Cycloid

A cycloid is a curve generated by a point on the circumference of the circle as the circle rolls along a straight line with out slipping..The moving circle is called the "Generating circle" and the straight line is called the "Directing line" or the "Base line".The point on the Generating circle which generates the curve is called the "Generating point"

Construction of a Cycloid

Step1: Draw the generating circle and the base line equal to the circumference of the generating circle

Step 2 : Divide the circle and the base line in to equal number of parts. also erect the perpendicular lines from the division of the line

Step 3: with your compass set to the radius of the circle and centers as C1,C2,C3,.... etc cut the arcs on the lines from circle through 1,2,3, .. etc.

Step 4: locate the points which are produced by cutting arcs and joining by a smooth curve.

By joining these new points you will have created the locus of the point P for the circle as it rotates along the straight line with out slipping

As our final result is a cycloid