Interlocked shapes

Hi,

This is my third (and last) post in this section about the objects I received on Friday. There is more to show, but I will probably post about the other objects later, in other sections (problems of design or problems of printing).

I really like interlocked shapes, and I guess 3D printing is one of the best way to actually create them.

So to begin, here are two Brunnian (or Borromean) links.
First the famous Brunnian rings or Brunian circles (seen in the coat of arms of the Borromeo family).

Such an interlocking cannot be obtained with standard rings, so I cheated a little bit by giving them a kind of ondulation. All the 3 rings have the same shape and have a nice symmetry (I put the ondulation even where not necessary to keep this symmetry).

The property of all brunnian links is that that even though the 3 links are interlocked, no two of them are actually linked: as a consequence, if you remove (break) just one of them then the two other ones will fall apart.

The Brunian links with each link having an ellipse shape have the same topology as the previous one but don't required any trick.

It is an interesting object to play with.

And last but not least, I am really happy to have received the Dod'net: it is a network of interlocked dodecahedra.
The printing is just FANTASTIC: there is no defect. It is just perfect.

Here are some details.

Of course it is probably very fragile (I did not try to stress it), but I am amazed that such a structure could be printed and arrived with no damages!
Congratulation to all those who manipulated it without breaking it (including myself )!

In order to see these objects in action, I added a video of the two Brunnian models and of the Dod'Net on my channel at YouTube.
Enjoy!

I wonder if you could add some kind of cut that would allow the rings to be disconnected? Something like a carabiner gate used for rock climbing? The flexibility of WSF could help you out here.

That's a good idea, and only one cut on one circle should be enough. Unfortunately, it is not so easy, since the special shape of the rings prevent them from rotating: so it would be impossible to position the cut to a particular place (the cut is stuck to its initial position).
I have to think about it: perhaps it could be done by modifying the design, with for instance one of the ring being planar?

O.K. wow. The explanations make threads more interesting than just pictures especially for we not-so-mathematically/spatially-minded.

Hey bud,

I was so fascinated by your object that I had to copy it and build my own.



And another one I'm tinkering with, 5 equilateral triangular pyramids intersecting (stl at bottom of post);

That's incredible where fascination can lead to!
Actually, your design seems a little bit different from mine: the thickness seems different depending on where you are along the ellipse, while mine has always the same section. Or perhaps is it an illusion due to the camera?
Anyway, the links look great in Blue Jeans.

I also like the five interlocked tetrahedra (I have seen in another post that you also have a multicolored version that is even more beautiful).

By the way, I have designed a new shape made of interlocked "rounded stars".
I will show it as soon as it arrives. Stay tuned!

Okay, I've had a question about interlocking shapes being printed and I guess this is a good place to ask it: How do you design it in the computer - for example are the sides touching with very very small tolerances so that the printer can't actually reproduce the touching sides, or are they sent to the printer as objects with no sides touching? Hope, I made myself clear there :confused

No side touching. At the contrary, you must keep some minimal distance between the different parts to avoid they get fused during printing.
This distance depends on the area that is in "quasi-contact". The larger the area, the larger the clearance.

If I had to give some values, I would say that:
- 0.5 mm is probably the minimum for Detail Material
- 0.75 mm the minimum for Strong and Flexible material.
- 1 mm should be safe whatever material.

Please if someone has a different experience, do correct my statements.

Thanks very much for the reply. That has cleared things up for me.

are these possible in metal? it isn't clear with the latest metal design rules...

Unfortunately no. Silver no way, stainless used to but no more. The pieces are just too fragile in their green stage. You could make them connected with a sprue that you could then cut off when you receive it.

how thin / thick a sprue would be necessary for this to work?

Hi smiteo,

First off...

Welcome to Shapeways!

re: support sprue sizing... the size of the sprue would depend upon the dimensions of the part it is supporting. You can find the base stainless steel design rules here, but if you want to ignore those and push the boudaries, the advanced stainless rules are here. Also, see the design rules for Silver for silver info, in particular, check out Duann's ring that broke with 0.7mm wires.

Have Fun!

Paul

given the example design Brunnian Links, say 5cm x 8cm (1cm thick), would the design work with spurs connecting the three links of 0.7mm? 1mm? this material is just going to be dremel'd off afterwards...

No, because the only materials that support a 0.7mm wire structure are WSF, FD and FUD.

With the dimensions you give, you'd be looking minimum 2mm for stainless and probably around 1.2mm for silver (I've not got any real experience with silver, but this is my 'educated guess' as the dimensions are really for 3D printed wax that is invested and cast)... you need to start thinking along the lines of material volume and supported material mass - there's no real hard and fast answer unless someone has done it already.

I'd say no with silver, even with sprues.