How much torque can the Dewalt Trannies take?

[IKE]

Simple torsional stress calculation:
I couldn't find my old notes, but here is an example if you are direct drive with a 6" wheel that only the torque is causing stress (i.e. no bending load). The shear stress is equal 16*Torque/(pi*d^3) for a round shaft. So back to our 6" wheel example a scenario might go like this: because you are pushing against an opponent all of your robots weight is on one side and your wheels are slipping. Axle torque is the Normal force (weight) * traction coefficient (1.3 peak from team 494 testing)* radius of wheel 3" or about 500 in*lbs (132lbs*1.3*3in). You throw this into the equation above with a 5/16" diamter shaft (I think that is the dewalt output shaft minor diameter) and you get ......... a stress of 83 KSI. So that people get some perspective mild steel (1010) is around 26 KSi (hot rolled) 44 KSI (cold rolled). If you made your direct drive output shaft out of that material you would probably be able to drive your robot around just fine since the loads would be split with the other side. You wouldn't break a shaft until someone hit you. If you went with something like 1050 cold rolled you would begin yeilding a shaft when pushed. Do this a few times and eventually you will break a shaft. For fully reversed torque, it is common to use a factor of safety around 2 when you want to make sure you won't break that part. 170+KSI steel tends to be special grades of heat treated 4130.
Moral of the story for robotics: If your design starts requiring above 50KSI material you either want to rethink your design or be very careful with your design AND your material selection. I have often seen failed designs where the designer was designing for 1010 Cold Rolled (44 KSI), and part was made with 1010 Hot Roller (26 KSI). What was once a factor of safety of 2 goes to 1 and eventually the shaft fails.

This is a very simple version of a much more complicated shaft. In reality the D-shaped shaft has a stress concentration factor that makes the actual stress a lot higher than the what you would see in a round shaft. There are a lot of good books out there about machine design The one I have is "Machine Design: an integrated approach". If has a ton of examples that are easy to follow once you have a good understanding of what Stress and Strain are and how to apply loads. If you don't know what Stress and Straing are, read the book from cover to cover. This was the book for Purdue's Machine Design class while I was there. While figuring out the exact load scenario is best, simple calcs like the one above will tell you if you are in the ball park. I tend to use calculations like that to sort out should never fail, might fail, or garuanteed to break.