Device for milling a pentagon.
r: pitch radius of the fixed green sun gear
R: pitch radius of the yellow planetary gear
k = R/r = 5
Distance between the red tool axis and the sun gear axis is (8/30)r for getting a locus in shape of rounded corner pentagon (in relative motion between the tool and the yellow planetary gear). The input link is the pink disk. Select tool of larger diameter for getting a pentagon with sharp corners.
Similar device permits to get other regular polygons.