gears

A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called cogs), which mesh with another (compatible) toothed part to transmit rotational power. While doing so, they can change the torque and rotational speed being transmitted (in inverse proportion) and also change the rotational axis of the power being transmitted. The teeth on the two meshing gears all have the same shape.
The basic principle behind the operation of gears is analogous to the basic principle of levers. Meshing gears of different diameters produce three changes — (i) a change in torque, creating a mechanical advantage, (ii) an inverse change in rotational speed and (iii) a change in the sense of the rotation, a clockwise rotation becoming an anti-clockwise one and vice-versa. The ratio of the output torque to the input torque is equal to the ratio of the diameter of the output gear to that of the input gear τout⁄τin = diaout⁄diain. This is called the gear ratio. The ratio of the output rotational speed to the input rotational speed is equal to the inverse of the ratio of the diameter of the output gear to that of the input gear ωout⁄ωin = (diaout⁄diain)-1 = diain⁄diaout. The diameters of the gears are measured at a point between the root and tips of the gear teeth called the pitch circle.
A gear may also be known informally as a cog.
Two or more meshing gears, working in a sequence, are called a gear train or a transmission. The gears in a transmission are analogous to the wheels in a crossed, belt pulley system. An advantage of gears is that the teeth of a gear prevent slippage. In transmissions with multiple gear ratios—such as bicycles, motorcycles, and cars—the term "gear" (e.g.,e "first gear") refers to a gear ratio rather than an actual physical gear. The term describes similar devices, even when the gear ratio is continuous rather than discrete, or when the device does not actually contain gears, as in a continuously variable transmission (CVT). Sometimes a CVT is referred to as an "infinitely variable transmission".
Furthermore, a gear can mesh with a linear toothed part, called a rack, producing movement in a straight line instead of rotation (movement in a circle). See Rack and Pinion for an example.

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