A spur gearset has a module of 6 mm and a velocity ratio of 4. The pinion has 16 teeth. Find the number of teeth on the driven gear, the pitch diameters, and the theoretical center-to-center distance

The driven gear has 64 teeth.
The pinion has a diameter of 96 millimeters and the driven gear has a diameter of 384 millimeters.
The theoretical center-to-center distance is 240 millimeters.

First, we proceed to find the number of teeth of each gear ([tex]N_{D}, N_{P}[/tex]) based on the fact that gear only fit when they have the same module ([tex]m[/tex]). The velocity ratio ([tex]r_{v}[/tex]) is defined by the following relationship:

[tex]r_{v} = \frac{N_{D}}{N_{P}}[/tex] (1)

If we know that [tex]r_{v} = 4[/tex] and [tex]N_{P} = 16[/tex], then the number of teeth of the driven gear is:

[tex]N_{D} = r_{v}\cdot N_{P}[/tex]

[tex]N_{D} = 4\cdot (16)[/tex]

[tex]N_{D} = 64[/tex]

The driven gear has 64 teeth.

The pitch diameter ([tex]D[/tex]) is obtained by multiplying the number of teeth ([tex]N[/tex]) by module ([tex]m[/tex]), in milimeters.

Pinion

[tex]D_{P} = m\cdot N_{P}[/tex] (2)

([tex]m = 6\,mm[/tex], [tex]N_{P} = 16[/tex])

[tex]D_{P} = (6\,mm)\cdot (16)[/tex]

[tex]D_{P} = 96\,mm[/tex]

Driven gear

[tex]D_{D} = m\cdot N_{D}[/tex] (3)

([tex]m = 6\,mm[/tex], [tex]N_{D} = 64[/tex])

[tex]D_{D} = (6\,mm)\cdot (64)[/tex]

[tex]D_{D} = 384\,mm[/tex]

The pinion has a diameter of 96 millimeters and the driven gear has a diameter of 384 millimeters.

Lastly, the theoretical center-to-center distance is calculated by the following formula:

[tex]d = \frac{1}{2}\cdot (D_{P}+D_{D})[/tex] (4)

([tex]D_{P} = 96\,mm[/tex], [tex]D_{D} = 384\,mm[/tex])

[tex]d = \frac{1}{2}\cdot (96\,mm + 384\,mm)[/tex]

[tex]d = 240\,mm[/tex]

The theoretical center-to-center distance is 240 millimeters.

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