Construction of Involute of Circle

Sample Problem 1:A coir is unwounded from a drum of 30mm diameter. Draw the locus of the free end of the coir for unwinding through an angle of 360º. Draw also a normal and tangent at any point on the curve.

Steps for Construction of Involute of Circle:

1. Draw the given circle. Divide it into 12 equal parts as 1,2,3,…,12.
2. Let P be the starting point i.e., One end of the thread. Draw PQ tangential to the circle at P and equal to πd (=π * 30mm).
3. Divide PQ into 12 equal parts as 1′,2′,….,12′. Draw tangents at 1,2,3,…,etc.
4. Mark P1,P2,….,P12 such that 1P1= P1′, 2P2 = P2′,… etc.
5. Draw a smooth involute of the circle through P,P1,P2,…,P12.
6. Mark any point M on the curve.
7. Draw a line joining M and center of the circle O. Mark the mid-point C on OM.
8. C as center and MC as radius , draw a semi-circle to cut the given circle at B.NOTE:Two semi-Circles can be drawn, one on the converging side of the   involute and another on the diverging side.It is important to note that the semi-circle on the diverging side of the involute alone should be considered.
9. Join MB, the Normal. At M, draw a line perpendicular to MB, to get Tangent TT.

NOTE:
Tangent to the circle at M is the normal to the involute at the same point M.

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