Textbook of Engineering Drawing, Second Edition

---------------__ GeometricaIContructions 4.31

The curve through A, PI' P 2 , P 3 and P 4 is the required involute.

A P 4 is equal to the perimeter of the square.

Note: To draw a normal and tangent to the curve at any point, say M on it, as M lies on the arc
P l4 with its centre at A, the line AMN is the normal and the line TT drawn through M and
perpendicular to MA is the tangent to the curve.

Involutes of a triangle, Pentagon and Hexagon are shown Figs 4.45 to 47

To draw an involute of a given circle of radus R.

T~

N

/

T

a \

\

I.

\

i

L ____ -¥~------~~-------~P4 4 X a

1---------·---

Fig. 4.44

Construction (Fig. 4.48)

1. With 0 as centre and radius R, draw the given circle.


2. Taking P as the starting point, draw the tangent PA equal in length to the circumference of
   the circle.


3. Divide the line PA and the circle into the same number of equal pats and number the points.


4. Draw tangents to the circle at the points 1,2,3 etc., and locate the points PI' P 2 , P 3 etc., such
   that !PI = PI 1, 2P2 = P21 etc.
   A smooth curve through the points P, PI' P 2 etc., is the required involute.
   Note:


5. The tangent to the circle is a normal to the involute. Hence, to draw a normal and tangent at
   a point M on it, first draw the tangent BMN to the circle. This is the normal to the curve and