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Reuleaux Triangle Spheroforms [message #11301] Thu, 01 April 2010 02:07 UTC Go to next message
avatar ualrkids  is currently offline ualrkids
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This is my first order from shapeways. These are reuleaux trianlges(commonly used in rotary engines) rotated about one of its vertices. The interesting property of this shape is its ability to roll just like a sphere, meaning that it has a constant width regardless of orientation. I am very pleased with the results.


index.php?t=getfile&id=3131&private=0


index.php?t=getfile&id=3132&private=0


Sorry for not giving any sense of the scale. They are about the size of a quarter. Here is a link to my shop: http://www.shapeways.com/shops/greatgeometers.

[Updated on: Thu, 01 April 2010 12:21 UTC]

Re: Reuleaux Triangle Spheroforms [message #11327 is a reply to message #11301 ] Thu, 01 April 2010 14:57 UTC Go to previous messageGo to next message
avatar RalphVdB  is currently offline RalphVdB
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HI ualrkids

i actuality saw this model, but i was wondering what it was for. Now i know, enjoy your models Wink


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icon14.gif  Re: Reuleaux Triangle Spheroforms [message #11349 is a reply to message #11327 ] Fri, 02 April 2010 00:45 UTC Go to previous messageGo to next message
avatar gibell  is currently offline gibell
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Very cool!! Nice idea!

How about making them larger, and hollow?
Re: Reuleaux Triangle Spheroforms [message #11350 is a reply to message #11301 ] Fri, 02 April 2010 01:00 UTC Go to previous messageGo to next message
avatar rawkstar320  is currently offline rawkstar320
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rotary engine eh?
You should consider making a replica rotary engine. That would be awesome. I would probably do it...except that I am really super busy haha.
Check out my shop when you get a chance, I have a model RC Engine and a 3 Speed Transmission. I really want to revisit the transmission project to make it work correctly.....

Anyways, those are pretty awesome!

good luck !!


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Check out http://JakeDrews.Com and http://WondrousWidgets.Com for more designs by Jake!
Re: Reuleaux Triangle Spheroforms [message #11351 is a reply to message #11349 ] Fri, 02 April 2010 01:49 UTC Go to previous messageGo to next message
avatar ualrkids  is currently offline ualrkids
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I am planning on doing that. These were really just a proof of concept. I wanted to make sure they were precise enough to maintain there physical properties (constant width). I created them using Maple 13, and I'm not sure how to make hollow objects with it. I have some idea, but I'm not really familiar with any 3d modelling tools. I actually made others with more sides, and they also have a constant width. Here's a link to a video that illustrates why they are special.

http://www.youtube.com/watch?v=jYf3nOYM_mQ&feature=relat ed

Re: Reuleaux Triangle Spheroforms [message #11352 is a reply to message #11301 ] Fri, 02 April 2010 02:21 UTC Go to previous messageGo to next message
avatar Ushanka  is currently offline Ushanka
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It should be pretty straightforward to hollow those out using just Meshlab! I could help out if you want.

How well do they roll?
Re: Reuleaux Triangle Spheroforms [message #11353 is a reply to message #11352 ] Fri, 02 April 2010 03:52 UTC Go to previous messageGo to next message
avatar ualrkids  is currently offline ualrkids
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They actually roll very well. I only ordered two so it makes difficult to keep the book level. If I had three it would make the rolling a lot smoother because I wouldn't have to keep the book perfectly level myself.
Re: Reuleaux Triangle Spheroforms [message #11360 is a reply to message #11301 ] Fri, 02 April 2010 14:53 UTC Go to previous messageGo to next message
avatar gibell  is currently offline gibell
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That video is really cool! Three of them, LARGE, in stainless steel would make for a really unusual coffee table base.

