**Gear Trains**

Gear teeth are designed so that the number of teeth on a gear is proportional to the radius of its pitch circle, and so that the pitch circles of meshing gears roll on each other without slipping. The speed ratio for a pair of meshing gears can be computed from ratio of the radii of the pitch circles and the ratio of the number of teeth on each gear, its gear ratio.

The velocity *v* of the point of contact on the pitch circles is the same on both gears, and is given by

where input gear *A* has radius *r _{A}* and meshes with output gear

*B*of radius

*r*therefore,

_{B},where *N _{A}* is the number of teeth on the input gear and

*N*is the number of teeth on the output gear.

_{B}The mechanical advantage of a pair of meshing gears for which the input gear has *N _{A}* teeth and the output gear has

*N*teeth is given by

_{B}This shows that if the output gear *G*_{B} has more teeth than the input gear *G*_{A}, then the gear train *amplifies* the input torque. And, if the output gear has fewer teeth than the input gear, then the gear train *reduces* the input torque.

If the output gear of a gear train rotates more slowly than the input gear, then the gear train is called a *speed reducer*. In this case, because the output gear must have more teeth than the input gear, the speed reducer will amplify the input torque.

Read more about this topic: Leverage

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### Famous quotes containing the words trains and/or gear:

“In this country, you never pull the emergency brake, even when there is an emergency. It is imperative that the *trains* run on schedule.”

—Friedrich Dürrenmatt (1921–1990)

“But Lord, remember me and mine

Wi’ mercies temporal and divine!

That I for grace and *gear* may shine,

Excelled by nane!

And a’ the glory shall be thine!

Amen! Amen!”

—Robert Burns (1759–1796)