limit, I have a straightforward way of folding any number of arbitrary models from a single rectangle. In practice, of course, if the added layers or thread make things too bulky, the model might look quite awful :-)

I did just have a bit of a break through that makes the "threads" potentially much less bulky or at least easier to lock.

Note, all of this is possible with the Elias stretch, but in practice there are some differences that make my split more beneficial to this project. For box pleating... not so much ;-)
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Re: Fold a 2x1 rectangle to a line, locked, with a fixed edge

Post by Cadix »

Actually... the Elias stretch might work BETTER for this o_O

It would naturally and easily create a thin bridge between two squares. If I could lock it, it might be near perfect. The one question mark is the distribution of paper. The squares would have rather thick edges. But I'll have to try it. It might be as good or better! And Lang has already used is to create his rock-scissors-paper: https://langorigami.com/artwork/rock-paper-scissors/ (or at least I think he did something similar there...).
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Re: Fold a 2x1 rectangle to a line, locked, with a fixed edge

Post by Gerardo »

Sounds really interesting! Let us know how it goes.
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