# CYCLOIDS AND THEIR CONSTRUCTION

·                     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