Cycloid
From DT Online
Description
An Cycloid is the path traced by a point on the circumference of a circle as it rolls without slipping along a straight line. The curve has been used to design gear teeth and has sometimes been used by architects to design the shape of a curved roof. The term ‘cycloid’ is used also to describe the shape of some fish scales.
A line produced by a point following a set of rules in this way is known as the locus of a point (plural is loci).
Constructions
Drawing a Cycloid 

Note: The cycloid is a special case of Trochoid in which the point traced is on the circumference of the rolling circle. Using a similar technique, Superior and Inferior Trochoids can also be generated by plotting points either outside (as the tip of a paddle wheel as a boat is propelled by it) or inside the rolling circle (as if marked on a rolling disc for example) . Also, by similar trechniques, the base line can be replaced by a base circle and the rolling circle rolled around either the inside or the outside of it to generate Hypocycloids or Epicycloids  as used in Epicyclic Gearing for example ,