Textbook of Engineering Drawing, Second Edition

---------------------GeometricaIContructions 4.33

2. The gear tooth profile is nonnally of the involute curve of circle as shown in Fig 4.49.

EXAMPLES

"

Fig. 4.48

Problem: Construct a conic when the distance of its focus from its directrix is equal to 50 mm
and its eccentricity is 2/3. N arne the curve, mark its major axis and minor axis. Draw a tangent at
any point, P on the curve.

Solution : (Fig. 4.50)

1. As the eccentricity is less than 1, the curve is an ellipse.


2. Draw one directrix, DD and the axis, AA' perpendicular to DD and mark the focus, F such
   that FA = 50 mm.

3. As the eccentricity is 2/3, divide FA into 2 + 3 = 5 equal parts. Bydefmition VFNA=2/3 and

hence locate the vertex, V. Draw VE perpendicular to the axis such that VE = VF. Join AE

and extend it as shown in Fig. 4.50. This is the eccentricity scale, which gives the distances

directly in the required ratio. In triangle AVE, VENA=VFNA=2/3

4. Mark any point 1 on the axis and draw a perpendicular through it to intersectAE produced
   at I'. With centre F and radius equal to I-I' draw arcs to intersect the perpendicular through

INVOLUTE I I

I-I

Fig. 4.49 Involute of a circle as gear tooth profile