polar coordinates

5 Articles

Two geared plastic disks can be seen on a platform. One disk rotates around a central column, while the other is mounted on a platform that extends from the edge of the first disk. The second disk holds a print bed, and a print head mounted on the column is positioned just above a half-finished 3D print.

A Toolchanging Inverse SCARA 3D Printer

October 18, 2025 by 17 Comments

There are some times when a picture, or better yet a video, really is worth a thousand words, and [heinz]’s dual-disk polar 3D printer is one of those projects. Perhaps the best way to describe it is as an inverted SCARA system that moves the print bed around the hot end, producing strange and mesmerizing motion paths.

The Z-axis runs on a column through the center of the printer, while the print bed is a geared disk that can independently rotate both around its own center and around the central column. This gives the printer a simple way to use multiple extruders: simply mount the extruders at different angles around the central pillar, then rotate the bed around to whichever extruder is currently in use. (See the video demo below.) Since the extruder only moves in the Z direction, there’s also no need to make it as light as possible. In one test, it worked perfectly well with a five-filament direct-drive extruder assembly weighing two kilograms, though it proved a bit unwieldy.

[heinz] 3D printed the rotating disks and a few other parts of the printer, and used two GT2 timing pulleys and the bearings from a Lazy Susan to drive the disks and let them rotate. The print bed’s surface is made out of fiberglass, and since it’s unheated, it has a pattern of small holes drilled into it to let molten plastic seep in and adhere. One nice side effect of the rotating print bed is that it can produce a turntable effect on time-lapse videos.

We’ve covered this project once before when it was a bit earlier in development, and somehow we missed when it got upgraded to its current status. Let’s just say we’re impressed!

Polar 3D printers may make it a bit harder to visualize paths, but they can do unique things like print with four heads at a time or print in non-planar paths.

Continue reading “A Toolchanging Inverse SCARA 3D Printer” →

Automating The Process Of Drawing With Chalk

January 31, 2025 by 15 Comments

Chalk is fun to draw with, and some people even get really good at using it to make art on the sidewalk. If you don’t like tediously developing such skills, though, you could go another route. [MrDadVs] built a robot to scrawl chalk pictures for him, and the results speak for themselves.

The robot is known as AP for reasons you’ll have to watch the video to understand. You might be imagining a little rover that crawls around on wheels dotting at the pavement with a stick of chalk, but the actual design is quite different. Instead, [MrDadVs] effectively built a polar-coordinate plotter to make chalk pictures on the ground. AP has a arm loaded with a custom liquid chalk delivery system for marking the pavement. It’s rotated by a stepper motor with the aid of a 3D-printed geartrain that helps give it enough torque. It’s controlled by an ESP32 running the FluidNC software which is a flexible open-source CNC firmware. [MrDadVs] does a great job of explaining how everything works together, from converting cartesian coordinates into a polar format, to getting the machine to work wirelessly.

Building a capable sidewalk chalk robot seems like a great way to spend six months. Particularly when it can draw this well. Video after the break.

Continue reading “Automating The Process Of Drawing With Chalk” →

Fast 3D Printing With A Polar, Four Quadrant Custom Machine

August 26, 2024 by 14 Comments

3D printing is all well and good for making low numbers of units, so long as they’re small enough to print in a reasonable time, but what if you want to go really big? Does a 35-hour print time sound like a fun time? Would it even make it that long? [Nathan] from Nathan Build Robots didn’t fancy the wait, so they embarked on a project to build a huge parallel 3D printer with four independent print heads. Well, kind of. Continue reading “Fast 3D Printing With A Polar, Four Quadrant Custom Machine” →

Pen Plotter Uses Polar Coordinates

August 23, 2023 by 12 Comments

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 [André] 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.

Continue reading “Pen Plotter Uses Polar Coordinates” →

Sand Drawing Plotter Runs On ESP32

July 21, 2023 by 3 Comments

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.

Continue reading “Sand Drawing Plotter Runs On ESP32” →