Arc length of one arch of cycloid [color=#0B5394]X(t) = ([i]rt[/i] – sin [i]t[/i],[i] r[/i] – cos t)[/color] is [i][color=#0B5394]8r[/color][/i] where [i][color=#0B5394]r[/color][/i] is radius of the rolling circle. Units of measurements are the same as axis units.

For different values of c you get a various type of cycloid.[br][list][br][*]Curtate cycloid: Here the point tracing out the curve is inside the circle, which rolls on a line.[br][/*][*]Prolate cycloid: Here the point tracing out the curve is outside the circle, which rolls on a line.[br][/*][/list]