Does a gear retain its mechanical advantage in a 1 2 1 ratio?

Question

For example if the first gear has 32 teeth and the second 64, if the third also has 32 teeth would the output of the third retain the mechanical advantage created by the first 32 tooth gear powering the second?
32:64:32 or 1:2:1
Thanks for your time and help!

NMech · Accepted Answer

if you have them in line like the following picture then NO.

The first and the last gear will have the same speed and the same torque (actually slightly less due to losses).
if you wanted to retain a mechanical advantage you'd need 3 shafts and at least 4  gears like in the following image.

nick012000 · Answer

No. We can show this with math.
The first gear pair has a ratio of 1:2, and the second pair has a ratio of 2:1. So, discounting losses, for every turn of the input shaft, the second shaft will make 1/2 of a turn. For the second pair, for every turn of the second shaft, the third shaft will turn twice.
We can then multiply these together to see how many turns the third shaft will make compared to the first shaft: 1/2 * 2 = 1. Therefore, for every turn of the first shaft, the third shaft will turn once, and there is no mechanical advantage for the overall system.

Does a gear retain its mechanical advantage in a 1 2 1 ratio?

2 Answers

No. We can show this with math.

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