I bought my kids a spirograph (a favorite toy of mine in my youth), and it seems that the manufacturers have had a few fun ideas in the intervening decades. In particular, there's a wider variety of gear-toothed laminae one can now roll inside or outside of a gear-toothed annulus, resulting in a wider variety of pictures. But one of the basic problems of spirography circa 1970 remains a problem in 2014: slippage. The gear-teeth only serve their stabilizing function if one continually makes sure that one is applying force to the pen (inserted into a hole in the moving lamina) in such a way that the normal component between the lamina and the annulus has the correct sign, while with the other hand steadily pushes down on the annulus to keep it stationary. This is hard work for my five-year-old daughter, who would probably use the spirograph more if slippage weren't such a problem. (One could argue that the main purposes of a spirograph never was mathematical enlightenment but the encouragement of hand-eye coordination, and that the slippage thing is a feature rather than a bug, but I'm going to pretend I didn't say that.) Has anyone designed a mechanism that permits the spirographer to focus on circumferential force? I'm imagining something like a latchable/unlatchable zipper. Once you've zipped the lamina and the annulus together (making use of the fact that they're in three dimensions), they stick together like the two halves of a zipper, and permit only a single, circumferential degree of freedom. If someone could solve that problem, then I think the other problem (holding the annulus stationary) wouldn't be as big an issue (though it might still be good to have a wax tray and some pushpins to hold the annulus and the paper to the wax tray, so that one-handed people could do spirographs). Does anyone know of progress that's been made along these lines, or does anyone have any good ideas for mechanisms that would prevent slippage? Jim Propp P.S. Wikipedia tells me that "spirograph" is a registered trademark of Hasbro, so please pretend I capitalized it, etc.