Epicyclic Train Overall Ratio Calculation | ||||||||||||||||

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 non-intuitive configuration with the following table. For this discussion, a positive turn is defined to be counterclockwise.
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To demonstrate the derivation of the above table, we will go through the procedure step-by-step.
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With the rotation of each element of the gear train in hand, the overall gear ratio becomes easy. If the arm is the input and the planet is the output, the overall gear ratio is 3/1 = 3. For a more involved epicyclic gear train example, please refer to the Epicyclic Gear Train Example section. |