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.

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

Video Material for Construction of involute of Circle

Construction of Involute of circle


More in sem1
Construction of Involute of Square