Why do reduction gear boxes have varying sizes of gears throughout the gear train? Why can’t the boxes have multiple of the same compound gear?

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Ive seen boxes that have a starting gear real small, which turns the larger cog of a compound gear, but that compound gear turns a different compound gear of a different size. Whats the purpose of this?

Can you just copy the same compound gear multiple times or does this lead to mechanical disadvantage? Does it lead to less precision in the gear ratio? Are there other reasons?

In: Engineering
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The two reasons you need a gearbox are: to change the speed of the rotation, or to change the output torque compared to input torque.

To change the speed and torque you choose a gear ratio that when multiplied by your input, gives you the desired output.

Sometimes this is best done by just having two gears, but sometimes it’s much more economical (especially on very large reductions) to have multiple sets of gears that change the speed/torque in steps instead of through just one set of gears.

To further increase the economy, you don’t want to overbuild your gears. So each time you step up in torque, you need to make sure the gears, shafts, and housings that are supporting that step can withstand the new torque level, but not by insanely large factors. (This is a large reason why gears are different sizes and widths throughout a gearbox)