Circle Involute

The involute of the circle was first studied by Huygens when he was considering clocks without pendula for use on ships at sea. He used the circle involute in his first pendulum clock in an attempt to force the pendulum to swing in the path of a cycloid. For a circle of radius ,

			(1)
			(2)

the parametric equation of the involute is given by

			(3)
			(4)

The arc length, curvature, and tangential angle are

			(5)
			(6)
			(7)

The Cesàro equation is

(8)