## Trigonometry Style

Last summer we designed a series of customizable bracelets whose shapes were determined by trigonometry:

You can read about these specific variations at the old MakerHome blog, and use the Thingiverse Customizer for each individual design to make size and style modifications:

TRI bracelet: Day 320 on MakerHome, Customizable TRI design on Thingiverse
SUN bracelet: Day 328 on MakerHome, Customizable SUN design on Thingiverse
RIB bracelet: Day 329 on MakerHome, Customizable RIB design on Thingiverse
POW bracelet: Day 330 on MakerHome, Customizable POW design on Thingiverse

To wrap up this series, we’ve posted the master file that created all of these as one general customizable design on Thingiverse:

Thingiverse Customizer link:  Customizable Trig Bracelet

With this more general code we make even crazier bracelets, including ones with oval shapes, gaps to make wrap-style instead of bangle-style, flares, low-poly sampling, and crazier trigonometric combinations. Here are just a few of the many examples:

The crazy thing is that every one of the bracelets shown above was created with the same code, and each only differs by a handful of function, sizing, and extrusion parameters!

You can try it out in the Thingiverse Customizer right in your browser by using the link above, and use the Customizer parameter sliders to design a personalized bracelet model for printing. Or you can download the OpenSCAD code at the link below (it will run a lot faster on your local machine) and modify the numerical parameters yourself using the free software program OpenSCAD:

To design a bracelet with the OpenSCAD code, change parameters and hit “F5” to update the preview image; then repeat, changing other parameters and hitting “F5” again, as shown in the following (soundless) video:

The following video (no sound) demonstrates the mathematical effects of the frequency, amplitude, translation parameters in the code. You should imagine that the translation parameter represents the radius of your wrist, and that the function shown will get wrapped around the circle to form the bracelet.

And if you want to get really crazy, you can add more trigonometric functions to the mix (again, there isn’t any sound so stop turning up your volume!):

Here’s one more video showing how the function gets wrapped around the circle to make a bracelet shape. Maybe someday I’ll narrate over this video, but hopefully it is somewhat clear even without sound that we are building up a function a little at a time until we arrive at a final bracelet design:

Finally, to make it a little easier to size your bracelet design appropriately, here is a set of quick-printable wrist/hand sizers to help.

You can also get the OpenSCAD code at that link, if you are interested in looking at a basic example showing how to use the OpenSCAD library write.scad. The bracelet sizing set is a set of thin rings with numbers etched along their sides that describe the diameters. The rings are bendable so you can try squishing them to fit them over your hand, or not, depending on whether or not your bracelet design is similarly flexible. Alternately you could just print a couple of layers of your bracelet to test it out, but it feels all fancy to have a real set of sizers, so here they are:

## Menger Menagerie

I swear that this blog is not going to be only about Menger sponges. However this One Last Post About Menger Sponges is about Menger sponges. Lots of them, in fact. And we’re going to put our 3D-printing boots back on!

Today’s models are collection of Menger sponges with different Levels and slices, designed to print effectively on various types of printers. Download the files directly below and/or go to our One-Stop Menger Shop on Thingiverse and drop us a “like”.

1. Menger sponges on stands for supportless printing on filament printers

First, plain old Menger sponges, Levels 0 through 3, for printing on filament/extrusion printers like MakerBots, Afinias, and Printrbots. You can scale these to any size you like, but be careful about making the high-Leveled designs too small. I’ve had success with 20mm Level 2 sponges, but for Level 3 I’d suggest not going below 30-40mm. These files are modified/repaired versions of the genius custom-standed Menger models by owens. To print these models I recommend using a raft, but you have to have supports turned *off*.

Level 0 with stand – http://www.geekhaus.com/hacktastic_files/Menger0_stand.stl
Level 1 with stand – http://www.geekhaus.com/hacktastic_files/Menger1_stand.stl
Level 2 with stand – http://www.geekhaus.com/hacktastic_files/Menger2_stand.stl
Level 3 with stand – http://www.geekhaus.com/hacktastic_files/Menger3_stand.stl

2. Menger sponges without stands for printing on fancy printers

These files are for printing on FormLabs resin printers, Statysys/3DSystems powder printers or printers with dissolvable support material, or Shapeways.  On the FormLabs you’ll need to use exterior, but not interior, supports; in oriented position the model will hang upside-down at an angle so you won’t need a stand. On a powder printer you’ll be able to just shake the powder out of the holes (as long as you don’t make them too small). With dissolvable support material you can probably manage a 30mm-sided sponge and still be able to see through the smallest channels. With Shapeways things should work beautifully except that sometimes cleanup is required if you make the channels too small. General theme: Don’t make stuff too small.

Level 0 plain sponge – http://www.geekhaus.com/hacktastic_files/Menger0.stl
Level 1 plain sponge – http://www.geekhaus.com/hacktastic_files/Menger1.stl
Level 2 plain sponge – http://www.geekhaus.com/hacktastic_files/Menger2.stl
Level 3 plain sponge – http://www.geekhaus.com/hacktastic_files/Menger3.stl

3. Menger sponges sliced in half to see the inside, with stands

These print with stands for filament printers. You could technically print these without supports even without stands, by putting the sliced side down on the platform (as done by Gaya). However, I’ve had problems with that sliced half sticking to the platform and breaking when I try to pull it off. Or, when my printer is in a mood where it refuses to print without a raft, then the sliced half doesn’t look at nice after printing on top of that raft.

Level 0 sliced sponge – http://www.geekhaus.com/hacktastic_files/Menger0_stand_sliced.stl
Level 1 sliced sponge – http://www.geekhaus.com/hacktastic_files/Menger1_stand_sliced.stl
Level 2 sliced sponge – http://www.geekhaus.com/hacktastic_files/Menger2_stand_sliced.stl
Level 3 sliced sponge – http://www.geekhaus.com/hacktastic_files/Menger3_stand_sliced.stl

I know what you’re thinking. You’re thinking that you would like to print a Level 4 Menger sponge. But you really don’t; Level 4 designs take way too long to compile, slice, and print. Maybe someday but not today.