Draw an involute to a circle of diameter 50 mm. Also draw a tangent and normal to the curve at any point.
1 Answer

Ans – Given Data:-

Diameter of circle Φ = 50 mm


1) Draw a circle of 50 mm diameter.

2) Draw horizontal and vertical axis and mark centre of the circle say C.

3) Divide the circle into 12 equal parts and name each division 1, 2, 3, ….12 as per shown in fig.

4) Draw a straight horizontal line of length πD from the contact point of circle and ground.

5) Divide the line into 12 equal parts 1’, 2’, 3’…..12’ (same no. as that of circle).

6) Draw tangent from each point 1, 2, 3….12.

7) Taking 1 as centre on circle and 1’-P’ (distance on horizontal line) as radius cut the line tangent at point 1. Mark that point P1.

8) Repeat the same procedure for all the points changing the centre and radius accordingly.

9) Draw smooth curve passing through all points (P1, P2, ….. P12) and name the curve.

10) Take any point M on the curve. Join M and centre point C of the circle.

11) Locate the midpoint of line CM. Mark it as C1.

12) Taking C1 as centre and C1-M as radius, draw a semi circle which will cut the circle at point say N.

13) Draw a line passing through M and N (Norman NMN)

14) Draw a line perpendicular to normal through point M (Tangent TMT). enter image description here

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