Robotics Application of Lissajous Curves

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This Demonstration shows a polishing robotic arm whose pad moves following a Lissajous curve, which is being drawn in the screen during the animation. You can vary the frequencies of the vertical and horizontal movements using their respective controls. According to these values, different curves are constructed. The animation finishes when the curve has completed a whole period. The animation simulates the movement of the individual parts that form the robotic arm.

Contributed by: Francisco Velázquez (March 2011)
Open content licensed under CC BY-NC-SA



The movement is determined by the parametric function (horizontal movement) and (vertical movement), where and are the frequencies for each function. Since these frequencies are multiples of , the period of the Lissajous curve is calculated as the least common multiple (LCM) of the vertical and horizontal periods; the animation finishes when the period of the curve is completed. If you change the frequencies, the period will be recalculated instantly. The animation progress control does not depend on the period of the curve.

Based on an exercise taken from [1].


[1] H. Anton, I. Bivens, and S. Davis, Calculus—Early Transcendentals, 9th ed., New York: John Wiley & Sons, 2008.

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