Mobius strip with Cuboctahedron feet

thingiverse

Created By: Hope Roberts Date, School & Place: March 4, 2016 George Mason University located in Fairfax, Virginia. The creation took place in Mathematica for a Math 493 class project titled; Math Through 3D Printing. Background of Object: German mathematicians August Ferdinand Mobius and Johann Benedict Listing discovered the Mobius strip also known as the Mobius band in 1858. The Mobius strip is special because an object circling the inside loop would circle twice before reaching the starting point. Cutting the band in certain ways will produce a longer band of the original shape, not multiple bands. I have included pictures from my Mathematica file of the base, the frame and both meshed together. Print Settings: Printer Brand: MakerBot Printer: MakerBot Replicator 2X Rafts: Yes Supports: Yes Resolution: 0.30mm Infill: 10% Notes: Extra support was used for this project. The print time took about four and a half hours. The size of the whole object was x:85.74mm, y:99.30mm, z:98.02mm. The feet sizes separate from the whole object were x:20.93mm, y:20.93mm z: 14.80mm. The Mobius size separate from the whole object was x:70.88mm, y:99.30mm, z:88.58mm. Post-Printing: The finished product was successful on the first attempt. Removing raft took approximately half an hour using fingers and a pencil. How I Designed This of Creation and Instructions for Printing: The coding for the Mobius strip was created in Mathematica using a code example of a Monkey Saddle Dual, which was given by the instructor. The Mobius strip has parametric equations different from the Monkey Saddle Dual, which are: x = [R + scos(1/2t)]cost y = [R + scos(1/2t)]sint z = s(sin(1/2t)) The Parametric Equations of the Mobius strip used in the coding were found in Mathematica. The equations were incorporated into the code with the Mobius base being made first and the frame being made second. The gridsteps of the frame were adjusted to add or take away lines and the radius was adjusted for how thick the lines would be. The objects are then combined so that the frame is raised on the Mobius base. This gives more texture to the Mobius strip. The combined Mobius base and frame rests on top two Cuboctahedrons, which are used as supports because of their flat faces. The Cuboctahedron was created in Mathematica. Using supports allows the overall print to stand upright. All three of the STL files are included. I have included the Mathematica files of the whole code used for this project. Putting it together: The Mobius Base STL file is the first file I uploaded in Makerbot with no immediate modification, then I uploaded the Mobius frame STL file also with no immediate modifications. I then added two supports, which were Cuboctahedrons. I then selected both the base and the frame shrinking them down to a size that would print around four hours. I positioned the supports by visually deciding where on the build plate would give the best support for the Mobius strip being sure that the mobius object was slightly embedded in the feet supports. Lastly, I selected the Mobius base and Mobius frame rotating them 90 degrees to lay the object flat. Sources: https://simple.wikipedia.org/wiki/Möbius_strip http://mathworld.wolfram.com/MoebiusStrip.html