Free Spirograph Generator for 3D Printers and Laser Cutters
A toothed ring and wheels with pen holes, sized by you, drawn for you before you make them. One file, any pen, endless patterns.
About the Spirograph Set Designer
Choose how many teeth the ring has and how many each wheel has, and the Drawing view rolls the wheel round the ring and draws the pattern a pen would, hole by hole. The Pattern view shows the finished result for every hole at once, inside the ring and around its outer teeth. The Parts view shows the pieces as they will sit on your print bed, with the largest wheel nested inside the ring to save space. Switch to Laser cutting and the Sheet view shows the cut file instead: red cut lines, blue engraving, the largest wheel cut from the ring's own middle. Download one STL and print it flat with no supports, or one SVG and cut it.
The math under the pen
The number of petals is the ring's teeth divided by the largest factor it shares with the wheel. 96 and 60 share 12, so 8 petals in 5 laps. 105 and 50 share 5, so 21 petals in 10 laps. Teeth that share nothing, like 96 and 35, draw the dense lace patterns: 96 petals in 35 laps. The curve itself is a hypotrochoid, and some ratios draw curves with names: 3 to 1 is a deltoid (a rounded triangle), 4 to 1 an astroid (a four-pointed star), 6 to 1 a six-cusped hypocycloid, and 2 to 1 an ellipse, which becomes a straight line when the pen sits at the wheel's very edge and a circle when it sits at the centre. The Shapes presets set these up with one click.
What you need
A 3D printer and about 40 g of PLA, or a laser cutter and a sheet of 3 mm plywood or acrylic (13 by 18 cm covers the three-wheel Classic set); then paper, masking tape (or three push pins and a cork board) and a ballpoint pen. Many public-library makerspaces have one or both machines, free to use with a library card.
How to use it
- Print or cut the set. On a 3D printer, open the STL in your slicer at 100 percent: PLA, 0.2 mm layers, no supports. The Classic set takes roughly an hour and a half; Mini about 40 minutes. On a laser cutter, switch to Laser cutting first, open the SVG at 100 percent, engrave the blue and then cut the red from 3 mm plywood or acrylic.
- Hold the ring down. Put a sheet of paper on a table and tape two edges of the ring's flat rim to the paper so it cannot slide; masking tape peels off cleanly. On a cork board or a piece of cardboard, push pins through the ring's three small holes instead.
- Set a wheel inside. Drop a wheel inside the ring and turn it until its teeth sit between the ring's teeth. For the outside patterns, set it against the ring's outer teeth instead.
- Pen in a hole. Push a ballpoint pen through one of the holes until the tip touches the paper. Hole 1, nearest the edge, draws the biggest pattern.
- Go round and round. Press the pen lightly outward against the ring and move it in circles. Keep going until the line meets itself: the Drawing view shows how many laps that takes.
- Change one thing. Move the pen to another hole, swap wheels, or roll around the outside. Every change is a new pattern; layer them in different colours.
In the classroom
One set serves a table of four. Each student picks a wheel-and-hole pair, predicts the petal count from the teeth, draws it, and the table compares results: the quickest way into factors, ratios and symmetry that also ends with something to take home. Print the Mini set for small hands and short library sessions.
Frequently Asked Questions
Which pens fit the holes?
The default 3 mm hole takes most ballpoint pens (the cone of the tip rests in the hole and the ball reaches the paper). On the 3D-printed wheels each hole also widens toward the top face, so a pen with a long cone seats deeper. Fine liners and gel pens with a slim tip work too. For a sharpened pencil or a thicker marker, set Hole Ø to 4 mm under Advanced Design before you download.
Why does the pattern never seem to close?
It always closes; some pairs just take many laps. The wheel comes back to its start after wheel teeth ÷ shared factor laps. 96 and 60 share 12, so 5 laps and 8 petals. 96 and 35 share nothing, so 35 laps and 96 petals: the lace patterns. The Drawing view tells you the lap count before you print.
Why does moving the pen to another hole change the shape?
The hole sets how far the pen sits from the wheel's centre. Near the edge, the pen swings wide and draws pointed petals; near the centre, it barely moves and draws a rounded, almost circular shape. Same ring, same wheel, five holes, five patterns.
What bed size do I need?
The Classic set lays out at about 129 by 179 mm with the biggest wheel nested inside the ring, so it prints on a 180 mm bed such as the Bambu A1 mini. The Lace preset's 144-tooth ring is 177 mm across and its three-wheel set runs to 245 mm tall, so on a 220 mm bed print it as two jobs (every slicer can split the parts). The Size line under the sliders shows the exact footprint for your settings.
Can I laser cut it instead?
Yes. Switch the tool to Laser cutting and download the SVG. Red lines are cuts and blue shapes are engraving (the hole numbers, the tooth counts and the designerbee.build mark), so engrave first, then cut. Use 3 mm plywood or acrylic at 100 percent scale. The biggest wheel is cut from the ring's own middle, so a set needs little material, and every tooth is drawn 0.1 mm fuller to make up for the width of the laser beam.
Which filament and settings?
PLA, 0.2 mm layers, three walls, 15 percent infill, no supports and no brim. Parts are flat, so they stick well. A slightly stiff filament such as PLA keeps the teeth crisp; TPU is too soft to mesh.
The wheel skips or jams on the teeth. What now?
First check the slicer did not scale the file: the ring teeth should be about 1 mm apart at the pitch line. If it still jams, your printer prints a little wide: set Tooth size to 1.1 mm. If it skips, press the pen gently outward against the ring while you draw, which is also the trick with the original toy.
Do I need to create an account?
No. The Spirograph Set Designer is free and runs in your browser. No sign-up, and nothing is uploaded. Designer Bee keeps only anonymous usage stats, like which settings get downloaded, to keep improving the tools.
