GT2 pulley

After some search I found this way to make a pulley of various size , for a GT2 belt with a 2mm  pitch.

First, you need to know the number of tooth, and the pitch of one tooth (2mm ). Then compute the diameter of a circle which will contain a polygon. The side of the polygon is the pitch, and the number of side of th epolygon is the number of tooth. This site is great  to help that computation:
https://www.calculatorsoup.com/calculators/geometry-plane/polygon.php
otherwise this formula:
Inradius r

• r = (1/2)a cot(π/n) = R cos(π/n)

where r  is the distance between the center of wheel, and the nearest point of the side, and n the numer of sides of the polygon:

 

Once r value is found, then the wheel can be created under CAO software with this method:

1) make a solid wheel a little bigger than r, thinckness 8mm is fine for GT6

2) extrude draw on the surface , one tooth  like this:

The distance between both extrmimites of the tooth should 2mm. The diameter should be .78.

The center of the circle should be at r distance from the center of the pulley. 

3) do a circular repetition of the function , based on the center of the wheel

4)done