When a flexible thread is unwound from a circle or square etc., (the thread being kept stretched), the curve traced out by the end of the thread is called an “Involute”.
PRACTICAL APPLICATION
The profile of a gear teeth is an involute of a circle. Although theoretically, an involute profile is not the correct shape for maximum efficiency, but it is the most convenient shape from the point of view of the manufacture and provides satisfactory compromise. Cams are often designed to the involute shape, because such designs furnish constant speed and also it ensures the rolling contact between the roller and the follower.
TO DRAW AN INVOLUTE
The following examples show the procedure for drawing an involute..
Q.Draw the involute of an equilateral triangle of 15 mm side.
SOLUTION:
Draw the equilateral triangle ABC. Produce the lines AB, BC, and CA. With the c. and radius CA draw an arc to intersect BC produced at 1. Now with the centre B and radius B1 draw an arc to intersect AB produced at 2. Lastly with the centre ‘a’ and radius A2, draw an arc to intersect CA produced at 3 and complete the curve.
INVOLUTE OF A POLYGON
Q.Draw the involute of a pentagon of 15 mm side.
SOLUTION:
Draw the given polygon say, a pentagon. Produce the sides BA, CB, DC, and AE with the centres and radius BA draw an arc to intersect CB produced at 1.
Here BA B1; C2 CB + BA 2BA; D33BA E4 4BA; and A5 = 5BA
Now with the centre C and radius C1, draw an arc to intersect DC produced at 2. Similarly, with the centres D, E and A, and radii D2, E3, A4 draw arcs and complete the curve.
This procedure should be followed to draw the involute of any other required polygon.
Q.Draw the involute of a circle of diametre 30 mm.
SOLUTION:
Draw the given circle. Divide the circle into twelve equal divisions. Draw tangents at all the divisional points. Measures PQ equal to the circumference of the circle and divide it into twelve equal parts. On the tangent drawn at point 1, cut off 1 P_{1} = P_{1} . Similarly obtain the points P_{2} P3, P_{4} etc., and draw a smooth curve passing through these points.
Here 1 – p_{1} = P – 1 1 – P_{2} = P – 2 1 – P_{3} = P – 3 and so
