# Generating Lissajous Figures

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Given two wheels connected by a belt and a point on the outer rim of each, one can generate a Lissajous figure by the motion of the wheels. The coordinates of a point on a wheel can be described by sine functions of a certain frequency and phase shift. The ratio of the radii at the ends of the belt determines the relative frequencies of the coordinate of the red point on the upper left wheel and the coordinate of the red point on the lower right wheel. If the starting position of a point on a wheel is offset by a certain angle, a phase shift occurs in the sine functions describing the coordinates of the point.

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Contributed by: Michael Rogers (Oxford College/Emory University) (March 2011)

Open content licensed under CC BY-NC-SA

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