### Gear Speed and Ratio:

When two or more gears are in a mesh, one will drive the other. As such, one of the gears will be referred to as a driving gear and the other a driven gear.

### Definition of Drivier Gear:

This is the gear that transmits power, force or speed to the other gear.

### Definition of Driven Gear:

This is the gear that receives the force, power or speed transmitted to it.

### Definition of Driven Gear Ratio (GR)

Gear ratio is the relationship between two gears in which one gear has a larger speed than the other. For instance, gear A (driver gear) has 120 teeth and gear B (driven gear) has 40 teeth. The gear ratio will be 3:1, which means that there is an increase in speed. If the ratio is 1:3, it means there is a speed reduction of ratio 1:3.

**Gear Ratio (GR)** = \( \frac{Number \: of \:Teeth \:on\:Driver\: Gear}{Number\: of \:Teeth\: on \:Driven\:Gear} \\ = \frac{120}{40} \\ =\frac{3}{1} \\= \scriptsize 3\: :1 \)

### Definition of Speed Ratio (SR)

Speed ratio is the ratio of the rotation per minute of the driven gear to the rotation per minute of the driver gear.

\(\scriptsize Speed \: Ratio = \normalsize \frac{Rotation \: per \:minute \:for\:Driven\: Gear (S_D)}{Rotation \: per \:minute \:for\:Driver\: Gear (S_d)}\)

### Example:

The speed of a driver gear is 60 rev/min and that of a driven gear is 30 rev/min. What is the speed ratio of the gear system?

**Solution:**

S_{d} = 60rev/min

S_{D} = 30rev/min

Spped Ratio (SR) = \( \frac{Rotation \: per \:minute \:for\:Driven\: Gear (S_D)}{Rotation \: per \:minute \:for\:Driver\: Gear (S_d)} \\ = \frac{30}{60} \\ = \scriptsize 1\: :2\)

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