Mobius Strip Solid

[Moesian]

Hi

Im using AutoCAD2004 and was wondering if there was anyway I could make a solid Mobius Strip, Ive seen a post about making a mobius mesh, is this all ill need to make a mobius solid or is it going to be more complicated.

Thanks

Heres the link to the Mobius mesh post

http://www.cadtutor.net/forum/showthread.php?t=471

[fuccaro]

The Mobius strip is a … strip. The best approach is to model it with a surface without any thickness. It could be done as a thin solid as in this image, but how thin should it be?


Changing parameters (the thickness) you will get something different. Do you think that this is a Mobius strip too?


Or how about the solid in this last image? It is almost a Mobius strip -just it is completely different.

The lisp is HERE

[CADTutor]

Great work Fuccaro. Once we get some feedback on this, I'll add it to the LISP Archive.

[Moesian]

Thanks alot, perfect!

[fuccaro]

Glad to help!
Just curious: what is it good for a solid Mobius?

[Moesian]

Im trying to make a mobius strip lego set thing. Basically I want to have sections of mobius strips to create sculptures. Although I am having problems on deciding how to divide them ( i though an 8th of a strip would have enough info to piece together the whole strip, would be interested to know if you could offer any help on that one). Eventually i shoud have six pieces which should put together six different strips (1,2,3,5,8 and 13 twists), Ill have them printed and then take casts and should then be able to make like resin lego bits out of them and piece them together into all kinds of different ways. Dont know if that makes any sense (can post some draft pics if your interested).

Thanks again

P.S would be interested to know if you think that a whole strip could be created by taking an 8th of a strip and then repeating it eight times, would be good to have a second opinion before I pay to have the things made.

[fuccaro]

Moesian

In a top view of a Mobius strip you may define say N radial slicing planes. All the pieces are identical. Having N identical pieces it is possible to rebuild the strip.
If the strip twists twice (or more times) and you slice it also in N (identical) pieces you get also identical pieces but they are different as the pieces of the once twisted Mobius. Putting them together you will get a twice-twisted strip. It is not possible to build from the same parts single and twice-twisted strips.
But if you accept small errors, probable the pieces used to build a say 5 time-twisted strip are good for a 6 time twisted strip too –especially if you sliced the initial solid in more pieces.
I think you should try on the computer first to see how the pieces are linked together. This is why computers and CAD programs exists

[fuccaro]

I hope it is not too late.
The pieces I mentioned in my previous post are identical only in particular cases.
As I wrote: try first on your computer if the model is as you dreamed it.

[Moesian]

Fuccaro wrote:

"The pieces I mentioned in my previous post are identical only in particular cases."

Hi, been busy so haven't been able to get the pieces made, just started thinking about it again. You dont happen to know which particular cases the components are identical?

[fuccaro]

Sorry for the delay, here is my opinion:
Let’s consider a Mobius strip with the vertical axis AB and a plane trough this axis. If we cut the strip with the plane we get the cross section showed in the next image.


If the strip rotates (arrow 1) the cross section rotates too (arrow 2). To obtain identical parts you must rotate the strip until the cross section will be in the same position as at the previous cut.
If the cross section is a rectangle you are out of luck: it must be rotated with 180%%d. For a square like cross section you will have the same position after a rotation with 90%%d.
If the strip is twisted with 180%%d, as the real Mobius strip is the cross section rotates with 180%%d for a whole rotation of the strip (360%%d). With other words: you can section the solid twice if the cross section is a square and only once if it is a rectangle.
This is a theoretical number. If you will make two times more equidistant cuts the parts are still identical (to be more precise: symmetrical) but half of the pieces will have the joints on one side and the other half on the other side.
In conclusion: you will have more pieces if the solid twists more time and if the cross section is a polygon with more sides.