Draw vertical lines from all the divisions 1 – 12.
Draw horizontal lines from the points intersection of the radiating lines 1 – 12 and the inner circle to intersect with the vertical lines.
Join their points of intersections to get the ellipse.
THE CYCLOID This is the locus of a point on the circumference of a circle rolling along a fixed straight line without slipping.
To construct a cycloid given the radius of the rolling circle e.g. 21mm
Procedure: Draw the circle with the given radius 21mm
Divide the circle with a number of equal parts e.g. 12
Draw a line AB horizontal and tangential to the rolling circle at O.
Make AB equal to the circumference of the circle i.e. D or 2R =
Divide lines AB into the same number of equal parts as the circle and draw vertical lines on each division.
Using radius of the rolling circle centres at the points of intersection of the vertical lines and the centre line draw arc to cut the corresponding horizontal lines.
Join the points with a smooth curve to get the cycloid.
