answer:From Wolfram MathWorld article on Circle Involute Pedal Curve: The pedal curve of circle involute f = cos t + t sin t g = sin t – t cos t with the center as the pedal point is the Archimedes’ spiral x = t sin t y = -t cos t. ———————— @prasad, it looks like you start with a circle, then take its involute, which is approximately an Archimedes’ spiral, then take the pedal curve of the involute, which is exactly an Archimedes spiral. The two curves are compared in this image from Wikipedia (black = circle involute; red = A. spiral).