I managed to create one that is hollow (see screen shot below). Let me know if you need any help with this.

index.php?t=getfile&id=3143&private=0

  • Attachment: Reuleaux1.jpg
    (Size: 112.19KB, Downloaded 1690 time(s))

Re: Reuleaux Triangle Spheroforms [message #11361 is a reply to message #11360 ] Fri, 02 April 2010 14:58 UTC Go to previous messageGo to next message
avatar ualrkids  is currently offline ualrkids
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Do they have to have a hole, or is there a way to make it hollow without one?
Re: Reuleaux Triangle Spheroforms [message #11362 is a reply to message #11361 ] Fri, 02 April 2010 15:07 UTC Go to previous messageGo to next message
avatar gibell  is currently offline gibell
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ualrkids wrote on Fri, 02 April 2010 14:58

Do they have to have a hole, or is there a way to make it hollow without one?


Unfortunately, to be hollow it has to have a hole, or the support material can't be removed. I put the hole in the top where the surface is flattest. But it still might affect the rolling ...
Re: Reuleaux Triangle Spheroforms [message #11363 is a reply to message #11362 ] Fri, 02 April 2010 15:44 UTC Go to previous messageGo to next message
avatar ualrkids  is currently offline ualrkids
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The top and the bottom could be separate pieces, and then they could either thread together or interlock in some way, so the rolling would be unaffected.
Re: Reuleaux Triangle Spheroforms [message #11364 is a reply to message #11301 ] Fri, 02 April 2010 15:45 UTC Go to previous messageGo to next message
avatar rawkstar320  is currently offline rawkstar320
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you could alwasy fill in the hole, or have several small holes that you fill.

Depending on the size (if its stainless) you might be able to fill the holes with solder or something? Sand it smooth, and you should be good to go.

Of course, i dont know how easy it is to solder the stainless...but it seems like it might work.

Coffee table idea: Awesome. I would deff like to see that one made a reality.


Aut Viam Inveniam Aut Faciam
Check out http://JakeDrews.Com and http://WondrousWidgets.Com for more designs by Jake!
Re: Reuleaux Triangle Spheroforms [message #11424 is a reply to message #11301 ] Sun, 04 April 2010 22:59 UTC Go to previous messageGo to next message
avatar Ushanka  is currently offline Ushanka
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If it's made of one of the strong/flexible materials or Sandstone, then yes, there needs to be a hole in the model. But you don't need a hole for the white/black/transparent detail materials or for grey robust! Those can be hollow and have no escape hole.
Re: Reuleaux Triangle Spheroforms [message #13096 is a reply to message #11424 ] Sat, 22 May 2010 21:19 UTC Go to previous messageGo to next message
avatar gibell  is currently offline gibell
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I made some of these on my own. Mine are 3cm in diameter, they are hollowed out but I tried to do something clever to avoid a bump or flat spot when they are rolled over the hole.

index.php?t=getfile&id=3644&private=0

It's interesting to place these between two books or boards and shift or spin the top board. It feels just like there are marbles rolling between them!

index.php?t=getfile&id=3643&private=0

You can see lines in these in certain directions. This happened because the print orientation was not as I had planned, they got flipped 90 degrees for some reason.

index.php?t=getfile&id=3645&private=0

Here is a link to this model in my shop.

Re: Reuleaux Triangle Spheroforms [message #13129 is a reply to message #11301 ] Mon, 24 May 2010 12:46 UTC Go to previous messageGo to next message
avatar Youknowwho4eva  is currently offline Youknowwho4eva
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The green one looks like a pentagon in the picture, but when I think of the shape, I don't see how it would turn into a pentagon. It hurts my head a little Razz. Very awesome idea, I'll have to catch up on rotaries, I've only briefly looked it up a while ago.


