# Video: Loopy Wheel-Within-a-Wheel Design

I keep trying new combinations of Wild Gears to make “wheel-within-a-wheel” designs. While I (more or less) understand the math for predicting the number of points you’ll get when using one gear inside one ring, I haven’t figured it out for the patterns you get when you use a gear inside a hole in a wheel going around inside a larger ring. If someone can help me with this, please explain it in the comments.

I do know, however, that if your small gear isn’t much smaller than the hole in the larger gear you’re using, you get loops. This pattern has lots of loops, as it uses a #40 gear in a #45 hole. The larger wheel is 140 and the large ring is 180. All except the 40 are in Wild Gears’ Full Page Gear Set. The 40 came from the Plentiful Gear Set.

It’s fun to watch the pattern emerge, so I made a video of it (below). I messed it up 5 times before I gave up and used the blooper anyway. I tried again without the camera running and got it perfect the first time. Go figure.

The first time I discovered this combination of gears, I found the pattern interesting and coloured it. So I made it in black as a colouring page, and here are some results. A couple are done by an Australian correspondant, Suze.

In case you’d like to try colouring it yourself, you can get the colouring pageย for $1.77 USD. Send me your pictures and I’ll add them to the gallery.

In the video, I’m using a Micron 05 pen (.45mm). This is a pricier pen than most that I use, but I wanted some archival ink to create more serious artwork with my Wild Gears and Spirograph. Christmas is coming, after all.

Colouring page available at https://www.etsy.com/ca/listing/573353165/adult-coloring-page-loopy-spiro-pattern

Iโm loving these Wild Gears videos! I canโt help you with the maths side of it at all! Iโve ordered my first Wild Gears set, and am so excited.

I am wondering if it’s got anything to do with the prime factorization but it isn’t coming to me. I can tell the above pattern has 72 loops, well the coloring helped with counting ๐ If I ever figure it out I’ll be sure to let you know.

So far I’ve found the most pleasing {to me} patterns use wheels and gears that all have at least one common factor: 5 in this case of a combination of 40/45/140/180. It seems if I use an innermost wheel that’s a prime number it’s likely the pattern will be very dense with hundreds of loops.

Yes, it must have something to do with prime factorization, as ones with more common factors give fewer loops. And yes, some designs (especially with prime numbers) get too dense to be useful and take a long time to produce.

First off, I am super happy I came across your website after taking the Spirograph plunge last month. I already have the Compact and Full Wild Gears sets now, with the Strange Shapes on the way. It’s amazing the kinds of designs you can come up with!

But I wonder if you have any suggestions for organizing all the Wild Gears wheels. Right now, I have multiple-sized ziploc bags and it’s driving me a bit crazy! I was thinking it would be nice to find a photo album of sorts with multiple-sized plastic sleeves, but I haven’t been able to find anything really that’s got different-sized pouches, like little ones for the small gears and increasing in size from there. It sounds like you have more wheels than I do–how do you keep them organized and easy to find the ones you’re looking for without constantly digging around for them? I am all ears. ๐

I’m afraid to say that I don’t have them well organized. I have a bunch of ziploc bags. It’s a problem, but you’re making me think. I suppose a 3-ring binder or photo album with different pages with pouches: slides for the small ones, different photo pouches for the mid-sized ones etc. I’m exploring using an accordion folder for larger wheels and gears. For the large frames, they’re sitting in a computer box or against the wall or between two pieces of furniture, but I’ve thought of getting a pizza box, painting it and drawing designs on it. If I do, I’ll definitely write a post about it.

Thanks a bunch! I’ve looked at a bunch of different products on Amazon for ideas and am still mulling over the best solution. I did finally find some loose sheets with different size pockets to put into a binder, and I may very well just go that route. An alternate I’m still considering is using a scrapbook/album with thicker pages that accept self-adhesive corners for holding photos, but using those corners to position and hold the wheels on the page instead. I also thought about using putty to stick the wheels to the pages but I don’t think that would work as well. If I come up with something brilliant, I’ll let you know. ๐

For the very small gears and the donuts I bought a Creative Options double-sided micro utility box. This works very well. One side has mostly very small compartments (1-1/4″x5/8″) I use for the donuts. The other side has three larger compartments. I put the smallest gears (<19) and my large blobs of putty in the two smaller ones and the larger gears (20-30) in the larger compartment. I stick small blobs of putty on the inside of the lid. I'm very happy with this solution.

I've not found a solution I really like for the larger gears. I tried using a large CD wallet for the gears smaller than a CD that won't fit in the little utility box. It sort of works but the smaller gears keep wanting to fall out.

I think an old 5.25" floppy disk case might work okay but I can't put my hands on one.

The larger gears and rings I have in a project box and a zippered poly envelope. The frames are just leaning against the wall.

I've been thinking about getting a wheeled cart with a lot of drawers. Amazon has one with six drawers about 18"x12"x2-3/4" deep and two about 5" deep. Put a piece of pegboard in the bottom of each drawer and you could insert short pieces of dowel to help keep the gears in place. I'm just debating if this is worth $110 for the cart, plus all the hours assembling it, plus more time cutting up pegboard and dowels.

You have some good sophisticated ideas. ๐ For a while now I have been more or less content with using one of the flat tri-fold cardboard boxes that my Wild Gears shipped in. I used little dots of putty to organize the wheels in order of size starting with the smallest. This isn’t perfect, but it works pretty well, and I can see every wheel at a glance. Except for the large frames, I’ve been able to secure all of the wheels and rings from the Compact, Full, and Strange Shapes sets on the wide back and inside of one flap. I had browsed through Amazon, Office Depot, and The Container Store without really finding anything I liked better, though I almost spent too much on various size compartments Tupperware-type containers before I decided to try adhering the gears to the box. I would like a more polished and less unwieldy solution so I’d be interested in hearing if you come up with an arrangement you just love!

Regarding the question of the number of points you’ll get when doing wheel-in-a-wheel-in-a-wheel designs with Wild Gears I think it’s simply a product of the number of points you get with each pair of wheel combinations your using.

For example I have a design that used the 42 wheel inside the 56 ring (of the 126 wheel), inside the 140 ring.

On their own the 42 wheel in the 56 ring results in 4 points and the 126 wheel in the 140 ring results in 10 points. Counting the loops in this design gives a total of 40 loops.

I have another design that’s a little more complicated than this one but it seems to follow the same logic. (Realizing 2 data points doesn’t prove a theory, but it seems to be correct).

I also posted this on your Facebook page with a picture of the design I talked about above. It makes it easy (I think) to see what I’m talking about.

Sadly, it’s not that simple. I don’t know what the formula is but I know it’s not just a product of the separate combinations. Many of them do come out that way, but then there are some that don’t. For instance 140/120/24/14 should give 6 for 140/120 times 7 for 24/14 but it actually produces 7 loops.

One of the strangest ones I’ve run across was with the 120 gear set. I was using 176/120/29/x, starting ‘x’ at 14 and working my way up. They all produced very dense, complex patterns, which is to be expected since 176/120 produces 15 loops and 29, being prime, produces the same number of loops as teeth in the smallest gear. Until I got to 22. 176/120/29/22 produced an asymmetrical pattern with just 22 loops. It was so vastly different than all the others I was rather dumbfounded.

I’ve tried to experimentally determine the proper formula but it hasn’t worked out as well as I’d hoped. I’m fairly certain there are at least two least common multiple functions involved, maybe three.