With regards to differences between wheels, distance between holes and distant to first hole, Heather’s assumptions are correct. I had a look at the GB Spirograph Patent.

It stipulates, on page 2, lines 11 to 22:

(a) Each successive aperture 7* in the spiral relationship is progressively closer to the geometric centre of the member by an equal and standard difference in radial position.
(b) The geometrical centres of the apertures lie on radial lines which intersect the external tooth form of the periphery at points which are one quarter of the pitch of the teeth distant from the centre of a tooth.
(c) The outermost aperture is a constant distance from the externally toothed periphery of each member.

* This number refers to the label for the holes, in the drawings supplied with the patent application.

Interestingly, there are patents for many of Denys Fishers other Spirograph and similar toys, including the: GB Super Spirograph Patent.

Hi Hany,
All I have is an ordinary ruler so my precision is limited. The largest ring has 150 teeth on the outside and the diameter (not radius, d=2r) is about 97 mm. You can do the math from there for the other rings and wheels. Maybe you can buy a Spirograph set and check your math against the pieces, then try drawing some patterns by hand for a whole different experience!

Heh heh. Sorry about that… Have a great Thanksgiving holiday.

Thanks for the review…. I just lost another 20 min of my life, lol. I see a review article about simulators in my future, but they will need more study. A holiday project, perhaps.

http://mathiversity.com/online-spirograph/app

It is very user friendly, allows you to sign up so you can save your work, and has many many options, including ‘rotors’ and ‘stators’ that don’t exist in the real world. I am duly impressed. 🙂

Yah, I don’t know where that rogue version came from. It’s difficult to use and the patterns don’t always close. The original ones, developed by Andy Katz, are much better. I told him how he could improve them by using splines so they generate nice smooth scalable patterns now. The interface is all point and click.

That spirograph program is Windows only. I use a Mac. But I prefer to write my own code anyway.

The next thing you should get is a Magic Designer. They can be had cheap on eBay. They’re easier and faster to use than Spirograph and are built solid out of thick steel. Avoid the last plastic model they made. It is crap. I’d love to see you write an article about your experience with it. If you have time… 🙂