The cycloid is defined as the locus of a point on the circumference of a cylinder which rolls without slip along a flat surface. The method of construction is shown in Fig. 10.14.
1 Draw the given circle, and divide into a convenient number of parts; eight divisions are shown in Fig. 10.14.
2 Divide line AA1 into eight equal lengths. Line AA1 is equal to the length of the circumference.
3 Draw vertical lines from points 2 to 8 to intersect with the horizontal line from centre O at points O2, O3, etc.
4 With radius OA and centre O2, describe an arc to intersect with the horizontal line projected from B.
5 Repeat with radius OA from centre O3 to intersect with the horizontal line projected from point C. Repeat this procedure.
6 Commencing at point A, join the above intersections to form the required cycloid.
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