Voronoi Cuff in Tinkercad

Tinkercad has a fun Voronoi generator that can be used to create a 3D-printed wrist cuff - if you have access to a 3D printer. But if you're happy with a virtual cuff then all you need is a computer and an internet connection. Here's my model if you'd like to look at it in Tinkercad:

The Voronoi generator can't produce a curved shape, so I made my cuff polygonal instead of round. I went for a dodecagon because 12 sides seemed like a good compromise between roundness and keeping the amount of work to a reasonable level. If you don’t mind taking a bit longer then you could use a polygon with more sides, but choose a number that’s divisible by 4 to make sizing it easy in the next step. (Also, the number needs to be a factor of 360 to make rotation simpler in Step 5.)

Most of the Tinkercad-created designs you'll see that incorporate Voronoi patterns have a discrete pattern on each face of the body with a plain border framing it. My method wraps a single pattern around all the sides of the cuff to give a more cylindrical, less faceted appearance.

What we’re going to do is make a Voronoi strip that’s (almost) the same width as the cuff and the same length as the cuff’s circumference. We’ll use it as a hole-making tool on each face in turn, rotating the cuff and moving it along the strip as if it were a wheel rolling across it. The end result is a continuous Voronoi hole pattern around the cuff.

First, some measurements. I wanted a cuff with a 19cm / 7.5” circumference (including the gap) to fit round my arm, and about 6cm / 2.5” wide. I'll be working in mm from now on.

Start by resizing the Tinkercad workplane to 250mm wide x 200mm high (Edit Grid at the bottom right of the screen) and set the grid snapping to 1mm. Set the view (icon on the left hand side) to flat / orthographic. Use the view cube to set the view to Top.

Now for a little maths. We’re going to make a 12-sided cuff with one of the sides open to allow it to slip on and off. For a cuff of 190mm circumference, each side will be 190/12 = 15.8mm. Let’s go with 16mm to make life easier.

But the Tinkercad polygon generator (find it in the Basic Shapes) doesn’t allow you to input a side length, only the overall X and Y dimensions. So we need to work out what those should be.

Looking at the diagram of a dodecagon, the length r (which is the radius of the circumcircle) is given by

r sin α = d/2 where d is the length of a side.

α is 1/24 of a full circle, ie 360°/24 = 15°, and in this case d = 16mm.

This gives r = 30.91mm and the width and length of the dodecagon (ie the distance between opposite corners) is twice that, 61.82mm. So, having dragged a polygon shape generator onto the workplane and set the number of sides to 12, 61.82mm is the size you need to stretch it to in both the X and Y directions. Then change its height (in the Z direction) to 60mm.

Now copy this solid body (using copy and paste) and turn the copy into a hole. Resize the hole to make it 2mm smaller in the X and Y directions (ie 59.82mm). This will give a wall thickness of 1mm.

Align the centres of the two bodies - select them both by clicking with Shift held down, or by drawing a selection box round them - then use the Align tool in the top menu. While they’re both still selected, Group them (top menu again) to make them merge and create a hollow cuff. Then rotate it by 15° so that the top and bottom sides are parallel with the X-axis.

We need to remove one of the faces of the dodecagon to make a gap in the cuff so the wearer can get it on and off.

Create another polygon-shaped hole, this time triangular in cross section. Again, rotate it so that its base is parallel with the X-axis, set the width of the base to 16mm (same as the side of the dodecagon) and the height in the Y direction to 30.91mm (the circumcircle radius). Make it as least as tall (Z direction) as the dodecagon, 60mm. Align its tip with the centre of the dodecagon. Group the two bodies together to cut away the lower side of the cuff. Rotate the cuff 30° anticlockwise to bring the gap to the 5 o’clock position. Then drag it so that the right-most side snaps against a major grid line near the right hand side of the workplane while the bottom side snaps against a major grid line somewhere near the centre line of the workplane.

Now we make a sheet of Voronoi holes.

