Geometric Honeycomb Ring

Rings can be fun to wear, but it's also fun to design a ring. Creating rings from metal can be expensive and requires multiple tools depending on how you do it. A simpler method, however, is creating rings using 3D modeling software and then printing them.

For this ring, I wanted to create a geometric ring featuring a honeycomb pattern. While this instructable walks through modeling a geometric ring with a honeycomb design, the same method can be used to create geometric rings featuring other patterns as well.

Ruler

Calculator (I used Desmos)

CAD / 3D modeling software (I used Autodesk Fusion)

3D printer (if you want to print the ring)

The first part of planning out the ring is determining its size. This can be done by finding a ring you like wearing and using your ruler to measure its diameter. If you don't have a ring, you can always try to eyeball the diameter of your finger using the ruler as well.

It's best to use whatever measurement you'll use to model the ring, so I measured in millimeters. Although, you can always convert your measurements if needed.

The honeycomb pattern is made up of a geometric arrangement of hexagons. To ensure the size of the hexagons forming the pattern make a full ring, with only a small gap, it helps to calculate the hexagons' parameters before modeling it. This includes the size of the hexagons, their borders, and how many hexagons are in the ring.

I found it easiest to do this in Desmos, as I could adjust parameter values until I was happy with the resulting numbers.

(Note: it's best to use whatever measurement you'll model the ring in, so I used millimeters)

Variables:

c = circumference of the ring

w = width of hexagons (from vertices, not sides)

b = border width around each hexagon

o = overlap between each hexagon (width-wise)

n = number of hexagons forming the ring

Initial Parameter Values:

c = pi * (your measured diameter)

w = 6mm (I found this to be a good starting point)

b = 1mm (If you want a slightly thicker border, 1.5mm)

Equations:

o = (w - 2b) / 4 + b (see diagram)

n = (c - o) / (w - o)

Adjusting Parameters:

The only value that needs to be adjusted is w (the width of the hexagons). The goal when adjusting w is to achieve as close to an even number as possible for the value of n (number of hexagons).

While adjusting parameters, note that the more hexagons in the ring the smaller the hexagons will be, and the fewer hexagons the larger they will be. It's a personal design choice whichever, one you choose.

Now, going into your 3d modeling software, start by creating a sketch in the front plane.

First Hexagon:

First, you'll create two inscribed polygons with 6 sides (hexagons) centered on the axis. Then using the sketch dimension tool, set the width of the larger hexagon to your value for w, and set the width between the larger and smaller hexagons to your value for b. Also, constrain the bottom lines of each hexagon to be horizontal so your sketch is fully defined.

With your first hexagon created, copy and paste that hexagon, making sure to move the new hexagon off of the original one.

For the new hexagon, you can alter the sketch dimensions so that they're a function (fx) of the original hexagon, this is done by selecting the measurement you wish to change, then instead of typing a new number click the measurement you want from the original hexagon. (You don't have to do this, but it can help if you want to adjust your values later)

Now, to combine the two hexagons, select the outer right vertex of the original hexagon and the inner top left vertex of your next hexagon (you can select both by holding down shift), then click on the coincident constraint.

To speed up adding hexagons, you can copy and paste the pair of hexagons you just created. Copy and paste the original pair, dragging the new hexagons off the original.

If you want, you can set all the sketch dimensions to be based on the original hexagon and then copy your new adjusted hexagons, so future hexagon pairs you paste will all have dimensions with functions based on the original hexagon.

To add the pair of hexagons onto the preexisting hexagons, select the outer left vertex of your new hexagon pair and the inner top right vertex of the preexisting hexagon pair, then add the coincident constraint.

Repeat the process of pasting hexagon pairs, and connecting them to the existing hexagons using the coincident constraint, till you have all the hexagons needed to form the honeycomb pattern for your ring. Then you can click finish sketch.

The next part involves creating a cylinder to form the ring around.

Create a new sketch in the top plane. Then create a circle and set its diameter to the diameter you measured for your ring. Once done, you can click Finish Sketch.

With the sketch done, you now want to extrude your circle to form the cylinder. This is best done by extruding from both sides and using the honeycomb pattern sketch as a reference to ensure the cylinder is tall enough.

Using two embosings the ring is formed around the cylinder.

The first emboss is used to create the inner hexagons for the ring.

Select the emboss feature from the Create section in the Solid tab.

Then for the emboss parameters select:

sketch profiles: all inner hexagons in your honeycomb pattern

faces: round portion of the cylinder

effect: emboss (not deboss)

depth: 1.5mm (you can adjust this value to make the inner hexagons in the honeycomb more overt or subtle)

Then select ok, as the other parameters don't need to be adjusted.

The second emboss adds the hexagon borders to the ring.

(If the sketch with the honeycomb pattern disappeared, go into sketches and set it back to visible)

For the emboss parameters select:

sketch profiles: all parts of the hexagon borders in your honeycomb pattern

faces: round portion of the cylinder

effect: emboss (not deboss)

depth: 2mm (this will be how thick your ring is)

With the ring formed around the cylinder, all that's left is removing the cylinder. This is done by selecting the top of the cylinder and clicking extrude. For the extrusion, select the cut operation and adjust the parameters so the cylinder is cut away.

Once the cylinder is removed, you are left with the finished model of your ring. You can then export your model as an STL file, upload it to a slicer, and print it on a 3D printer.

You now have a cool geometric honeycomb ring you can print and then wear whenever you want!