Fully 3D-printable mechanical movement

This design is the result of a Jugend forscht project (science competition in Germany) that won the fourth place in mathematics

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Description

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:

Materials and methods

- The clockwork itself was designed in [FreeCAD](https://www.freecadweb.org), version 0.19 . There are two source files, one for most of the parts required to build it (Clockwork) and one dedicated to experimenting with profile curves (Profilewheel).
- All the parts print well in standard PLA. Depending on the particular part in question, 0.3 mm layer height will suffice, but I recommend printing
- the hairspring and profile wheel in 0.1 mm.
Remember however that any imprecision will affect clockwork performance!
- A better option than PLA might be any other material that has a low coefficient of friction against itself – my experiences show that iglidur tribofilament made by a company called igus in particular reduced problems inflicted by friction, thus improving the clockwork's performance (mainly it's accuracy).
- Before printing, be warned that fine tuning in the end requires a lot of effort before the clockwork will work as reliably as desired.

On generating custom profile wheels based on a parametric curve formula:
- Find attached a slightly modified version of the popular FreeCAD macro "3D parametric curve". After making it available to FreeCAD, open the Profilewheel project file.
- Now you can run the macro and enter a formula to generate a corresponding curve (a "wire" in FreeCAD terminology).
- You may find my more complicated functions defined in the python source file useful; there is:
- stepf(…,m,w): the function proposed in the attached pdfs: applys a simple impulse to the balance wheel at the beginning of the first half period of it's oscillation cycle followed by a similar impulse into the opposite direction at the beginning of the second half period. Parameters m and w represent the force transmission ratio and the angle of the escapement wheel's rotation over which it ought to be applied, respectively.
- stepfk(…,m,w,k): the same thing but with some scaling factor k required for comparability with the ellf function family described below
- ellf(…,m,w): like stepf, but interpolates corners using ellipses (not in the final geometry, but in the angle vs. force transmission factor graph)
- ellfk(…,m,w,k): like ellf, but with parameter k which allows the range of the ellipse function for interpolation to be chosen.
- ellfkv(…,m,w,k): some variant of ellfk.
- protip: to view the angle vs. force transmission factor graph before actually applying it (which may take a while depending on the resolution/interval you choose), just enter "t" for "X(a,b,c,t)" and "a" for "Y(a,b,c,t)". I recommend deleting the wire after viewing, as the project structure will become even more confusing with increasing number of objects ;)
- To apply this wire, navigate to: SchnittT002 -> AdditivT002 -> Slice.2 -> Slice -> Extrude -> Offset2D. Select this element and edit it's "source" property. Here you can select whichever wire you want to have applied to the profile wheel.

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Comments

949a30409c37305a943eb1eea6e75139?default=blank&size=40reesejosie commented ago

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268bfbe6b399d3f09b00883c17b51218?default=blank&size=40etothepii published this design ago