Calculating and Designing a Ring Gear for LEGO

I'm working on 3d printing a planetary gear for LEGO. I've got a constrained set of planetary + sun gears and was looking into designing a custom ring gear.

I've read a little bit into the design of gears but am currently confused. This is what I've found.

Sun gear: 20 teeth, OD=21.3mm
Planet gear: 12 teeth, OD=13.38mm


In both cases, module (m) = 1 (for the gears to mesh the module has to be the same?)

Pressure angle = 20 degrees.

I was just wondering how I would go about designing such a ring gear in CAD, i.e. figuring out the number of teeth, tooth size, height etc. Thanks in Advance.

The module (or pitch in American units) and pressure angle needs to be constant across the gear mesh for all the gears to mesh properly. 20 degrees is the standard pressure angle for most applications.

Your ring gear number of teeth = # teeth sun gear + twice the # teeth of planet gear. Rest of the geometry is pretty standard derivation from gear formulas. This is a useful link for that: https://khkgears.net/new/gear_knowledge/gear_technical_reference/calculation_gear_dimensions.html

As for the CAD, there are plenty of online tutorials (YouTube) based on whatever package you're using. It can get a little hairy producing a true involute curve (profile of gear tooth) but there are ways to do it.

As jko suggests, one would search for tutorials based on your selection of CAD software. Fusion 360 has a gear generator as to others. I purchased a gear generator program to create SVG files for laser cutting. It also allows one to adjust the parameters to meet requirements.

I used your figures for outside diameter in the program, which resulted in a variety of parameters:

12 tooth gear: 11.886 pitch diameter

20 tooth gear: 19.810 pitch diameter

shaft spacing 15.848

The 20 degree pressure angle is taken as a constant.