We present here a simple, methodical procedure for determining the final gear ratio of an epicyclic gear train. This method is extremely procedural, which is appropriate since use of intuition is often quite futile when applied to complex gear trains.
We can use the following superposition concept for determining rotational speeds of the gears:
Rotation_{planet gear} = Rotation_{arm} + Rotation_{planet gear relative to arm}
In the following illustration and analysis, the sun gear has twice the diameter of the planet gear.
We can analyze this nonintuitive configuration with the following table. For this discussion, a positive turn is defined to be counterclockwise.
Action 
Arm Turns 
Planet Turns 
Sun Turns 
With all moving parts locked, the entire assembly is given one positive turn (CCW). 
+1 
+1 
+1 
With the arm fixed, the sun is given one negative turn (CW). 
0 
(N_{SUN}/N_{PLANET})=+2 
1 
Add the above two values to obtain the RESULTANT TURNS. 
+1 
+3 
0 
