Cycloïdal reduction drive: the math

The reduction

 I need an aproximate 1/300 reduction.
 This is Physically impossible so i make 2 1/17 reductions stacked on top of each other because:
 17 x 17 = 286

R = Reduction
P = number of "theeth" on the ring
U = number of teeth on the disk
        P - U          18 - 17            1
R = ---------  => ----------  => -----
           P                 17              17 

The outer Diameter

I want a pin diameter of 6 and a gap of 6 between each pin.
so the Perimeter is 18 x (6 + 6) = 216
Perimeter = diameter x pi => diameter = perimeter / pi



216 / 3.14159 = 58.75