# Gears

Gears are toothed wheels which are used to transmit force to other gears or toothed parts by meshing with minimal slip.

When two gears are meshed together, the smaller gear is called a pinion. The gear transmitting force is referred to as a drive gear, and the receiving gear is called the driven gear.

When pinion is the driver, it results in step down drive in which the output speed decreases and the torque increases. On the other hand, when the gear is the driver, it results in step up drive in which the output speed increases and the torque decreases.

Plastic gears

## Gear tooth system

A gear tooth system is defined by its unique tooth proportions,pressure angles etc.

### Law of gearing

Before we take a look at the actual gearing systems let us see what is the fundamental law that governs the gearing system. The law of gearing states that

 the angular velocity ratio of all gears of a meshed gear system must remain constant
also the common normal at the point of contact must pass through the pitch point.


Example: if $\omega \ _{1}$ and $\omega \ _{2}$ are the angular velocities and $D_{1}$ and $D_{2}$ are the diameters of two gears meshed together then ${\omega _{1} \over \omega _{2}}={D_{2} \over D_{1}}$ ### Gear profiles

Gear profiles should satisfy the law of gearing.

The profiles best suited for this law are:

1. Involute
2. Cyloidal
3. Circular arc or Novikov

### Gear Nomenclature

Various nomenclatures related to a gear are shown in the figure

Let us consider a spur gear and define the following terms-
Pitch circle:Can roughly be defined as the circle having radius as the mean of the maximum radius(to the tip of the gear teeth) to the radius of the base of a gear tooth. However tooth proportions can vary considerably, with both root and tip adjusted to suit running conditions and manufacturing processes, making this definition somewhat unreliable.
Addendum:The tooth portion above the pitch circle (towards the tooth tip).
Dedendum:The tooth portion below the pitch circle (towards the tooth root).
Flank:The face of a gear tooth which comes in contact with the teeth of another gear. So,a flank is an important part of a gear.
Fillet:Fillets in the root region are of less importance since they don't come into contact with other gear teeth. However root fillets are of great importance with regard to tooth bending strength, and therefore power ratings. Gears with little or no fillet in the root are prone to tooth breakage, as the sharp corner acts as a stress raiser.
Circular pitch:The sum of the width of a tooth and a space between the tooth of a gear. Circular pitch is an important parameter as it indicates the size of the tooth of a gear.If $P_{c}$ is the circular pitch,Z is the number of teeth on a gear and D is the pitch diameter then,$P_{c}={\pi D \over Z}$ So the size of a tooth is given by $m={D \over Z}$ where m is the unit of size called module.And hence for two meshed gears we must have the same size of tooth,then we can have the following relations, $m={D_{1} \over Z_{1}}={D_{2} \over Z_{2}}={P_{c} \over \pi }$ ---(1)

In case of a rack the diameter and the number of tooth tend to infinity but still the module remain finite.

Circular thickness or tooth thickness: It is the thickness of the tooth measured on the pitch circle.It should be noted that this thickness is measured as the arc along the pitch circle and should not be taken as the displacement
Diametral Pitch: It is defined as the number of tooth per inch of the diameter of the pitch circle of a gear.It is indicated by the letter P.Therefore, $P={Z \over D}$ ---(2)

So using equation (1) and (2), we can have $P_{c}P=\pi$ 