# Calculating the output torque of a two-input epicyclic gear system

For a simple planetary gear system with a single input shaft of a known torque, the output torques of the other two shaft can be calculated using the equations below (for a steady state system).

If I were to apply torques to two of the shafts how could I go about calculating the torque of the final shaft for a steady state system?

My intuition is that for a steady state system the sum of external torques (the shafts) must be 0. In this case the output torque will be the sum of the two inputs.

Edit: By the above comment I mean Tt + Tc + Ts = 0

Am I missing something?

• Not worth a whole answer but you're correct. Some automatic transmissions work on a similar principle.
– jko
Commented Mar 8, 2021 at 12:50
• @jko I'm thinking that the sum of the power should be equal ( not of the torques). The torque depending on the diameter would be different? Am I wrong in thinking that?
– NMech
Commented Mar 8, 2021 at 13:41
• @NMech power is torque x speed, you usually evaluate the gear train independent of speed for systems like this. You can use either the pitch diameter or number of teeth (N in the above equations) to determine the torque ratio, that is what normalizes the torques relative to radii.
– jko
Commented Mar 8, 2021 at 13:57
• That's what I thought. If I understand your reply correctly then the statement from the OP that steady state system the sum of external torques (the shafts) must be 0 is not accurate.
– NMech
Commented Mar 8, 2021 at 14:00
• I assumed the intent of OP's statement was the net output torque is the sum of input torques multiplied by their respective tooth ratios. This may require a complete answer after all.
– jko
Commented Mar 8, 2021 at 14:29