# Pen Plotter Uses Polar Coordinates

To keep track of a location in a two-dimensional space, two measurements are needed. Most of the time, we would naturally think to do this by the Cartesian method, measuring position along one axis and then again along a second axis. But this isn’t the only way of keeping track of position. Polar coordinates, where the distance from the origin and an angle are used as the two measurements, works just as well, and sometimes can be a preferred method. This pen plotter tosses the expected Cartesian methodology we would typically expect in favor of this polar system.

The first prototype that [AndrĂ©] built was a good proof of concept. A pen attached to a movable carriage on a single rotating arm produced passable drawings, but as all prototypes go this one needed some refinement. Limit switches at the ends of the table, as well as within the arm, served to orient the plotter so that it didn’t manually need to be zeroed out every time. A linear actuator was added to give finer control over the pen’s pressure on the table, and finally an encoder was added to the base of the plotter to more accurately correct positional errors in the rotating arm mechanism.

With everything said and done, the polar coordinate plotter seems to work just as well as its Cartesian cousins might, orienting it like this has some advantages as well. Specifically, it is more adapted to drawing curves or circles than an X-Y device might be able to, like we saw with this similar sand-drawing plotter. Also, if allowed to rotate its entire 360-degree reach instead of just the 90 degrees shown in the video, a machine like this could theoretically reach a wider workspace more easily than other plotters.

# Sand Drawing Plotter Runs On ESP32

Humans have always drawn lines in the sand, whether it’s to communicate a plan of attack or to indicate metaphorically a very real boundary. It’s also something we do just for the aesthetic pleasure, and this plotter from [aidenvigue] is great at performing in just that role.

The plotter traces patterns in the circular sand tray by dragging a small marble with a magnet. This is achieved with a pair of NEMA 17 stepper motors, set up in a polar coordinate fashion. One stepper motor controls the angle, while another motor controls the marble’s distance from the center point of the circle. It’s a simple way to build a circular plotter, and works far better than a Cartesian setup would for this geometry. The build uses an ESP32 as the brains of the operation. It hosts a web interface that allows various patterns to be selected and run on the device. It also runs a set of addressable SK6812 LEDs that light the sand rather nicely.

We’ve seen some great sand plotters before, and have always been particular fans of the larger variety. Video after the break.

Posted in Art