Most primary drives (motors, turbines) and suchlike) spin at quite high speeds but don’t have a lot of oomph behind them. Most applications, by contrast, need a lot of oomph, delivered at relatively low speeds.
Torque (or ‘oomph’), could be described as twisting power. Think about opening a jam jar, or a bottle of sauce. A new jar (or one where the jam has stuck the lid to the jar) needs a lot of twisting power to loosen the lid. Once loosened, however, you need much less twisting power to actually remove the lid. That’s all there is to it. The harder something is to twist, the more torque you need to twist it.
This being the case, we need some kind of gizmo which can boost the torque of the primary drive, and at the same time, reduce the speed a bit.
And, you guessed it: that is exactly what a gearbox does. It uses an arrangement of gear wheels, shafts and other bits and pieces to increase the torque and reduce the speed.
In many ways, a simple gearbox is analogous to a lever. You put in one type of motion (a small force delivered over a long distance), and get out something else which has (almost) the same energy, but delivers more force through a shorter distance.
And—just like a lever—depending on how you set it up, you can either get a really big difference in speed and force, or a more moderate difference. If you set up the gearbox to have a ratio of 10:1, for example, then the input shaft has to turn ten times before the output shaft turns once. The speed is reduced by a factor of ten, but the torque is increased by the same multiple.
A simple gearbox might be fixed at one such ratio: 10:1 or 25:1 or even 300:1. But a more complicated gearbox can have four, five or more different ratios, depending on how the thing is designed and built.
The reason for needing all those complicated ratios lies in the limitations of the primary drive. A primary drive is an internal combustion engine, or an electric motor, or something else which converts one form of energy into rotational motion. Almost all such drives work best over a fairly limited range of speeds. The engine in your car, for example, will work from about 1200 rpm up to 6000 rpm, but delivers by far the best performance in a narrow speed band near the top of that range. Even taking the lowest speeds into account, there is only a multiple of five between the lowest speed and the highest.
In Europe, at least, most ordinary cars are expected to cover a range of speeds from 0 up to around 150 kph. That is an infinite range, but because the clutch takes care of the lowest speeds, the transmission only needs to deliver something like a factor of 20 from a bit under 10 kph up to 150 kph.
So we have a car which needs a speed range of 1:20 or more and an engine with a useful speed range of 1:5 or less. The only way to get this wide range of vehicle speeds out of such a limited engine, is to have multiple gear ratios.
Gearboxes are used in a number of different types of situation. The most common is when the speed or torque of the drive does not match the speed or torque of the application. That is the main application for gearboxes, and can be seen in all sorts of machines used in the home and elsewhere. Powered screwdrivers, analog watches, , electric mixers, washing machines and cars and trucks all use a gearbox to perform this type of task.
Of course that is not the only application. Another common reason to put a gearbox in, is to turn the drive through an angle, so that the ouput shaft is not parallel with the input shaft. Almost always, this angle change is combined with a speed change as well. An outboard motor for a small boat would be a good example of this kind of drive. The main drive shaft is more or less vertical, but the propellor which actually drives the boat, needs to be on a horizontal axis.
Another reason is to change the moment of inertia. You can see it most obviously in those childrens’ toy trucks and cars which carry on going after you have zizzed them along the ground once or twice. This is a strange one, but a reduction gearbox has a strange effect on the moment of inertia of things on either side of the gears. A small flywheel can have a much bigger inertial effect if you drive it through a gearbox. You can either have one big flywheel, driven with no gearing, or one a quarter the size, driven through a 2:1 gearbox. A 3:1 gearbox will give nine times the effect and so on.
As noted above, if you need an output with a very wide range of speeds, such as in a car, or in a domestic hand drill, then a gearbox with multiple ratios is a very good way of getting that wide range from a motor which only operates over a small range of speeds. The extension of this is a continuously variable drive, which relies on belts and cone-shaped pulleys to give an infinitely variable gear ratio. Such drives are expensive and can be unreliable, but they can be used in low-power systems (up to the size of a small car) to maintain the primary drive at its most efficient operating condition, while delivering a variable output speed.
For a detailed description of different gears and arrangements, look under gear
Many people first become aware of gearboxes in connection with their cars. I am based in Europe, and I drive a car with a manual gearbox (also known as a stick shift). However, the main transmission gearbox is far from the only gearbox on a car. As noted elsewhere, the differential is another type of gearbox, and on a 4 wheel-drive vehicle, there are three differentials, some with limited slip capacity as well.
Another type of gearbox, used frequently in sport bikes and other motorcycles is the racing box, in which the change up involves just one step each time, but a change down always covers three, four, or even five steps. This is designed to speed up the business of negotiating a corner, where the speed drops rapidly from the straight parts of the track to a sharp turn, necessitating a lot of gear changes in quick succession
This piece written, formatted and edited in Dann's E2 offline scratchpad