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Introduction
Gears are commonly used to transmit rotational motion between machinery shafts. When gears of different types and sizes are combined, they can change the rate of rotation, the direction of the axis of rotation, and change rotary motion to linear motion. The most commonly used gear systems are illustrated in the following figures:

External Spur Gears

Perhaps the most often used and simplest gear system, external spur gears are cylindrical gears with straight teeth parallel to the axis. They are used to transmit rotary motion between parallel shafts and the shafts rotate in opposite directions. They tend to be noisy at high speed as the two gear surfaces come into contact at once. Internal spur gears: The internal spur gears works similarly to the external spur gears except that the pinion is inside the spur gear. They are used to transmit rotary motion between parallel shafts but the shafts rotate in the same direction with this arrangement.
External Spur Gears

Internal Spur Gears
The internal spur gears works similarly to the external spur gears except that the pinion is inside the spur gear. They are used to transmit rotary motion between parallel shafts but the shafts rotate in the same direction with this arrangement.
Internal Spur Gears

Rack and Pinion
Rack and pinion gear system is used to transmit rotary motion into linear motion. The rack is a portion of a gear having an infinite pitch diameter and the line of action is tangent to the pinion.

Helical Gear

Step gears have two or more spur gears fastened together and each gear is advanced relative to the adjacent one by a small amount. Helical gear can be seen as a stepped gear with an infinite number of steps. Helical gears used to transmit power between parallel shafts are called parallel helical gears and the ones used to transmit power between non-parallel shafts are called crossed helical gears. The advantage of helical gears is they form a gradual contact across the teeth as oppose to spur gear, which make contact across the entire face at once during operation. This results is less impact loading and thus helical gears operate more quietly than spur gears, have longer life, and stronger.
Helical Gea

Worm Gears

Worm gears are made up of two parts: the pinion and the worm gear. The pinion has a small number of teeth, usually one to four, and since they wrap around the pitch cylinder they are called threads. The worm gear, while looks like a helical gear, has concaved faces to fit the curvature of the worm in order to provide line contact instead of point contact. Worm gears can provide a high angular velocity reduction between nonintersecting shafts at right angles. They are capable of transmiting high tooth loads but the disadvantage is the high sliding velocities across the teeth.
Worm Gears

Compound Train

A pair of gears are compounded if they have a common axis and are integral, such as gear A, B, C, D and E in the illustration below. A compound gear train is one that contains compound gears.

Compound Train

The following example illustrates the speed reduction achieve by a compound gear train.

Example 1:
If the speed of gear A is 500 rpm, what is the speed of gear F and its direction of motionThe speed of the various gears will be:








 
 

For a simple gear system, the ratio of the angular velocities of any pain of gears in the mesh is the inverse of their number of teeth.


 



Where Wa and Wb is the angular velocity of gear A and B, respectively. Na and Nb is the number of teeth on gear A and B.