Textbook of Engineering Drawing, Second Edition

4.48 Textbook of Enginnering Drawing------------------

Problem: Draw a hypocycloid having a generating circle of r1iameter 50 mm and directing

circle of radius 10 mm. Also draw a normal and a tangent at any point M on tile curve.

Solution : (Fig.4.67)

The construction of a hypocycloid is almost the same as that for epicycloid. Here, the centre of the

generating circle, C a is inside the directing circle. The tangent and the normal drawn at the point M

on the hypocycloid is shown in Fig.4.67

Fig. 4.67 Hypocycloid

Problem : Draw a hypocycloid of a circle of 40 mm diameter which rolls inside another

circle of 200 mm diameter for one revolution. Draw a tangent and normal at any point on it.

Solution : (Fig.4.68)

1. Taking any point 0 as centre and radius (R) 100 mm draw an arc PQ which subtends an
   angle e = 72° at O.


2. Let P be the generating point. On OP mark PC = r = 20 mm, the radius of the rolling circle.


3. With C as centre and radius r (20 mm) draw the rolling circle. Divide the rolling circle into 12
   equal parts as 1,2,3 etc., in clock wise direction, since the rolling circle is assumed to roll
   counter clock wise.


4. With 0 as centre, draw concentric arcs passing through 1, 2, 3 etc.


5. With 0 as centre and OC as radius draw an arc to represent the locus of centre.


6. Divide the arc PQ into same number of equal parts (12) as 1121 31 etc.

7. Join OIl 021 etc., which intersect the locus of centre at CIC 2 C 3 etc.

8. Taking centre CI and radius r, draw an arc cutting the arc Uirough 1 at PI. Similarly obtain
   the other points and draw a smooth curve through them.
   To draw a tangent and normal at a given point M:


9. With M as ce,ntre and radius r = CP cut the locus of centre at the point N.


10. Join ON and extend it to intersect the base circle at S.


11. JoinMS, the normal.


12. At M, draw a line perpendicular to MS to get the required tangent.