Comments on: Expanded table of points for drawing hypotrochoids and epitrochoids

By: XhanLuIsOfficial

XhanLuIsOfficial — Tue, 16 Sep 2025 23:35:34 +0000

In reply to holmpage.

Indeed, for some of these I really like doing partial designs, stopping the pen before it gets back to the start. I counted another gear to have 83 teeth.
Also, the first ratio was actually 80/133, and not 79/132. Oops on my end.
Another Cheap Spirograph that I found has a ring of size 96 (Compatible with normal spirographs) and has 3 gears of size 63, 52, and get this, 36.

By: holmpage

holmpage — Tue, 16 Sep 2025 16:42:42 +0000

In reply to XhanLuIsOfficial.

The gears in the official Spirograph must have been carefully selected to (mostly) give patterns that weren’t so dense. Prime numbers like 79 wouldn’t, when you look at the math of it.

I’ve seen cheap sets for sale online, so it’s disappointing that they aren’t necessarily compatible with the official sets. Thanks for sharing about that.

By: XhanLuIsOfficial

XhanLuIsOfficial — Tue, 16 Sep 2025 05:12:55 +0000

This is cool. I found this cheap Spirograph that had five gears (1 oval) and two rings, one of which had 132 teeth (Smaller teeth, not compatible with Official Spirograph gears). Also, I counted one of the wheels to have 79 teeth. It draws almost a 5-pointed pattern, almost like 63/105, but lands one tooth off at the end, so it creates gradually a dense design.

By: xavier

xavier — Mon, 15 Jun 2020 09:21:01 +0000

Haether no the teeth are twice as big

By: Heather

Heather — Sat, 16 May 2020 23:34:39 +0000

In reply to Heather. I expanded the table to go down to 40.

By: Heather

Heather — Fri, 15 May 2020 02:23:07 +0000

In reply to xavier. Interesting! If the teeth are the same size as the regular spirograph, it must be small! Can you send me a picture? Actually, given the wide range of rings in Wild Gears, expanding the table would be a good idea.

By: xavier

xavier — Thu, 14 May 2020 04:21:57 +0000

I have an old 1990s hasbro spirograph with a circular ring that has only 48 teeth plus 7 wheels: 17,18,22,27,29,30,33. Too bad the list only starts at #50 ring.

By: Ron Peters

Ron Peters — Sat, 08 Sep 2018 18:07:13 +0000

Thank you for this table. It’s been a great help for sorting out the most usefull epitrochoids using the wheels. It is now easy to combine different outside wheels for a nice result with equal petals. Too bad the chart starts only at wheel 50, but there is very very much to try and figuring out!

By: Scott

Scott — Thu, 09 Feb 2017 01:28:10 +0000

In reply to Catherine.

You can also download an excel spreadsheet from here:
https://www.instructables.com/id/How-to-design-a-laser-cut-Spirograph-like-toy/
The instructable includes the formula to make your own sheet if you’re so inclined.

By: Heather

Heather — Sun, 22 Jan 2017 02:14:51 +0000

In reply to Charles Tomberlin. Yes, the fixed gear is along the top and the moving gear is down the side. The formula in cell B2 is =LCM(B$1,$A2)/$A2. I could delete the impossible combinations where the moving gear is larger than the ring. However, those numbers are useful for epitrochoids in cases where a large gear moves around the outside of a smaller fixed gear.