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Re: Reuleaux Triangle Spheroforms [message #13145 is a reply to message #13129 ] Mon, 24 May 2010 21:45 UTC Go to previous messageGo to next message
avatar Ushanka  is currently offline Ushanka
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Youknowwho4eva wrote on Mon, 24 May 2010 12:46

The green one looks like a pentagon in the picture

That's because it probably is a pentagon Razz

You can make solids of constant width by rotating any Reuleaux polygon: reuleaux triangles, reuleaux pentagons, reuleaux heptagons...
Re: Reuleaux Triangle Spheroforms [message #13146 is a reply to message #13145 ] Mon, 24 May 2010 21:54 UTC Go to previous messageGo to next message
avatar gibell  is currently offline gibell
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Yep, all 3 are different. Blue = Reuleaux triangle, orange = rounded Reuleaux triangle, green = Reuleaux pentagon. Each one is just these 2D shapes turned on axis, making a 3D "solid of revolution". The green one looks a lot like a muffin!!

I want to make a Meissner Tetrahedron, but I can't quite figure out its shape from the descriptions.
Re: Reuleaux Triangle Spheroforms [message #13163 is a reply to message #11301 ] Tue, 25 May 2010 13:10 UTC Go to previous messageGo to next message
avatar Youknowwho4eva  is currently offline Youknowwho4eva
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I find wikipedia is good for shape dimensions http://en.wikipedia.org/wiki/Reuleaux_tetrahedron


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Re: Reuleaux Triangle Spheroforms [message #13655 is a reply to message #11301 ] Mon, 14 June 2010 03:47 UTC Go to previous messageGo to next message
avatar ualrkids  is currently offline ualrkids
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I wrote a paper on the physical properties of these objects. Thought you all might be interested.

Re: Reuleaux Triangle Spheroforms [message #13656 is a reply to message #13146 ] Mon, 14 June 2010 04:20 UTC Go to previous messageGo to next message
avatar ualrkids  is currently offline ualrkids
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This is the best description I could find, and I couldn't think of a way to make it out of functions in Maple. Maybe you will have more luck.

[Updated on: Mon, 14 June 2010 04:21 UTC]

Re: Reuleaux Triangle Spheroforms [message #13681 is a reply to message #13656 ] Mon, 14 June 2010 22:14 UTC Go to previous messageGo to next message
avatar Ushanka  is currently offline Ushanka
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ualrkids: Thanks a ton for those papers! I had seen papers before on the construction of Meissner tetrahedra, and all of them mentioned "rounding," but this is the only one I've seen that actually explained the process clearly. I don't know about Maple, but I made models of both Meissner tetrahedra in Solid Edge in about an hour.

Next challenge: an open-source Gömböc model! Any tips?

[Updated on: Mon, 14 June 2010 23:31 UTC]

Re: Reuleaux Triangle Spheroforms [message #20190 is a reply to message #13681 ] Sun, 07 November 2010 15:09 UTC Go to previous messageGo to next message
avatar gibell  is currently offline gibell
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Thanks to clsn aka Mark Shoulson, I printed out two of his Meissner Tetrahedrons. He designed the objects using Blender such that they had the same width as my Reuleaux Spheroforms (3 cm). I now have 5 solids of constant width to roll with.

Here are some photos of the new solds, and then all 5 of them. I've found the best demo is to put 3 of them on a table and then cover them with a glass plate. This way you can see them rolling around underneath.

index.php?t=getfile&id=5815&private=0

index.php?t=getfile&id=5816&private=0

index.php?t=getfile&id=5817&private=0

index.php?t=getfile&id=5818&private=0

index.php?t=getfile&id=5819&private=0

Re: Reuleaux Triangle Spheroforms [message #20202 is a reply to message #20190 ] Sun, 07 November 2010 19:08 UTC Go to previous message
avatar clsn  is currently offline clsn
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Wow, excellent! Thanks for the pics, gibell! (I still haven't ordered the Meissner solids myself). I've been pondering/tinkering with ways to improve on them, to make the shapes smoother, etc., but looking at the pictures I may not need to. Looking forward to getting a set of all five myself.

 
   
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