How many teeth on a driven spur gear will create a 2:1 ratio when the drive gear has 90 teeth, and the idler has 10 teeth?

To create a gear ratio, the relationship between the number of teeth on the drive gear and the driven gear must be established. In this case, you have a drive gear with 90 teeth and an idler gear with 10 teeth. The driven gear is what we need to determine to achieve a 2:1 ratio.

A 2:1 gear ratio means that for every two revolutions of the drive gear, the driven gear makes one revolution. This implies that the driven gear must have half the number of teeth of the drive gear when not considering the idler, which merely transmits motion rather than affecting the gear ratio directly.

To set up the equation:

1. The gear ratio formula can be expressed as:

[

\text{Gear Ratio} = \frac{\text{Number of Teeth on Drive Gear}}{\text{Number of Teeth on Driven Gear}}

]

2. Plugging in the numbers for a 2:1 ratio:

[

2 = \frac{90}{\text{Number of Teeth on Driven Gear}}

]

3. Rearranging to solve for the number of teeth on the driven gear:

[

\text{Number of Teeth on