teaching machines

Stolen Rings

October 11, 2018 by Chris Johnson. Filed under madeup, public.

Recently, I stole something precious from a friend. I was sitting in Andy’s office, and there it was. An interesting shape. Three rings nestled inside each other. They could rotate independently, but if any translated, the others would follow. I had to have these rings.

So, I stole them. Well, I stole the idea of them. Andy still has his rings. I took the stolen idea, went to Madeup, and coded up the rings.

I started with a function that generated a spherical shell, a larger sphere with a slightly smaller sphere subtracted away from it:

  

    to shell radius, gap
  .radius = radius
  moveto 0, 0, 0
  outer = sphere
  .radius = radius - gap
  move 0
  inner = sphere
  outer - inner
end

nsides = 15
shell 7, 1

    
    
    
  
  
    

    to shell radius, gap
  .radius = radius
  moveto 0, 0, 0
  outer = sphere
  .radius = radius - gap
  move 0
  inner = sphere
  outer - inner
end

nsides = 15
shell 7, 1

  
  expand

You can’t tell it’s hollow unless you switch to wireframe.

Then I added two more spherical shells. You won’t be able to see those either, since they’re concentric, so I won’t share that step. But then I added two square dowels around the top and bottom of these spheres:

  

    to shell radius, gap
  .radius = radius
  moveto 0, 0, 0
  outer = sphere
  .radius = radius - gap
  move 0
  inner = sphere
  outer - inner
end

nsides = 15
shell 7, 1
shell 8.5, 1
shell 10, 1

nsides = 4
.radius = 20
moveto 0, 4
moveto 0, 11
dowel

moveto 0, -4
moveto 0, -11
dowel

    
    
    
  
  
    

    to shell radius, gap
  .radius = radius
  moveto 0, 0, 0
  outer = sphere
  .radius = radius - gap
  move 0
  inner = sphere
  outer - inner
end

nsides = 15
shell 7, 1
shell 8.5, 1
shell 10, 1

nsides = 4
.radius = 20
moveto 0, 4
moveto 0, 11
dowel

moveto 0, -4
moveto 0, -11
dowel

  
  expand

These dowels overlapped the sections of the spheres I did not want. So I subtracted them:

  

    to shell radius, gap
  .radius = radius
  moveto 0, 0, 0
  outer = sphere
  .radius = radius - gap
  move 0
  inner = sphere
  outer - inner
end

nsides = 15
shell 7, 1
shell 8.5, 1
shell 10, 1

subtract

nsides = 4
.radius = 20
moveto 0, 4
moveto 0, 11
dowel

moveto 0, -4
moveto 0, -11
dowel

    
    
    
  
  
    

    to shell radius, gap
  .radius = radius
  moveto 0, 0, 0
  outer = sphere
  .radius = radius - gap
  move 0
  inner = sphere
  outer - inner
end

nsides = 15
shell 7, 1
shell 8.5, 1
shell 10, 1

subtract

nsides = 4
.radius = 20
moveto 0, 4
moveto 0, 11
dowel

moveto 0, -4
moveto 0, -11
dowel

  
  expand

And I had my rings. They rotate independently:

Now I just need to get these printed in stainless steel. Or gold, with which I could pay back Andy.