Möbius strips

[imatfaal]

...

 

 

Trey kewl figure, though I suspect impossible to physically build and operate.

 

No - I think it is realisable. Would take me a fair while - quicker if I could get my hands on a 3d printer... You would have to have the correct number of cogs otherwise it would not move (either odd or even havent thought deeply enough yet to say)

The support structure would be a single wire - it would pass around the loop four times. Imagine each cog is on a narrow ring bearing.

 

• Envisage a spur at right angles to the blue cog at the front attached to a ring bearing on which the cog rotates, positioned at the top and orientated into the page. Add another to the light blue to its right - the same position (ie still exactly between where the cog meshes with its neighbours) and similar orientation.
• Carry on.
• By the time you make one circuit you are up to the green cog with orange edge just right of centre - the spur will be on the edge of ring bearing towards you and pointed directly up.
• Carry on.
• After one more circuit the spur will be on the initial blue cog, positioned at bottom of ring bearing and pointed directly out of page.
• Carry on.
• After a third circuit you will have reached the green/orange cog again, this time the cog will be at the far side of the the ring bearing and oriented down the page.
• Carry on.
• After final circuit the spur will return to the initial cog, same position, same orientation.
• Join all the distal ends of the spurs and you have a structure that would hold the cogs, doesn't interfere with them and can actually exist.

 

 

The Support structure would be the edge of a square cross section prismatic ring I think.

[Acme]

 

Trey kewl figure, though I suspect impossible to physically build and operate.

No - I think it is realisable. Would take me a fair while - quicker if I could get my hands on a 3d printer... You would have to have the correct number of cogs otherwise it would not move (either odd or even havent thought deeply enough yet to say)

 

The support structure would be a single wire - it would pass around the loop four times. Imagine each cog is on a narrow ring bearing.

 

• Envisage a spur at right angles to the blue cog at the front attached to a ring bearing on which the cog rotates, positioned at the top and orientated into the page. Add another to the light blue to its right - the same position (ie still exactly between where the cog meshes with its neighbours) and similar orientation.
• Carry on.
• By the time you make one circuit you are up to the green cog with orange edge just right of centre - the spur will be on the edge of ring bearing towards you and pointed directly up.
• Carry on.
• After one more circuit the spur will be on the initial blue cog, positioned at bottom of ring bearing and pointed directly out of page.
• Carry on.
• After a third circuit you will have reached the green/orange cog again, this time the cog will be at the far side of the the ring bearing and oriented down the page.
• Carry on.
• After final circuit the spur will return to the initial cog, same position, same orientation.
• Join all the distal ends of the spurs and you have a structure that would hold the cogs, doesn't interfere with them and can actually exist.

 

The Support structure would be the edge of a square cross section prismatic ring I think.

 

I love it when a plan comes together.

 

A further note on Unity+1's Wolfram article. They say Goodrich patented a Möbius conveyor belt that lasts twice as long as a no-twister and while I haven't looked up the particulars I have come across the idea in a couple forms. As an actual conveyor belt, 3 rollers/pulleys will hold the band in tension.

 

I have also seen Möbius bands used as drive belts on early steam tractors driving threshers with their power out-take wheel as well as Möbius drive bands in early factory settings whether driven by steam or water wheels. Looks like a steam driven printing press in this vid using a Möbius band. (about the 1:30 mark)