This week’s selection is the fascinating Morton’s Rolling Knot by Canadian DIY designer DaveMakesStuff.
“Dave” is a prolific designer who has published many designs to a variety of online 3D model repositories, and his works have been featured previously as our Design of the Week — twice! Those were the clever “Nose Box” and the mind-bending “Wormhole Chess Board”.
This round we have the amazing Morton’s Rolling Knot. It does indeed roll, as you can see in this video:
While this would appear to be a rather simple design, it is most definitely knot. I mean, not. There is a very specific feature to the design that makes it roll. Dave explains:
“This is a type of knot is known as “tritangentless” because there are no planes which are simultaneously tangent to three distinct points on the curve. Being tritangentless means that the curve can never have more than two points touching the flat surface at any given time. This is what makes models of tritangentless knots roll.
The knot can come in different shapes and proportions, but this model minimizes the vertical variation of this center of mass making it the best proportion for rolling.”
There is considerable science behind this design, and I even found a research paper on the topic, entitled, “Optimizing Morton’s Tritangentless Knots for Rolling” by researchers from James Madison University.
In the paper they describe these knots beautifully:
“Tritangentless knots have a curious and beautiful property: when realized as physical 3D printed models, they roll. Some tritangentless parameterizations roll more easily and freely than others. In this paper we numerically optimize parameters to obtain the most “aesthetically pleasing” rolling knots and then create physical models of these knots using 3D printing, thereby leveraging mathematical tools to obtain an elegant kinetic sculpture.”
In the paper there is a section entitled, “The Rolliest Morton Knot”, which explains exactly how to design such a knot. They identify the specific parameters for optimal rolling.
And that’s apparently what Dave has done in this amazing knot design.