Textbook of Engineering Drawing, Second Edition

_____ GeometricaIContructions 4.45

6. From'4 1 and 51 draw lines parallel to O~ and from 4 and 5 draw lines parallel to ORI to
   intersect at P 4 and Ps respectively


7. Join PI' P 2 ' P 3 ,P, P 4 , Ps by smooth rectangular hyperbola.
   R2

y

5

A x

30

o B R1

Fig. 4.64 Rectangular Hyperbola

Problem: Draw an epicycloid having a generating circle of diameter 50 mm and a directing curve
of radius 100 mm. Also draw a normal and a tangent at any point M on the curve.

Solution : (Fig.4.65)

1. Let, AB be the circumference of the generating circle of radius, r = 25 mm. Let, e be the
   angle subtended at the centre of the directing (base) circle of radius = 100 mm by the arc
   AB. Then,
   (Angle AOB)/360o= (Arc, AB/(Circumference of directing circle)
   I.e. e 1360 = (2 1t r) 1 (2 1t R)
   = (21t x 25) 1 21t x 100)
   e = (25 x 360°)/1 00
   =90°


2. Draw the arc AB with centre 0 and radius = 100 mm in such a way that the angle AOB = 90°.
   Join OA and extend it to C such that AC is equal to the radius of the rolling circle.


3. With centre C 2 and radius = 25 mm draw the rolling circle. Draw an arc CaCb with centre 0
   and radius = OCo Here, CaCb represents the locus of the centre of the rolling circle.


4. Divide the rolling circle into any number of equal parts (say 12). Also divide the arc CaCb
   into the same number of equal parts and mark the points as CI C 2 C 3 etc., as shown in
   Fig. 4.65...