Challenge:

With an FDM printer, design and fabricate (print) a 3D object that fulfills the following constraints:

  1. Object should be a single STL file.
  2. Object’s bounding box should be no larger than 2 inches on all sides.
  3. Object should consist of at least 2 interlocking parts, which:
    1. Are not fused to each other / free moving.
    2. Cannot separate from each other.

Solution:

Link to 3D Model STL

For Design Challenge 2 (3D printed, interlocking shapes), I chose what’s called a Mobius Torus, or a Twisted Torus. I started with an interlinked Mobius Strip. A mobius strip is an interesting geometrical construct where a loop curls back on itself similar to an Escher Drawing. If you were to walk on such a path, you would start on the inside of the ring and then as you walked you would find yourself on the outside of the ring. I could have stopped here with this sketch but I got to wondering if one could use the strip as a bisector in cubes and torii. Embedding it in a torus, a donut or bagel shape, really had me fascinated. Indeed, just putting a mobius strip inside a transparent torus is gorgeous. This twisted torus idea it turns out is not all that original. Japanese sculptor and artist Keizo Ushio popularized this in the early 2000s. Besides yummy treats, nature is full of torii which is evident in its organic shape.

I started off struggling with this sketch almost to point of giving up. I was having trouble creating the proper sweep of a rectangle around a circle. Sweep allows for not only creating the cylinder but also rotating it. I rotated the mobius strip 180 degrees and came up with a nice shape. I then added a torus, and my first attempts to bisect the toroid did not work so well. Neat shape actually but I was left with a weird artifact. Ultimately, upon examining the shape, I determined it was still joined; locked. After watching some videos and reading about this kind of math, it occurred to me that I needed one more half rotation; a full 360 degrees. Once adding that extra twist, it came together beautifully and surprisingly quick. Math is like that sometimes.

 


Torus Geometry Link

Art of Keizo Ushio (Sculpture by the Sea)