To leave a 2mm wide solid border all the way round the cuff, the sheet of holes it will be “rolled” along needs to be 4mm smaller in both directions. Find Voronoi in the featured shape generators, drag it onto the workplane and resize it to 172mm wide x 56mm high x 1.4mm thick (Z direction). Why 172mm wide? Because we have now only 11 sides of length 16mm and 11 x 16 = 176. And why 1.4mm thick? The Voronoi sheet needs to be just a little thicker than the cuff walls for the process of piercing holes by grouping it with the cuff to work without glitches in Step 5.

Then play around with the randomizer, number of cells and other sliders until you get a pattern you like. Somewhere around 200 cells works well for a cuff of this size. Turn it into a hole rather than a body once you're happy with it.

Rotate the sheet of Voronoi holes to stand it upright on the workplane, and also align its centre horizontally with the centre of the cuff. Then move the sheet 172/2 - 16/2 + 2 = 80mm to the left to line up its right side with the edge of the plain border that will be left along the open edge of the cuff, and 2mm up from the workplane to allow for the plain border along the lower edge.

The process of grouping a holey object with a solid object to cut away some of that solid uses up the holey cutting tool, which means that we need to create a copy of the Voronoi sheet for every cut we make beyond the first. So create 10 copies of the original using cut & paste.

As you paste each new copy, it will be shifted to the right by half its width. Move it back 86mm to the left and successively a few mm further down the workplane so that all the copies are lined up neatly, making it easy to use them to cut holes in each face of the cuff. Check the view from the right or left as well as from the front to make sure all the copies are 2mm above the workplane.

WARNING – These Voronoi sheets use a lot of processing power. Give your computer time to do each copying step, and time to upload to the Tinkercad servers. If it struggles and starts to respond slowly, then you can just make one copy at a time and use it as explained in the next step before making another copy.

Align the original Voronoi sheet (which should be the one nearest the cuff) in the Y direction with the lower side of the cuff. (Make the sheet move to the cuff, not vice versa.) Their lower edges are now lined up, but the Voronoi sheet is 0.4mm thicker than the cuff wall so it needs to be moved downwards (Y direction) by 0.2mm to centre it over the side of the cuff. Be careful not to move it in the X direction at all while you're doing this.

Group these two objects (cuff and holey sheet) to cut holes in the first side. When the red colour has gone check everything is OK by tilting your view before proceeding. If the holes haven’t gone all the way through, or there isn’t a 2mm border around the 3 edges, then something went wrong with the alignment and you’ll need to undo a few steps and work out where the problem is.

Once you’re satisfied that this first cut looks good, it’s time to roll the cuff along. We do that by rotating it anticlockwise through 30° (a twelfth of a full revolution) and also moving it 16mm to the left. Be very careful when making the move that you don’t move it in the Y direction (or the Z direction, for that matter).

Then, using the first of the 10 copies of the Voronoi sheet, do what you did before: align it with the cuff in the Y direction (be careful it doesn’t move X-wise) and Group to cut the holes. Check the holes have lined up properly after each step, it's annoying if you've done a few before noticing a mistake.

Repeat until all 11 sides have been pierced.

Having made the virtual cuff you can change its colour by selecting it then clicking on Solid in the Shape drop-down menu. You can also choose View in 3D from the Tinkercad dashboard to get a better view. But if you want to do more, then you need to download the cuff.

Click Export at top right of the screen and choose a 3D printing file type. (If you're not sure, go for .OBJ or .STL.) Save the file and slice it (beyond the scope of this Instructable, but there are plenty of others that will tell you how) before saving it to a memory stick ready to load into a printer.

If you're using a Windows computer, there is probably an app on it called 3D Viewer that will give a good rendered image. Search for it using the Windows search box if necessary, then open the .STL or .OBJ file in it and play around with the environment, lighting, projection mode, etc.

3D Builder (also within many Windows versions) can give some very nice renderings, eg metallics. The copper-coloured version at the top of this Instructable was rendered with 3D Builder.