# Op Amp Contest: Generate Spirograph Shapes Using Only Op Amps And Math

If you’re a child of the ’80s or ’90s, chances are you’ve spent hours tracing out intricate patterns using the pens and gears of a Spirograph kit. Simple as those parts may be, they’re actually a very clever technique for plotting mathematical functions called hypotrochoids and epitrochoids. [Craig] has spent some time analyzing these functions, and realized you can also implement them with analog circuits. He used this knowledge to design a device called Op Art which generates Spirograph shapes on your oscilloscope using just a handful of op amps.

To draw either a hypotrochoid or an epitrochoid, you need to generate sine and cosine waves of various frequencies, and then add them with a certain scaling factor. Generating sines and cosines is not so hard to do with op amps, but making an adjustable oscillator that reliably churns out matching sine and cosine waves over a large frequency range turned out to be tricky. After a bit of experimentation, [Craig] discovered that a phase-shift oscillator was the right topology, not only for its adjustability but also because it generates sine, cosine and inverted sine terms that all come in handy when drawing various Spirograph shapes. Continue reading “Op Amp Contest: Generate Spirograph Shapes Using Only Op Amps And Math”

# Arduino Drives Faux Spirograph

The holidays always remind us of our favorite toys from when we were kids. Johnny Astro, an Erector set, and — of course — a Spirograph. [CraftDiaries] has an Arduino machine that isn’t quite a Spirograph, but it sure reminds us of one. The Arduino drives two stepper motors that connect to a pen that can create some interesting patterns.

The build uses a few parts that were laser cut, but they don’t look like they’d be hard to fabricate using conventional means or even 3D printing. The author even mentions you could make them out of cardboard or foamboard if you wanted to.

# Jigsaw Puzzle Lights Up With Each Piece

Putting the last piece of a project together and finally finishing it up is a satisfying feeling. When the last piece of a puzzle like that is a literal puzzle, though, it’s even better. [Nadieh] has been working on this jigsaw puzzle that displays a fireworks-like effect whenever a piece is placed correctly, using a lot of familiar electronics and some unique, well-polished design.

The puzzle is a hexagonal shape and based on a hexagonally symmetric spirograph, with the puzzle board placed into an enclosure which houses all of the electronics. Each puzzle piece has a piece of copper embedded in a unique location so when it is placed on the board, the device can tell if it was placed properly or not. If it was, an array of color LEDs mounted beneath a translucent diffuser creates a lighting effect that branches across the entire board like an explosion. The large number of pieces requires a multiplexer for the microcontroller, an ATtiny3216.

This project came out of a FabAcademy, so the documentation is incredibly thorough. In fact, everything on this project is open sourced and available on the project page from the code to the files required for cutting out the puzzle pieces and the enclosure. It’s an impressive build with a polish we would expect from a commercial product, and reminds us of an electrified jigsaw puzzle we saw in a previous build.

Thanks to [henk] for the tip!

# Cycloid Drawing Machine Uses Sneaky Stepper Hack

Stepper motors are great for projects that require accurate control of motion. 3D printers, CNC machines and plotters are often built using these useful devices. [InventorArtist] built a stepper-based cycloid drawing machine, and made use of a nifty little hack along the way.

The machine uses a rotating turntable to spin a piece of drawing paper. A pen is then placed in a pantograph mechanism, controlled by another two stepper motors. The build uses the common 28BYJ-48 motor, which are a unipolar, 5-wire design. A common hack is to open these motors up and cut a trace in order to convert them to bipolar operation, netting more torque at the expense of being more complex to drive. [InventorArtist] worked in collaboration with [Doug Commons], who had the idea of instead simply drilling a hole through the case of the motor to cut the trace. This saves opening the motor, and makes the conversion a snap.

[InventorArtist] was able to create a machine capable of beautiful spirograph drawings, and develop a useful hack along the way. Reports are that a jig is in development to make the process foolproof for those keen to mod their own motors. We expect to see parts up on Thingiverse any day now. We’ve also covered the basic version of this hack before.

[Thanks to Darcy Whyte for the tip!]

# 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?

# Giant Spirograph Delights Children, Dwarfs Banana

Late 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

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.

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!