Each machine consists in principle of three basic parts: a motor or another prime mover (that sets the machine in motion), an actuating mechanism (which is directly doing the needed work:

digs a ditch, weaves cloth, peels potatoes, propels a ship, and so on), and a transmission that connects the first two parts. Sometimes, the transmission may be lacking, for example, in a fan the impeller is mounted  directly on the shaft of the electric motor. But in most cases, the transmission is indispensable, to

match the speed of the mover with that of the actuator, to set in motion several actuators from one

mover, or for another reason. For instance, on a big ship a steam turbine is usually used as a mover.

Its rotational speed is several thousands r/min, whereas the speed of the propeller (for better efficiency) should be about 100 r/min. Hence, between the turbine and the propeller shall be a

speed reducer.

On a small motor boat the propeller, with respect to the speed, may be mounted directly on

the shaft of the engine. But the engine is desired to be placed above the water (just to be maintained easily), and the propeller to work should be submerged; so in this case the transmission is needed as well.

A gear is the most common type of transmission; therefore, it is one of the mandatory  subjects when machine elements are discussed. The geometry of gears is well known, and it is not the subject of investigation here. But the analysis of strength and deformations in gears is impractical without some minimal presentation of tooth geometry. This is the theme of the following section.