Hi Alex, well if you convert each of your panels into 2 triangles, that would be developable and if you increase the density the lines would get closer to parallel.
Thanks again - Pilou thanks for you further investigation bugging me why the outside edges grow in length - I have made an analogue version in a light gauge steel it seems that a jelly bean shape is where it whats to be without distorting or kinking the shape. I tried putting an extra twist into the 3d model to see if it relaxed it but no change. The metal prototype I have made is only the x1 180 flip in the surface.
Maybe because you are trying to use your bending machine, a solution approach could be to Create the mobius curve, then "Place points" that simulate the data needed by the bender machine. Then you can export the point data and merge it into the NC file the machine is going to use to create the moves...?
Sortof an out of the box solution but should be doable. I don't know benders so am not familiar with the code generated that runs the machine so cant really get deeper...
Here is a result. I created a mobius with 60 degree angles which left it "unconnected" at the ends. Then i could unwrap the 2 edges to create the "unwrapped mobius base object.
Now doing curve to curve flow on that surface with varying lengths of base curve, you can see what is happening to your metal.
This result i made used the base curve of the shorted surface which results in "tip to tip" connection. If you shorten the base curve (Shown by text) you will see the surface created with overlap and also not really "meet at the edges". This is the stretching
If I adjust the mobius to "connect before the unwrap" you will see it is no longer a tangent surface with equal "width" throughout, but a variable.... I would have to adjust my unwrap to match this.
But either way, I can divide the text at the 180 and create surfaces that dont twist to match the distortion and then flow text undistorted...
But my previous post was "why"? Arent you just looking for bend points for the machine to bend metal? Why are we creating the surface?
This is Another way to make a Mobius Ring (Not Ribbon style Ring) that could be helpful to you.
1-Make Two circle positon them the way you need.
2- Loft with no Cap.
Many thanks for your input - Trying to create the surface just as an art manufacturing exercise I would like to make it up out of a steel band - trying to get my head around the forces required Ill try making a light gauge aluminium prototype and advance up the food chain - get a real world feel for what the material will allow rather than paper. Its put a twist in mind as to solving a simple real world exercise and transition that into a working computer model. Will post up some results once I do some analogue trials.
Hey Alex,
Awesome! I am looking forward to your project results.
""""" trying to get my head around the forces required """""
This is what makes it fun, yeah!
So with the non-developable shape, how is it best to get there.. (Dont get me wrong Alex, you are a very impressive Artist and metal worker. I am playing along to also learn or work through these things)
A few years back Michael shared a software that helped me with this alot. It's called Lamina Design
Even if you dont use this for result model, it can show you alot about the shrinking and stretching of your sheet. (This link is for people to follow easier. Dont be offended) Looking at the "Process" link on his page, shows output from lamina software. Note the "Paper output" because paper doesn't stretch or shrink
THis video is just a basic on stretching and shrinking metal to equate it to the discussion:
So with these tools, I would analyze how to shrink and stretch a flat sheet to do the non-developable Mobius.
I could use MoI to get some dimensions of "How much" and "Where to shrink or stretch" in my process. Also I can make decisions because if you look at Lamina's "Unfolds" you will see it "Slices out" the shrink or "tears open" the stretch. For ME, this is because for a fabricator, you need real numbers and accuracy to get you model to work. If you shrink or stretch metal after you model it, then the dims will be different. So it really depends if you can be totally organic is easiest. If you are trying to make and actual object that "Meets specific requirements, like Dims, then this is the hoop i am trying t shoot for. But that means I need to make my Sheet metal "Based off of my model"
I'll try to show in a video on how I would use this model I uploaded to get the "Stretch information" that is happening, so I can reverse it back to the metal.
Give me a bit to get at a computer where I can make the vid...
Here is a quick video of showing how I can use MoI to get some of the shrink and stretch data needed.
I cut the video off because I was looking to get great results and went down a rabbit hole. But I realized I was just grabbing data that was "too simplified" for when I am converting flat to circular. If I was great at this math, I could probably get pretty exacting data. In the past, I would ask Michael for help and he always came through, but I was basically making him teach me geometry (Not fair)
There are a few guys in here that may want to play along to try to achieve. But with that said, even the results I can get by "Faking it", are within .04 inches! If I was bending and welding, I could fix that with a hammer or a grinder. The nuclear sub guys would laugh me out of the shop!
Here is the video showing the "reverse thinking" which would be to create a model of the mobius and use THAT to cut out a piece of metal and why that gets more difficult.
The important part to note would also be where I draw a "curve into the end" of my unwrapped surface. This would also be true for "ALL SIDES".... For all the stretching or shrinking to actually "Meet Up" at the end, the PRE-Metal would need to start off with the material to shrink and bend. A much more complex shape and approach. You would need to NOT be starting with a rectangle, But a doubly curved piece of Sheetmetal
So instead of starting with a "rectangle", you would start with a shape more like this, and after you "Shrink and Stretch" it with something like those tools I linked too, it would roll into a rectangle that met up at the edges into a mobius... (This is metal on the table. Not in MoI) I suppose figuring out where the stretch and pinch is, is your point and where you mean you are at. I think the previous video can help with that part along with this demo
There is alot of calculation that would go into being able to do it that way. I would just get it close enough to hit with a hammer. Some young kid may do the calc and do precision work!
Many thanks for your detailed work flows very informative still getting my head around the twists and turns I will try Lamina see what results I can pull out off that.
I put this together today thin gauge steel took some work hammer and heat the shape is OK but not flowy and smooth definitely loaded with tension. This is the general direction I envisage it but in a much thicker gauge steel it perhaps maybe just a blacksmith exercise rather than a cad and CNC approach. Perhaps if I build a few more I maybe able to see where I can pass the metal through some rollers in different directions and get the planes flowing smoothly.
Hi Alex,
Have you considered a disk shape to make a Möbius strip?
It seems that making a Möbius ring out of a rectangular ribbon shape generates so many tension lines in different directions and requires a lot of force to tame it—but on the other hand, a disk-shaped ribbon produces a much smoother result with far less tension.
Here's a test on paper: I just cut the disk on the red line and then twisted it to form the Möbius shape.
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