Given two curves C_{1} and C_{2} and a point P attached to curve
C_{2}. Now let curve C_{2} roll along curve C_{1},
without slipping. Then P describes a roulette ^{1)}.
When P is on curve C2, the curve is called a pointroulette.
When P is on a line attached to C2, the curve is called a lineroulette.
When working in the complex plane and both curves C_{1 }and C_{2 }are
expressed as function of the arc length, the resulting curve z can be written as
a function of C_{1 }and C_{2 }^{2)}.
The first to describe these curves where Besant (1869) and Bernat (1869),
respectively.
The following roulettes can be distinguished, for a curve C_{2} that is rolling
over a curve C_{1}:
The pointroulettes for which a circle rolls on a line or on another circle,
are known as cycloidal curves.
Some authors name the roulette a spirographic curve.
The same curves can be defined as a glissette ^{3)}: as the locus of a point
or a envelope of a line which slides between two given curves C_{1} and
C_{2}.
An wideknown example of a glissette is the astroid.
notes
1) rouler (Fr.) = to roll.
In Dutch: rolkromme.
2) The formula follows from the isometric insight that C_{1}(t)
 z(t) / C_{2}(t)  z(0) = C_{1}'(t) / C_{2}'(t).
Example for the cycloid: C_{1}(t) = t and C_{2}(t)
= i  i e it where t is the arc length.
3) glisser (Fr.) = to glide.
