Sphere Slices

Independent Study under John Edmark - Winter, Spring 2019

Goal: Model and 3D print a slice of the surface of a sphere that can interlock and slide past itself.

Most Recent Version: Prototype 7

With this version, I was able to print enough slices to form an entire sphere, which presented the opportunity to explore the ways the pieces interacted with one another in mass.

Full Sphere Interaction Demo - Prototype 7

Design Process

Inspiration + Brainstorming

The inspiration: a chair with sliding slats that were each slices of a sphere spotted in Singapore

First sketches of the linking mechanism

Prototype 1

I hoped to master the "fit" of pieces, and in each version I adjusted the modification (or "mod," shown here in red), or how much of the "C" to remove.

After printing many short, straight links (to avoid the added complication of curvature), I was able to determine a relatively successful mod of .3 mm (for piece with wall thickness 2 mm). Printed in PETG on a Monoprice Select V3 printer.

CAD Model + Naming Conventions

Prototype 2

Bringing curves into the mix! Printed in PLA on a Monoprice Select V3 printer.

Stats on this version:

  • wall thickness - 2 mm
  • mod = pinch gap - .3 mm
  • sphere radius - 100 mm
  • wedge angle - some 10 degrees, some 5 degrees
  • arc angle - variable

I ended up printing out a bunch of these slices, and they were fun and surprising to interact with.

Prototype 3

To experiment with how fit changes in relation to scaling variables in the print, the wall thickness was decreased from 2mm to 1.75mm. 

In order to lessen the amount of plastic necessary, the file was augmented so that the "T" and the "C" were bridged by a thin wall instead of a block of plastic as before.

To make the pieces hold to one another more snugly, the pinch gap was also experimented with in this set of iterations. Printed in PLA on a Monoprice Select V3 printer.

Prototype 4

To experiment with how the slices would interact if the arc angle was maximized, I printed a few slices from the "equator" of the circle up to the 60 degree mark (had they been full prints, the arc angle would be 120 degrees). 

Stats:

  • wall thickness - 1.5 mm
  • mod - .3 mm
  • pinch gap - .25 mm
  • wedge angle - 7 degrees
  • sphere radius - 100 mm

These were printed in PLA on a Ultimaker 2, and the resolution of the prints were not very accurate (when measured with calipers, they were about .25mm smaller than their expected dimensions, compared to the prints on the Monoprice printer which were about 0.008 mm larger than expected), making them a poor indication of the fit of a final piece.

Prototype 5

A scaled down print, this time printed on the Monoprice printer to ensure fit.

Stats:

  • sphere radius - 70 mm
  • wall thickness - 1.4mm
  • mod - 0.3 mm
  • pinch gap - .25mm
  • wedge angle - 5 degrees
  • arc angle - 80 degrees (the Monoprice printer didn't have the height for larger)

Prototype 6

SLS print in nylon

The added support of Selective Laser Sintering allowed this to have the highest resolution and the largest arc angle of any print yet. It had to be sanded a bit for the pieces to fit into one another, but after they were able to slip into one another, they slid across each other well.

Stats:

  • sphere radius - 70 mm
  • wall thickness - 1.05 mm
  • mod - .3 mm (V1), .25 mm (V2)
  • pinch gap - .25mm
  • wedge angle - 7 degrees
  • arc angle - 120 degrees

Prototype 7

With this iteration, I was back on the Monoprice printer, this time trying to zero in on a print that was reproducible and would be able to interlock right off of the print bed. To do this, the mod was increased to .4 mm, and some tweaks were made to tighten pinch gap.

Stats of final version of prototype 7:

  • sphere radius - 70 mm
  • wall thickness - 1.4mm
  • mod - 0.4 mm
  • pinch gap - .05mm
  • wedge angle - 5 degrees
  • arc angle - 80 degrees

With this version, I was able to print enough slices to form an entire sphere, which presented the opportunity to explore the ways the pieces interacted with one another in mass.

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