Involute
An Involute is a curve traced by the free end of a thread unwound from a circle or a polygon in such a way that the thread is always tight and tangential to the circle or side of the polygon.Figure 1 shows the involute of a circle.

Construction of Involute of circle

• Draw the circle with c as center and CP as radius.
• Draw line PQ = 2ΠCP, tangent to the circle at P
• Divide the circle into 12 equal parts. Number them as 1, 2…
• Divide the line PQ into 12 equal parts and number as 1΄, 2΄…..
• Draw tangents to the circle at 1, 2,3….
• Locate points P1, P2 such that 1-P1 = P1΄, 2-P2 = P2΄….
• Join P, P1, P2….
• The tangent to the circle at any point on it is always normal to the its involute.
• Join CN. Draw a semicircle with CN as diameter, cutting the circle at M. MN is the normal.

Figure 1. Construction of involute of a circle.