Geoff Pitts

Professor Andras Bezdek of Auburn University tasked me with creating an educational sculpture that communicates what a hyperboloid is. Early on, I realized a way to do this with pencils. It's called the Proof Pencil Hyperboloid (PPH). What follows is the process of refining this idea into a product that’s intuitive, reliable, and manufacturable.

The goal was simple enough: create two radial arrays of holes, one in a stationary base, and one on a top that rotates. The top must have a handle that’s at least as tall as the pencils, and the base must stick to the ground plane somehow.

The top must be kept from spinning freely, yet turning it must be easy enough that weight and friction are enough to keep the base stationary. To achieve this, I designed a simple friction damper which would use a leather washer. That would damp the movement of a square drive peg. That peg would then engage the top with two set screws, completing the assembly.

The handle would be achieved by four converging ribs, which extend axially out of the mostly hollow top. The base would be weighted, either by molding it out of a heavy material, or making it hollow and filling it with a heavy material.

This was enough direction to start creating detailed cad models. Once assembled, the only visible hardware would be the two set screws.

... And even then, the set screws and the central parting line would become obscured by the pencils. After all, the pencils and the resulting hyperboloid are the focus of the design.

The kit of parts. The base was made out of two pieces which capture twelve rubber half-spheres. It's hollow, so it can be filled with concrete for added weight. The central nut and bolt can be secured together with a pin so they never backdrive.

The captive rubber half-spheres protrude out of the base to create friction against the ground plane.

The ribbed handle is just tall enough to be functional, but not so tall that it visually distracts.

The underside of the top is chamfered so that the pencils don't bind as they tilt and rotate.

The base exposes the flat tops of the twelve rubber half-spheres. This provides a soft surface for the pencil tips to engage.

The central stalk is just thin enough that the pencils can collide.

Here's an animation of the PPH in action.