Making Spirographs with LEGO and Math

Master LEGO builder [Yoshihito Isogawa] has been on a roll lately, cranking out a number of robots that make drawings reminiscent of the classic Spirograph toy. For instance, he built an elegant drawbot out of LEGO elements, seen above. At first glance the monicker “spirograph” seems wrong, because where are the gears? However, [Yoshihito] has them stashed underneath the sheet of paper, with magnets controlling the pens.

His drawbot consists of a platform (cleverly, an inverted LEGO plate) upon which a sheet of paper is laid. One or two pen holders, each with a pair of magnets underneath, rest on the sheet of paper. Beneath the plate, two pairs of spinning magnets rotate around a double layer of 11×11 curved racks, which then play the role of the classic spirograph rings. An EV3-controlled motor powers the whole thing.

He also makes use of an obscure part–the 14-tooth bevel gear, last manufactured by LEGO in 2002 and even then it was mostly sold in part assortments intended for the education market. It’s so obscure LEGO doesn’t even provide the gear in their online building program LEGO Digital Designer, though (of course) the LDraw folks re-created it — it’s brick 4143 in the library, seen below.

Spirograph Gear Math

This gear becomes important in spirograph-style projects because tooth count is everything. There really aren’t that many spirograph designs that can be made with LEGO, because there are a limited number of gears and they mostly have the same tooth counts–the smaller ones sport 8, 12, or 16 teeth, medium-sized ones 20 or 24 teeth, and larger ones 36 or 40 — see a pattern? Such predictability may be great for a building set, but it doesn’t engender a lot of spirograph diversity.

When you compute the number of vertices in a spirograph shape, you take the least common multiple of the two gears (or sets of gears) and divide by the small gear. So a 60-tooth turntable turning a pair of 14-tooth gears has an LCM of 420, and you divide by 28 to get the number of vertices: 15. Remove one of those smaller gears and the vertices increase to 30. The challenge in creating new shapes with a LEGO spirograph lays in swapping in new gears, just like the original toy, and having more ways to come up with unusual gear ratios makes for more interesting drawings.

Another that makes the 14-tooth gear so alluring to [Yoshihito] is that it’s one of the few LEGO gears with a number of teeth not divisible by 4. Among other things this means the gear meshes with an identical gear at 90 degrees. Usually the gears have the same number for each quarter of the circumference and meshing becomes a matter of jogging one gear a scosh. This can be a problem because LEGO axles have a “plus” shaped profile, and you may not want everything on that axle tilted as well — having a 90-degree solution makes a lot of sense.

[Yoshihito] designs LEGO robots out of Isogawa Studio and has written several books on advanced LEGO techniques, published by No Starch. He specializes in small and elegant mechanisms — finding the perfect set of elements that work together effortlessly. You can see an example in the gear assembly to the right — a pair of the aforementioned 14-tooth bevel gears, turned into a normal gear with the help of that golden spacer, none other than a One Ring from LEGO’s Lord of the Rings product line. You can find videos of his projects on YouTube.

[Yoshihito] has released a number of variants of the spirographing drawbot. What’s next? Maybe a harmonograph?

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Giant Spirograph Delights Children, Dwarfs Banana

giant spirographLate last year at a craft show, [hahabird] and a friend came across a laser-cut Spirograph and they both had a go at it. After mocking his friend’s lack of fine motor skills, [hahabird] was struck with the idea of making a giant-scale Spirograph that would (hopefully) be less frustrating for kids of all ages.

He generated the gears using an InkScape plugin, and then moved the project to Illustrator for adjustments. After nesting the inner gear drawings, he was able to print them out on one 3×3′ piece of paper at the local FedEx-Kinko’s. To make a template for routing he pieces that make up the eight-foot diameter outer ring, [hahabird] first cut it out of MDF and then bolted that to plywood. The outer ring’s size was dictated by the number of sections that fit on a 4×8 piece of plywood.

The challenge of the inner cogs was to make them move smoothly and still mesh with the teeth of the outer ring. [hahabird] solved this by mounting casters on raised platforms, which double nicely as handles. Each inner cog has a series of PVC couplers that take the 1″ PVC chalk holder insert.

So far, [hahabird] has cut 22-, 35-, and 44-tooth cogs, all of which are painted in nice, bright colors. According to his reddit comments, he will have a video or gif of it in a few days. We hope he makes the plus sign cog and the tongue depressor piece, too.

