Holiday Tutorial: Creating Celtic Knots with Fusion 360

March 15, 2018

Saint Patrick’s Day is almost here, and to celebrate we’ll do a step-by-step walkthrough tutorial on designing 3D Celtic knots from scratch with Fusion 360. Celtic knots make great pendants and earrings, and it’s easy to put your own style and spin on the knots that you create.

Drawing Celtic Knots from a Grid

There are lots of good tutorials online for drawing two-dimensional pictures of Celtic knots, for example this tutorial from Circle Line Art School:

How to Draw a Celtic Knot: Step by Step - YouTube

Celtic knot drawing methods like the one in the video above usually involve drawing a grid of dots and then drawing woven ribbons through the spaces between those dots. For constructing a 3D Celtic knot, it is easier to start with a grid of dots and then connect those dots with splines that you can later thicken into woven pipes. This is actually more similar to how mathematicians think about Celtic knots; for example, the image below is from the paper A Celtic Framework for Knots and Links by computer scientist Jonathan Gross and mathematician Thomas Tucker.

Tracing Knots with Splines

The quick overview of our technique is that we are going to make a grid of dots in a Fusion 360 sketch, then connect the dots with splines, then shift those splines up or down at the crossing points. This gives us a thin curve that traces out the desired knot, and we’ll be able to sweep a circle around that curve to make a round 3D tube that traces out the knot. Before we get into the details, let’s look at two examples.

Step-by-Step Celtic Knot Construction with Fusion 360

Okay, let’s get down to business. We’ll assume that you are a beginner at Fusion 360, and walk through each of the knot-constructing steps carefully. We will trace out curves to make this three-component Celtic knot:

Step 1: Get the software

Download Fusion 360 and sign up for an Autodesk account so you can use it. Fusion 360 is free to students, educators, and hobbyists. For tips on getting started, check out our earlier article Tutorial Tuesday 15: First Steps with 3D Design Software Fusion 360.

Step 2: Create a sketch and make a grid of points

Create a Sketch and then choose Point from the Sketch menu and place points at the locations of the knot crossings and corners. Compare the dots in the screenshot below with the crossings and corners of the three-component Celtic knot shown in the image above. These points will help you keep track of the knot as you make it.

Step 3: Create a spline for each component of the knot

From the Fusion 360 Sketch menu, select the Spline tool. Click dots in order to trace out the path of the knot. Sometimes this will be the entire knot, and the spline will cross itself; this is okay. If your knot has more than one curve in it, then your first spline will only be part of the knot, which is also okay. End your spline at the first dot you chose and then hit Escape to exit the Spline tool.

Step 4: Move the spline up or down at each crossing point

Each point that forms a crossing needs to shift up or down so that the curve of the knot will weave over and under. Right-click on a crossing point and select “move”, then use the vertical arrow to shift that point up or down a fixed amount.

Step 5: Create perpendicular circles on each component path

Now from the Construct menu, choose the Plane Along Path tool, and construct a Plane on each of the knot components.

Step 6: Sweep the circles along the spline paths

Finally, from the Create menu, select the Sweep tool.

Renders and Prints

Here’s how our Celtic knot looked at the end of this process (and adding some new Materials for style):

To export the knot for printing, open up the Bodies menu in the Browser list on the left of the window, and then right-click on each Body (one for each component) and select Save as STL.