30-degree knee joints in square tubes (Umulius variation)

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30-degree knee joints in square tubes (Umulius variation)

Postby PhizzFan » February 28th, 2017, 10:00 pm

Hello all,

This is my first post, so I hope it it is going in the right place, etc... thanks for bearing with me.

My current goal is to try to fold the variation of Umulius Rectangulum by Tjips posted here:
https://www.flickr.com/photos/tjips/190120620/in/faves-13245763@N00/
He calls it Umulius Dodecanum. I have sent a few emails reaching out to ask different folks about CPs (posted to this forum in the past) and diagrams but no luck so far.

I have successfully and comfortably folded the regular Umulius Rectangulum 5-6 times, no problem.

Instead of asking for the exact thing I want (diagrams) which doesn't seem to be available, I am asking here for any advice or resources more generally for the type of fold that is different in the Dodecanum from the Rectangulum. I've been working on the problem bit and I think If I knew how to do a single 30-degree knee joint in a square tube, I could work out the rest. Any help appreciated....

-Rafael
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Re: 30-degree knee joints in square tubes (Umulius variation

Postby mkosmul » March 4th, 2017, 9:03 am

The best way to approach this would be by analyzing the crease pattern. This one is simple since there is little overlap between different layers. Fold one 90-degree bent, unfold it, and trace the crease lines with a pencil. You will see a pattern which is typical for models of this kind: there's a line perpendicular to the longer axis of the paper, and two diagonal 45-degree lines which exit from the vertices of the frame, and then another line perpendicular to the paper's edge. The CP here is for a modular frame, but the knee looks just the same: https://www.flickr.com/photos/kosmulski ... ed-public/. The CP will be even simpler if you only want a frame without the extra slit which the frame has.

Now, think what will happen when you go from a 90 degree bend to another angle. Instead of 45 degrees, the diagonals will be half the angle of the bend. You can try it out by folding some other, arbitrarily picked angle instead of 45 degrees when you start collapsing the knee. The change in angle will then shift the other parallel crease along the length of the paper. And that's basically it. If you want a precise CP, it will probably be easiest to draw in Inkscape or another vector graphics program since it will allow you to rotate lines to exactly the angle needed, and then to snap other lines precisely to the intersection points. An of course, you need just 4 90-degree bends to close a full loop, and with an obtuse angle, you will need more bends to go the full round.

So, in summary: the CP will be very similar to that of the rectangular frame, but the diagonal segments will be at a different angle, the parallel lines shifted accordingly, and there will be more bends in total.
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Re: 30-degree knee joints in square tubes (Umulius variation

Postby PhizzFan » March 7th, 2017, 3:52 pm

Thank you! This is very helpful and is also more or less where I had gotten myself in the thinking process in the time between when I posted and now. It gets me to a place where I could more or less get the project done with time, trial and error, a protractor, etc...

I am realizing that part of my implicit question was actually about different kinds of models: Type 1 can be folded using diagrams, Type 2 can be folded only with CP, protractor, etc... (there is probably already good terminology for this distinction and I just don't know it...anyone?)

When I said in my original post: "If I knew how to do a single 30-degree knee joint" I meant via diagram. I was hoping (without saying/realizing it) that the Umulius Dodecanum was Type 1, but maybe that is just not the case and the only way to really get it done is trial and error, protractor, calculator, etc....
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Re: 30-degree knee joints in square tubes (Umulius variation

Postby mkosmul » March 10th, 2017, 6:31 pm

30 degree angles can be constructed easily using pure origami - see for example Francis Ow's 60-degree unit or any other model that uses 30- or 60-degree angles.
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Re: 30-degree knee joints in square tubes (Umulius variation

Postby Andre-4 » June 11th, 2017, 8:13 pm

PhizzFan wrote:Hello all,

This is my first post, so I hope it it is going in the right place, etc... thanks for bearing with me.

My current goal is to try to fold the variation of Umulius Rectangulum by Tjips posted here:
https://www.flickr.com/photos/tjips/190120620/in/faves-13245763@N00/
He calls it Umulius Dodecanum. I have sent a few emails reaching out to ask different folks about CPs (posted to this forum in the past) and diagrams but no luck so far.

I have successfully and comfortably folded the regular Umulius Rectangulum 5-6 times, no problem.

Instead of asking for the exact thing I want (diagrams) which doesn't seem to be available, I am asking here for any advice or resources more generally for the type of fold that is different in the Dodecanum from the Rectangulum. I've been working on the problem bit and I think If I knew how to do a single 30-degree knee joint in a square tube, I could work out the rest. Any help appreciated....

-Rafael

David Mitchell is an origami master who has a really interesting web page With a comprehensive index
YOU could take a Look At his Borromean module ,also his Omicron
http://www.origamiheaven.com/modularthirdsandfifths.htm
Another approach would be To assemble a sonobe ,from a rectangular base But not As 12 Or 30 but there are some designers Who used the 30° ....If you know Ekaterina Lukasheva page.....she exhibits one Or two 24 piece modules and 8 piece that look cubist With the angles required
https://www.google.co.uk/search?client= ... gAag3YOYDg
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