Had a bit of fun with this test pattern drawing. Every combination of gears I have that goes inside of a one-hundred-sixty tooth gear is represented here. Each plot is drawing in a different color making it a tutti-frutti concoction of lines across the page. And even though I generally know how many cusps around the exterior edge each combination will yield it’s always quicker to have a visual aide then to do the math quickly in my head.
Least common denominator.
The math is pretty easy to figure out by using the least common denominator between two numbers, the number of teeth on the moving gear and the stationary gear. So a forty tooth gear will make four cusps inside of a one-hundred-sixty tooth gear—four trips around the interior, 160 being the least common denominator between the two numbers.
A bit more difficult to figure out is a seventy-two tooth gear, 72 x 20 = 1440 ÷ 160 = 9, 1440 being the least common denominator between the numbers 72 and 160, that’s twenty cusps.
Drawings are available on my art shop.