Platonic Solid Vertices
by WilliamAAdams, published
Description
This derivative thing just makes a few 'improvements' to the original design.
First of all, I've modularized the code somewhat. This doesn't make any particular improvement, but it will make it easier to see what's going on, and how to add to it in the future when more vertices are needed.
Second, being the slave to phi (1.618) that I am, I changed things like the thickness of the connector to be proportional to the radius of the rods that you're using (instead of a fixed value).
I've also made a change such that the length of the connector is automatically calculated proportional to the length of the rods that you're using. The base size is 10mm, and it grows by an appropriately 'phi' influenced length. So, the ones for a 36" rod, for example, are closer to about 20mm, rather than 10mm.
With these changes, it becomes rather trivial to make good new connectors for any size, by just changing the single diameter value, and the rod length.
I've played with a lot of vertex designs over the past few months. This is one of the most compact, and easy to utilize. I give props to Sjoerd de Jong for the simplicity of the design.
In the picture, the struts are 36" long. The overall height of the structure is about 8'. With this design, the fit is strong enough that you can actually assemble the thing with one person. If you've ever done dome development, you might recognize this is a 'good thing'.
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This design works fairly well. With that big one in the picture, the oak dowels have enough bend that the thing is 'bouncy', but it does not fall apart.
If you had some bracing strut/chord thing, it would become very stable.
At smaller sizes, and using aluminum or carbone fiber, I'm sure it would be very stiff, if still weak from a vertical loading perspective.
really beautiful work; need to print out a set of these! i like how you integrate the golden ratio into your designs for pleasing proportions. beyond phi, some other good ones i know of are 1.414
&
amp; 1.732
I think I need a good book on doing vertex math for solids.
My non-math solution thus far has been to construct simple vertices which have the ability to rotate their joints. That saves my brain from having to steam up.
One thing I really like about your design work is that you did in fact do the maths. I was thinking it would be good to add in the '2v'
form as well, just to make structures that much more interesting.
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Instructions
2) Put in the appropriate rod radius (in millimeters)
3) Print out enough vertices to achieve the job
4) Slip rods into the appropriate places
5) Rejoice!
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Thanks William for this great update. You really enhanced the scad file; now I can even understand my own code ;)
Maybe it's important to say that, except for the tetrahedron connectors, it's easiest to print the connectors upside down.
I did some math on connectors for http://en.wikipedia.org/wiki/A.... The angles for these connectors are a lot more complicated though. Can you figure out how to make a http://en.wikipedia.org/wiki/T... for instance? It's a nice math challenge! O:-)
I think I need a good book on doing vertex math for solids.
My non-math solution thus far has been to construct simple vertices which have the ability to rotate their joints. That saves my brain from having to steam up.
One thing I really like about your design work is that you did in fact do the maths. I was thinking it would be good to add in the '2v'
form as well, just to make structures that much more interesting.
really beautiful work; need to print out a set of these! i like how you integrate the golden ratio into your designs for pleasing proportions. beyond phi, some other good ones i know of are 1.414
&
amp; 1.732
This design works fairly well. With that big one in the picture, the oak dowels have enough bend that the thing is 'bouncy', but it does not fall apart.
If you had some bracing strut/chord thing, it would become very stable.
At smaller sizes, and using aluminum or carbone fiber, I'm sure it would be very stiff, if still weak from a vertical loading perspective.