by 
The Curious Bag
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In the broadest possible context, underdrives can be found in practically every type of machine on the planet. This configuration can be adopted for many reasons, but it is usually done to increase torque output relative to input.
Definition
Underdrive is the opposite of overdrive and is defined as a condition wherein the power-producing (drive) unit is rotating faster than the driven unit.
Transmissions
In most transmissions, all gears except for the overdrives and the next gear down are underdriven. This is done to increase torque transmitted to the tires for quicker acceleration.
Transfer Cases
Four-wheel-drive vehicles often have a two-speed transfer case. The "high" setting is a direct drive, while "low" acts as an underdrive for increased torque output.
Differential Gearing
Differentials use a large ring gear and a small pinion gear to increase torque output. This is technically an underdrive unit, since the input shaft is turning faster than the output.
Engine Pulleys
Auto enthusiasts will often install a smaller pulley on the crankshaft and larger ones on the accessory drives. This reduces accessory drive speed (parasitic drag) and increases horsepower.
Source:
Resource:
Underdrive Pulley Test (Video)
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