It's hard to justify a deep dive into 17th century tech, though, so my goal here was to:

1. create a working escapement mechanism (pendulum-based, weight-driven)
2. using 3D printed parts of my own design (not copied from Thingiverse)
3. and a handful of other machine parts I already had on hand
4. with minimal investment of time, effort and expense!

Notice I said a working escapement mechanism, not clock! Arguably, most of the interesting physics is in the escapement. The rest is "just" drive train to reduce the seconds measured by the escapement to minutes and hours and indicate them with some hands. Yes, yes, gears are also an interesting rabbit hole, but it's really the escapement I'm interested in. We have 555's, xtals, cesium and LEDs for clocks, at least until the next direct hit by a CME happens. 

I was really just curious how hard is this? In particular, how finicky is the mechanism with respect to both design and implementation.

1. Could I make some good guesses about geometries and dimensions, and
2. do printed PLA parts have any hope of tick-tocking?

Of course, I know others have already done 3D printed clocks (whole clocks much more impressive than this feeble attempt), so #2 should perhaps be "how fast and loose can you be with PLA parts and still achieve tick-tocking?"

Results

And the answers are...yes and yes! I achieved approximately 1Hz tick-tocks for 1 minute, my test benchmark. In spite of burs on some of the teeth where my FlashForge tried (and failed) to achieve needle-sharp tips and almost no post-print-processing, it worked. ...or rather my 2nd armature worked with my first escapement wheel.

A slightly more verbose  write-up can (eventually) be found here.

CAD files and some other notes here.

Future?

It's complete in so far as  I answered my questions, but two things might motivate its continuation.

First, I intended to incorporate some 21st century tech. I was going to make the pendulum's bob self-tuning by using an ESP32-C3 monitoring an LIS3DH to measure the pendulum's deviation from 1Hz and drive a micro servo to adjust the vertical position of a weight to (maybe) achieve precise 1Hz ticks. The electronics were to be mounted in the bob, and that would've been ridiculous! Alas, I ran out of time for that, but maybe, dear Judge, this still qualifies for the ridiculous category since I've coupled high-precision machine parts to 3D printed PLA. I'm just saying...

Second, the escapement is a veritable physics (mechanics) playground. I can imagine this being dusted off in the future as a platform for some genuine experimentation in the context of a kid's science fair project.

Happy side effects

This project motivated me to learn Asymptote, a technical drawing language ideal for programmatically producing mathematical and especially geometric diagrams (rather like but different from OpenSCAD). This is perhaps the happiest result of this project. I can't recommend Asymptote highly enough.