After Cycloid Drawing Machine, Joe Freedman is back with a smaller, simpler version called the DuoGraph, making it easier than ever to create pretty swirling patterns. The DuoGraph has seven gears measuring 14-1/2 x 6-2/3 inches, and a number of parameters that can be changed quickly to produce infinite designs.
The Math behind the Curtain:
The turntable has 60 teeth. When combined with a drive gear that has 30 teeth you’ll get a pattern that has 2 nodes. Adding a prime number gear for the fulcrum makes the drawing into a non-repeating line. Using a stationary fulcrum the line will draw back onto itself after a number of turns.
Changing the penholder positions adds even more complexity to the drawings…. All of these drawings used the same setup: a 30 tooth gear as a moving fulcrum and a 41 tooth gear as the drive. The only difference is the position of the penholder. Infinite variations are possible. Imagine how many possibilities there are using the 16 gears in various combinations.