As we all knows that Gears are a very useful and simple machine. Gear is a toothed machine part, such as a wheel or cylinder that meshes with another toothed part to transmit motion or to change speed or direction. The common function and situation is for a gear to mesh with another gear, but a gear can mesh with any device having compatible teeth, such as linear moving racks. Sometimes Mechanical Engineers don't use gears and rely on the advent of electronic controls and the availability of toothed belts because gears for height power machinery are difficult to design.

There is so many categories in the that can be combined in a multitude of ways, some of which are meshing circular spur gears, spur gears, pinion, racks, helical and worm gears. Herringbone and helical gears utilize coved teeth for efficient, high capacity power transmission. Gears mate or mesh via teeth with very specific geometry. A gear's most important feature is that gears of unequal sizes (diameters) can be combined to produce a mechanical advantage, so that the rotational speed and torque of the second gear are different from that of the first.

If we talking about the applications of the gears, I would say there is no machine without gears, it's a important part of a machine have immense usage in all industries. Industries like automotive industries, defence, agriculture, coal plants industry, steel industry, paper industry, mining, garment and many more industries, in all these industries gears holding a wide area of applications.
These are using in conveyors, separators, lubrication systems, elevators and kilns.

Now gears are basically used for two basic purposes like increasing or decreasing of rotation spend and another is increasing or decreasing of torque or power. Torque is measure of force to produce torsion and rotation about an axis. For increasing and reducing torque a large drive gear is coupled to a smaller driven gear.

Geometry of Gears -

The essential features of a gear mesh are:
Center distance: The distance between the centers of two pitch circles.
Pitch diameters: The tangent to two basic circles is the line of contact in gear vernacular. Where this line crosses the line of center establishes the pitch. The ratio of pitch diameters gives the velocity ratio.
Pitch: It is a measure of tooth spacing along the pitch circle.
Number of teeth
Pressure angle of the contacting involutes: The angel between the line of force between meshing teeth and the tangent to the pitch circle at the point of mesh.