10182

Robotics Application of Lissajous Curves

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.

DETAILS

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

PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.