Involute of Regular Polygon (pentagon)

Figure 2 shows the construction of Involute of a regular pentagon. Draw the pentagon A-B-C-D-E.  Extend line AE to P6 such that length E-P6 is equal to 5 times AE.  Extend line BA, CB, DC, and ED. With A as centre and radius equal to AE draw an arc to intersect the line BA extended at P1. Next with B as centre and radius equal to A-1, draw an arc to intersect the line BA extended at P2. With C as centre and radius equal to A-2, draw an arc to intersect the line DC extended at P3. The procedure is repeated till point P5 is obtained. Draw a smooth curve passing through P1, P2, P3, …, P5 to obtain the involute of the pentagon.

 

Figure 2. Involute of a pentagon.