Forward to non-circular gears!

Jeff Schöner

April 10, 2002

CS285, Spring 2002 Final Project

Why non-circular gears?

Challenge and Curiosity: Circular gears are well studied and understood. Non-circular gears are usually mentioned in gear and

mathematics texts as possible, but not fully described.

Niche market exists for industrial use of these gears.

Sometimes, machinery needs to turn with un-even velocities.

Fun to look at and play with.

Some examples

above photos, from the Ohio State University

“Peanut” / “Trangle”

“Cardioid” / “Teardrop”

“Flower” / “ Square”

“elliptical gears”, from Nanni-Ingranaggi

The Product to be Delivered

Using the FDM machine, I will produce three or more interesting pairs of gears, like the ones shown on the previous slide.

To the gears, handles will be added.

These gears will be mounted on a piece of wood, where humans of all ages will be able to interact with them.

This will be an interactive art piece.

System could also be used to make real gears for industrial use.

One Method for Shape

Generate some interesting shapes, with parametric equations.

Sample many different radial slices, taking each radius and theta value to compute the corresponding for the complementary gear.

radius bradius a

rotation axis of a

rotation axis of b

theta

boundary of gear a

Limitations to Overcome, Questions to Answer

Only gears that have a fixed line of action can be done this way.

Won't work for elliptical gears.

Where are the teeth going to go?

How does all of this figure into standard gear theory?

Tk/Tcl in SLIDE can be a pain. Perhaps write a custom program to generate a SLIDE file containing the static gears.