# Gear Ratios

Gear ratios are one of the most common design decisions that a team must master in order to optimize mechanical advantage in their designs.

Sourced from RoboMatter

A

`Gear Ratio`

is defined as the ratio of the rotational speeds of the first and final gears in a train of gears or of any two meshing gears. Essentially, the ratio of the input speed to the output speed of a geared set of shafts. These can be decided to choose a ratio of **Speed**(large gear driving small gear) or**Torque****(small gear driving large gear).**Gear ratios are often simplified fractions of the number of teeth on each gear. This is because (at least in Vex) gears have a proportional number of teeth to their diameter which defines the difference in output speed. From the above image, there is a 12 tooth gear, driving a 36 tooth gear which would constitute a 3:1 ratio.

$Gear Ratio = \frac{Driven}{Driving} = Driven : Driving$

The benefit of gear ratios is the ability to choose

**speed**vs**torque**in a system. These have an inverse relationship however where a faster output will have lower torque. With the above example, the output shaft has 3x the torque, but also 1/3 the speed.

Last modified 5mo ago