This is a Cycloid-like family of curves, generated by its classical description: a rolling circle. I had several other studies on similar topics before. In this cycloid experiment, I used Grasshopper in which, we don’t need to roll the circle. Instead, we can divide a parametric curve, utilizing data lists to simply rotate a circle around it. Finally, evaluating the circle repeatedly creates a Cycloid-like result. I found this as the most simplistic way of showing and studying these special mathematical curves. I think this has good educational potential.

Although this study does not include the mathematical underpinnings of the family of curves called Cycloid, it becomes more and more interesting when you play with the definition. For example, choosing multiple evaluation points from the list of rotated circles creates interesting results. Here is an example you see below:

The Cycloid experiment is also a good educational exercise for the students of computational design and Grasshopper. I used graph mappers, my favorite data inputs for smooth and fast interactivity. I can improve this study by adding the mathematical calculations, and the animation of the rolling circles. Here is the Grasshopper definition I developed in 2014, and it still works without a problem in 2021: