Lesson 10, Topic 2
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# Simple Calculations Involving Gear Ratio

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#### Topic Content:

• The Relationship Between the Gear Ratio and the Speed Ratio
• Simple Calculations Involving Gear Ratio

### The Relationship Between the Gear Ratio and the Speed Ratio:

When solving problems involving gears, it is important to name all the parameters correctly.

• Number of Teeth on Driver Gear = ND
• Number of Teeth on driven Gear = Nd
• Speed of Rotation for Driver Gear = SD (rev/min)
• Speed of Rotation for driven Gear = Sd (rev/min)

Gear Ratio (GR) = $$\frac{N_D}{N_d}$$

i.e. $$\normalsize \frac{Number \: of \:Teeth \:on\:Driver\: Gear \:(N_D)}{Number\: of \:Teeth\: on \:driven\:Gear \:(N_d)}$$

For example, with 10 teeth on the Driver gear (ND) and 20 teeth on the driven gear (Nd)

The Gear Ratio (GR) = $$\frac{10}{20} \\ \scriptsize = 1\: :\: 2 \: or \: 0.5$$

The Speed Ratio (SR) is the ratio of the driven gear speed to the Driver gear speed

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

Note: It is important to note that the Gear Ratio (GR), determines the speed of the driven gear (Sd).

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