This section is from the book "Modern Shop Practice", by Howard Monroe Raymond. Also available from Amazon: Modern Shop Practice.

The epicycloid and the hypocycloid may be drawn in the same manner as the cycloid if arcs of circles are used in place of the horizontal lines. With 0 as a center and a radius of 3/4 inch describe a circle. Draw the diameter E F of this circle and produce E F to G such that the line F G is 2 3/4 inches long. With G as a center and a radius F G, describe the arc A B of the director circle. With the same center G, draw the arc P Q which will be the path of the center of the generating circle as it rolls along the arc A B. Now divide the generating circle into any number of equal parts - twelve for instance - and through the points of division H, I, L, M, and N, draw arcs having G as a center. With the dividers set so that the distance between the points is equal to the chord H I, mark off distances on the director circle A F B. Through these points of division R, S, T, U, etc., draw radii intersecting the arc P Q in the points R', S', T', etc., and with these points as centers describe arcs of circles as in Problem 25. The intersections of these arcs with the arcs already drawn through the points if, H, L, M, etc., are points on the epicycloid. Thus the intersection of the circle whose center is R' with the arc drawn through the point II is a point upon the curve. Also the arc whose center is S' with the arc drawn through the point I is another point on the curve. The remaining points are found by repeating this process.

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