is the attainment of a non fluctuating velocity ratio is
dependent on the profile of the teeth. Friction and wear between two gears
is also dependent on the tooth profile. There are a great many tooth
profiles that will give a constant velocity ratio, and in many cases, given
an arbitrary tooth shape, it is possible to develop a tooth profile for the
mating gear that will give a constant velocity ratio. However, two constant
velocity tooth profiles have been by far the most commonly used in modern
times. They are the cycloid
and the involute. The
cycloid was more common until the late 1800s; since then the involute has
largely superseded it, particularly in drive train applications. The cycloid
is in some ways the more interesting and flexible shape; however the
involute has two advantages: it is easier to manufacture, and it permits the
center to center spacing of the gears to vary over some range without
ruining the constancy of the velocity ratio. Cycloidal gears only work
properly if the center spacing is exactly right.