Circle Involute

First studied by Huygens when he was considering clocks without pendula for use onships at sea. He used the circle involute in his first pendulum clock in an attempt to force the pendulum to swing in thepath of a Cycloid.

For a Circle with , the parametric equations of the circleand their derivatives are given by

(1)

(2)

(3)

(4)

(5)

			(6)
			(7)

The Arc Length, Curvature, and Tangential Angle are

			(8)
			(9)
			(10)

(11)

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 83, 1993.

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 190-191, 1972.

MacTutor History of Mathematics Archive. ``Involute of a Circle.''http://www-groups.dcs.st-and.ac.uk/~history/Curves/Involute.html.

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