Divisible Möbius strip

Lego Divisible Möbius strip

Divisible Möbius strip


This is a follow-up of the Möbius strip, and is also inspired by a MOC made by LegoOri at Rebrickable.com. LegoOri gives a very good video introduction to the qualities of a Möbius strip. One of the things he shows is that when you split a Möbius strip it stops being one. Suddenly it has two sides and two edges again, even though it remains to be one ring! So, I wanted to make that too in Technic Lego only.

This version can be split in two, by removing the light bluis gray 3L pins with bush that hold the yellow and the red strips together. Unfortunately, the MOC looses it’s shape somewhat, but you can see that after splitting the strip it no longer is a Möbius strip. Just follow one side or one edge of the strip. You will not end up on the other side or edge.

Lego Möbius strip, split in two - after which it stops being a möbius strip

Möbius strip, split in two – after which it stops being a möbius strip

Below, you’ll find more pictures, notes on the design and photo instructions for building the model.

Notes on the design

This is a variation to the Möbius strip that I present elsewhere. There, the hinges are made out of 3L beams, but since I didn’t have enough of those, I used 5L beams. I think, it would have been better with 3L beams. Or, alternatively, in the 5L design you could fill the gaps between the black pin-with-pinholes with 3L beams. It will give more of a strip feel, rather than that of a chain-link as it is now.

Lego, Fixed connection between two strips, maximum twist

Fixed connection between two strips, maximum twist

One question, I had was how to connect the two strips: should they be fixed/straight like this, or should they be hinged. A quick experiment showed that fixed could work but permitted only a limited twist. In the picture, you see the maximum twist. Then I realized that the small twist that was possible could only happen because of slack. A twist like this can only work if the yellow bars bend along, like in the double helix of DNA. So, the two strips of this divisible Möbius strip had to be hinged – yes, I am sorry, yet another hinge.

So, here is the basic design of the connection. When you twist it, it indeed gets the shape of a double helix. The funny bit is that you can twist it all the way until the gray beams fold completely flat. You can run an axle through their centers. Even funnier is that you can un-fold and fold the entire thing with the axle in place! I don’t know an application for that, but it’s remarkable.

Building instructions

It’s not a difficult MOC. You just need a lot of parts : 90 5L beams (45 red and 45 yellow) , 30 7L beams (15 red and 15 yellow),  120 pins-with-pin-hole, 210 friction pins, and 15 3L pins with bush.

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February 2019

Updated 14 July 2020. As aamartin0000 pointed out on Rebrickable, the 3L pins with bush were missing in the parts list.