What is the rotational speed of a gear drive's driver gear if the driven gear is 1440 RPM, the drive consists of a 24-tooth driver and a 36-tooth driven gear?

To determine the rotational speed of the driver gear in a gear drive, you can use the relationship between the rotational speeds and the number of teeth on the gears. The formula for calculating the rotational speed of the driver gear based on the driven gear's speed and the number of teeth on both gears is as follows:

[

\frac{N_d}{N_r} = \frac{T_r}{T_d}

]

Where:

• (N_d) is the speed of the driver gear (in RPM)

• (N_r) is the speed of the driven gear (in RPM)

• (T_d) is the number of teeth on the driver gear

• (T_r) is the number of teeth on the driven gear

In this case:

• The driven gear has a speed of 1440 RPM and has 36 teeth.

• The driver gear has 24 teeth.

We can rearrange the formula to solve for the speed of the driver gear:

[

N_d = N_r \times \frac{T_d}{T_r}

]

Substituting the known values:

[

N_d = 1440 , \text{RPM} \times \frac{24}{36