Mechanical Advantage
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.
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: Gear Train
Famous quotes containing the words mechanical and/or advantage:
“No sociologist ... should think himself too good, even in his old age, to make tens of thousands of quite trivial computations in his head and perhaps for months at a time. One cannot with impunity try to transfer this task entirely to mechanical assistants if one wishes to figure something, even though the final result is often small indeed.”
—Max Weber (1864–1920)
“In action, the English have the advantage enjoyed by free men always entitled to free discussion: of having a ready judgment on every question. We Germans, on the other hand, are always thinking. We think so much that we never form a judgment.”
—Heinrich Heine (1797–1856)