Evolute and Involute

Let 𝐶 and 𝐶1 are two one-one correspondence space curves such that tangent at any point on 𝐶 is a normal to the corresponding point on 𝐶1 then C is called evolute of 𝐶1 and 𝐶1 is called involute of 𝐶. i.e. if C is evolute of 𝐶1 then

a. 𝐶1 lies in the tangent surface of C b. tangent vectors to 𝐶 and 𝐶1 are perpendicular

Blue curve- Evolute

Red curve- Involute

Blue curve- Evolute

Red curve- Involute

Circle- Evolute

Dotted curve- Involute