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 rA and meshes with output gear B of radius rB, therefore,
where NA is the number of teeth on the input gear and NB is the number of teeth on the output gear.
The mechanical advantage of a pair of meshing gears for which the input gear has NA teeth and the output gear has NB teeth is given by
This shows that if the output gear GB has more teeth than the input gear GA, 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
Other articles related to "gear trains, gear, gears":
... the renaissance scientist Georgius Agricola show gear trains with cylindrical teeth ... The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio ... Some important features of gears and gear trains are The ratio of the pitch circles of mating gears defines the speed ratio and the mechanical advantage of the gear set ...
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 (19211990)
“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!
—Robert Burns (17591796)