Construction of an inferior trochoid.
The construction procedure for obtaining an inferior trochoid is shown in figure 2. With centre C’ and radius R, draw a circle.  From A, draw a horizontal line  AB = 2πR. Draw C’- C” parallel and equal to AB and divide it in to 12 equal parts C1, C2, C3 ,…. C12. Draw the generating point Q’ along C’-A. With centre C’ and radius  C’-Q’ draw a circle and divide the circumference in to 12 equal parts and label tham as  1,2,3, ….,12.  With C1, C2, C3,etc., as the centres and radius equal to C’-Q’, cut arcs on the horizontal lines through 1,2,3,etc., to locate  the points Q1, Q2, Q3, etc. Join Q1, Q2, Q3, etc., to obtain the inferior trochoid.

Figure 2. Construction of an inferior trochoid.

 

Construction of a Superior Trochoid
The construction procedure for obtaining a superior trochoid is shown in Figure 3. With centre C’ and radius R, draw a circle.  From A, draw a horizontal line  AB = 2πR. Draw C’- C” parallel and equal to AB and divide it in to 12 equal parts C1, C2, C3 ,…. C12. Draw the generating point P’ along C’-A. With centre C’ and radius  C’-P’ draw a circle and divide the circumference in to 12 equal parts and label them as  1,2,3, ….,12.  With C1, C2, C3,etc., as the centres and radius equal to C’-P’, cut arcs on the horizontal lines through 1,2,3,etc., to locate  the points P1, P2, P3, etc. Join P1, P2, P3, etc.,  to obtain the superior trochoid.

Figure 3 Construction of a superior Trochoid.