Cycloid:

 Cycloids form a group of curve generated via the path of a fixed point on the circumference of a rolling circle. When the circle rolls on the straight line, the path is identified as a cycloid as display in diagram.

To sketch cycloid curve, sketch a horizontal line AA₁₂ and mark off the length of the rolling circle of diameter D. This length AA₁₂ is as same to πD. After that divide the rolling circle and its length, marked off on AA₁₂ into say 12 equal parts. Erect perpendiculars at point 1′ via 12′ to intersect the extended horizontal axis of the rolling circle at point O1 via O₁₂. Now sketch horizontal lines passing via the points of division of the rolling circle. From O₁ via O₁₂ centers and along with a radius equal to D/2 describe arcs to intersect the corresponding horizontal lines at the points A₁ to A₁₂ of the desired cycloid. A smooth curve is after that drawn via these points along with the aid of a French curve.