An epicycloid is defined as the locus of a point on the circumference of a circle which rolls without slip around the outside of another circle. The method of construction is shown in Fig. 10.15.
1 Draw the curved surface and the rolling circle, and divide the circle into a convenient number of parts (say 6) and number them as shown.
Epicycloid
Direction of rotation of rolling circle
Initial position of rolling circle
Epicycloid
Direction of rotation of rolling circle
Initial position of rolling circle
Final position of rolling circle
Base circle
Final position of rolling circle
Base circle
2 Calculate the length of the circumference of the smaller and the larger circle, and from this information calculate the angle 0 covered by the rolling circle.
3 Divide the angle 0 into the same number of parts as the rolling circle.
4 Draw the arc which is the locus of the centre of the rolling circle.
5 The lines forming the angles in step 3 will now intersect with the arc in step 4 to give six further positions of the centres of the rolling circle as it rotates.
6 From the second centre, draw radius R to intersect with the arc from point 2 on the rolling circle. Repeat this process for points 3, 4, 5 and 6.
7 Draw a smooth curve through the points of intersection, to give the required epicycloid.
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