Leveraging Math and Materials to Make Bangles That Fit

Leveraging Math and Materials to Make Bangles That Fit

Leveraging Math and Materials to Make Bangles That Fit 640 480 mathgrrl

Also published at Shapeways Magazine

Bangle bracelets are great, but they’re so darn bangly. A circular bangle bracelet has to be pretty big to fit over your hand, which makes it very loose around your wrist once you get it on. If you think about it, when you use a bangle bracelet you’re wearing it 99% of the time, but pulling it over your hand only 1% of the time. How do you make a design that’s optimized for the 99% instead of the 1%?  The answer is all about flexibility.

If your bangle design is made of silver or some other metal, then you’re stuck with the shape it is in; it can only be one shape, all the time, and trying to bend it is a pretty bad idea. You can get a circular bangle bracelet that fits somewhat more snugly by printing it with a flex-capable material such as Strong & Flexible plastic, since you’ll be able to smoosh the bangle into an oval as you pass it over your hand, and thus get away with using a circle of smaller diameter. But we want to do better than that, and somehow make a bangle bracelet that fits impossibly close around the wrist. One way to do that, if you are using a flexible printing material, is to increase the number of wraps.

For example, here is a triple-wrap bracelet designed in OpenSCAD. The bracelet wraps around three times without intersecting itself. The code for this design is built on top of the powerful curve-tracing “path_knot” code from power user Chris Wallace‘s excellent post on Borromean Rings and More.

3D printed bracelet design

The shape of this curve is a type of Torus Knot, but in this case the knot is unknotted, or “trivial,” which means that it can be deformed into one large simple loop. This property is precisely what enables the bracelet to fit so snugly; the bracelet can be put on by pulling it out into a large loop as shown in the video below, and then wrapping it around and over your hand three times.

The resulting Triple Wrap Bracelet can fit very snugly; it floats around your wrist closely and looks like it must have been impossible to put on over your hand. The flexibility to un-wrap the bracelet is what allows the bracelet to fit much more closely to your wrist than normal bangle bracelets. Here it the bracelet in action, shown with a blue gummy bracelet for comparison.

In a non-flexible material like metal, this bracelet would be just as difficult to put on as any normal circular bangle, but in flexing materials we can pull off the “wrapping” trick. Strong & Flexible, Premium Strong & Flexible, and HP Nylon Plastic materials all work well for this type of design.

What material, mathematical, and design tricks have you used to get an impossible fit? Let us know and we might feature your work in a future Tutorial Tuesday!



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