[JVN]

I went through this exercise in 2003/2004. In the end I stopped using any of the detailed mathematical modeling in favor of a simpler analysis.

What I ended up with is a model like this:
Output Rotational Speed = Motor Free Speed / Gear Reduction * Speed Loss Constant

Output Stall Torque = Motor Stall Torque * Gear Reduction * Gearbox Efficiency

I experimentally determined the Gearbox Efficiency and Speed Loss Constant values. These will vary from robot to robot. The value I use (which is about right for "my" robots) is 81% for speed loss. I use a different efficiency value depending on what gearbox I'm looking at.

This is all very inexact. The calculations end up being "about right."
The thing that it took me 3 or 4 years to learn? "About right" is totally okay for a FIRST Robot.

So that is where the simplified version of my spreadsheet came from.

Of course, this was from the design perspective -- if you're looking for a more detailed model for academic reasons, go to it!

-John