I designed a fully 3D-printable mechanical clockwork mechanism incorporating a main spring for energy storage, a balance wheel and a simple (probably novel) mechanical escapement, for which I developed a mathematical model to compute it's geometry (i.e. a special profile curve applied to a profile wheel that is being traversed by teeth on the escape wheel).
Early thoughts and the mathematical model were published in Mathematikinformation, which is a mathematical journal targeted to teachers, gifted students and other people interested in mathematics.
Later I entered the branch of mathematics of the German Jugend forscht science contest with this project and it won me the fourth place. As some people I met have requested me to release CAD files and details, I'd hereby like to comply with their requests.
You can also find the paper I wrote for and submitted to Jugend forscht for the jury to read as pdf (in German): 2021 M069 Uhrwerk Minimized. Also, there is a pdf presentation for even more recent results and details.
In addition, there exists a video of me explaining and showing off my project in 3 minutes, recorded to comply with Jugend forscht's request: [https://vimeo.com/550613551](https://vimeo.com/550613551)