Editing Mechanical advantage (section)

== Gear trains ==
{{main|Gear train}}
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]].
[[File:Gears animation.gif|frame|right|alt=Animation: Small gear (left) and large gear (right) with a black background|Two meshing gears transmit rotational motion.]]

The velocity ''v'' of the point of contact on the pitch circles is the same on both gears, and is given by  
:<math> v = r_A \omega_A = r_B \omega_B,\!</math>
where input gear ''A'' has radius ''r<sub>A</sub>'' and meshes with output gear ''B'' of radius ''r<sub>B</sub>,
therefore,
:<math> \frac{\omega_A}{\omega_B} = \frac{r_B}{r_A} = \frac{N_B}{N_A}.</math>
where ''N<sub>A</sub>'' is the number of teeth on the input gear and ''N<sub>B</sub>'' is the number of teeth on the output gear.

The mechanical advantage of a pair of meshing gears for which the input gear has  ''N<sub>A</sub>'' teeth  and the output gear has ''N<sub>B</sub>'' teeth is given by
:<math> \mathit{MA} = \frac{r_B}{r_A}  = \frac{N_B}{N_A}.</math>

This shows that if the output gear ''G''<sub>B</sub> has more teeth than the input gear ''G''<sub>A</sub>, 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'' (Force multiplier).  In this case, because the output gear must have more teeth than the input gear, the speed reducer will amplify the input torque.