R: pitch diameter of the fixed sun gear
r: pitch diameter of the planetary gear
R/r = a/b
a/b is an irreducible fraction
Here a/b = 4/3
Loci of various points on the planetary gear are shown.
The green curve is for a point on the pitch circle of the planetary gear. It is a hypocycloid. The other loci are hypotrochoid.
The red curve is a polygon of a sides with rounded corners.
Here a = 4. Radius of the point that traces the red square is Rc = 2.78r.
1 working cycle of the mechanism corresponds b revolutions of the input crank. Here b = 3.