Art-O-Matic Is Spirograph’s Young Hip Offspring

Art-O-Matic automatic spirograph

Some of our more senior experienced readers may remember a toy called the Spirograph. In case you don’t, it’s a geometric shape drawing toy. The way it works is a plastic disc with gear teeth around the perimeter and various holes on its face is spun around a plastic ring with gear teeth on the inside. A pencil is inserted in one of the holes in the disc and, when spun around the inside of the ring, draws different complex shapes called hypotrochoids.

 Art-O-Matic automatic Spirograph

This was fun enough to keep a kid entertained for a few minutes. It took a while to make a complete shape and sometimes it was easy to mess up (especially if the hole chosen for the pencil was near the outside of the disc). [Darcy] thought it would be neat to combine the Spirograph’s drawing style with modern technology. The result is called the Art-O-Matic and it draws some pretty wild art, you guessed it, automatically.

Click past the break for more!

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Laser Kaleidoscope uses more 3D printing and less scavenging


At first we thought that [Pete Prodoehl] was using the wrong term when calling his project a Laser Kaleidoscope. We usually think of a kaleidoscope as a long tube with three mirrors and some beads or glass shards in one end. But we looked it up and there’s a second definition that means a constantly changing pattern. This fits the bill. Just like the laser Spirograph from last week, it makes fancy patterns using spinning mirrors. But [Pete] went with several 3D printed parts rather than repurposing PC fans.

In the foreground you can see the potentiometers which adjust the motor speeds. The knobs for these were all 3D printed. He also printed the mounting brackets for the three motors and the laser diode. A third set of printed parts makes mounting the round mirrors on the motor shaft quite easy. All of this came together with very tight tolerances as shown by the advanced shapes he manages to produce in the video after the break. Continue reading “Laser Kaleidoscope uses more 3D printing and less scavenging”

Laser Spirograph


Here’s a weekend junk bin project if we’ve ever seen one. [Pat] used a quartet of computer fans to make his laser Spirograph. Deciding to try this simple build for yourself will run you through a lot of basics when it comes to interfacing hardware with a microcontroller. In this case it’s the Arduino Nano.

The Spirograph works by bouncing a laser off of mirrors which are attached to the PC fans. When the fans spin the slight alignment changes cause the laser dot to bob and weave in visually pleasing ways. You can catch twenty minutes of the light show in the clip after the break.

Three of the fans have mirrors attached, the housing of the fourth is used to host the laser diode and make assembly easier. A TC4469 motor driver is used to connect the fans to the Arduino. The light show can be manually controlled by turning the trio of potentiometers which are read using the Arduino’s ADC.

If you manage your way through this build perhaps you’ll move on to a setup that throws laser light all over the room.

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Laser Spirograph exhibit repair and upgrade

[Bill Porter] continues finding ways to help out at the local museum. This time he’s plying his skills to fix a twenty-year-old exhibit that has been broken for some time. It’s a laser spirograph which had some parts way past their life expectancy.

He started by removing all of the electronics from the cabinet for further study in his lair. He examined the signal generator which when scoped seemed to be putting out some very nice sine waves as it should. From there he moved on to the galvos which tested way off of spec and turned out to be the offending elements.

A bit of searching around the interwebs and [Bill] figured out an upgrade plan for the older parts. But since he was at it, why not add some features at the same time? He rolled in a port so that just a bit of additional circuitry added later will allow shapes and logos to be drawn on the screen. One of his inspirations for this functionality came from another DIY laser projector project.

Take a look at the results of the repair process in the clip after the break.

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Laser cut clock reminds us of a Spirograph

[Brian] from Louisville’s LVL1 hackerspace sent in this laser cut gear clock that’s almost unlike any other clock we’ve seen before. [Brian] also put up a wonderful Instructable for his build.

Since LVL1 got a better laser cutter a lot of neat projects have been piling up. [Brian] based his clock around two cheap stepper motors driven by a freeduino. A chronodot was used to keep accurate time. Making the gears, though, presented a few problems. While prototyping the gear clock face, it was apparent that the numbers should be oriented along a line coming from the center of the gear. The prototype also used 100 teeth and that didn’t translate well into a clock design. [Brian] designed the minute gear with 60 teeth, and the hour gear with 144 teeth so that each tooth would equal 5 minutes.

[Brian]’s clock is functionally similar to this $2500 gem, and certainly much less expensive even after the cost of the laser cutter is taken into account. Of course, the Spirograph clock keeps track of minutes so it may be worth upwards of $5k.