## Definition **:-**

**INVOLUTE** : IT IS A LOCUS OF A FREE END OF A STRING WHEN IT IS WOUND ROUND A CIRCULAR POLE.

**Construction**

**Step 1.** Point or end P of string AP is exactly πD distance away from A. Means if this string is wound round the circle, it will completely cover given circle. B will meet A after winding.

**Step 2.** Divide πD (AP) distance into 8 number of equal parts.

**Step 3.** Divide circle also into 8 number of equal parts.

**Step 4.** Name after A, 1, 2, 3, 4, etc. up to 8 on πD line AP as well as on circle (in anticlockwise direction).

**Step 5.** To radius C-1, C-2, C-3 up to C-8 draw tangents (from 1,2,3,4,etc to circle).

**Step 6.** Take distance 1 to P in compass and mark it on tangent from point 1 on circle (means one division less than distance AP).

**Step 7.** Name this point P1.

**Step 8.** Take 2-B distance in compass and mark it on the tangent from point 2. Name it point P2.

**Step 9.** Similarly take 3 to P, 4 to P, 5 to P up to 7 to P distance in compass and mark on respective tangents and locate P3, P4, P5 up to P8 (i.e. A) points and join them in smooth curve.

It is an **INVOLUTE** of a given circle.