• On Exponentials and Friction

    Ethan • 04/20/2026 at 00:26 • 0 comments

    Or: Why Nobody Does This At Large Scale

    Each stage is subject to a holding torque set by the static friction of the bearing used. The friction force develops a torque with the arm length set by the radius of the axle. 

    In the first few stages, this torque is negligible. But as the gear ratio increases from stage to stage, a sizeable input torque quickly scales down to a few microNm, even the tiny friction seen in a ball bearing supporting a few grams can become too great:

    This model doesn't include the gear teeth themselves, so it's probably much worse than this, but this illustrates the problem pretty well. 

    Currently I cannot seem to turn the 7th stage with the heaviest weight I can support (10lb) and the widest spool I can accommodate, 20mm. I may need to drop the last stage!

  • Mechanical log, past week

    Ethan • 04/20/2026 at 00:06 • 0 comments

    Update on the last ~week of mechanics work.

    I'm using Onshape to design the mechanical setup.

    I'm using a spur gear generator feature; I can't figure out how to link to it here but of the couple I've tried this is my favorite. 

    All parts shown in Onshape are 3d-printed with plain PLA. Structure is M3 threaded standoffs. Everything is set up to fit on the bed of my Bambu lab A1 mini.

    Stages are a series of double-reduction idler gears:

    axleinputoutputratioaxlebearingratio, tot.
    1spool for rope60T gear, m=1mm11/8" brass rodplain1
    212T m=1mm60T, m=0.75mm51/8" brass rodplain5
    312T m=0.7560T m=0.7553/64" brassplain25
    412T m=0.7560T m=0.7553/64" brassplain125
    512T m=0.7560T m=0.7551mm SSBall625
    612T m=0.7560T m=0.7551mm SSBall3125
    712T m=0.7560T m=0.7551mm SSBall15625
    812T m=0.75magnet disc51mm SSBall78125

    Input torque is determined by charge mass and spool diameter.

    The first few stages of the gear train use plain bearings -- simple brass rods from the art supply store as axles, through a bore hole in 3d-printed PLA. I'm using 1/8" and 3/64" rods for the first 2 and second 2 bearings, respectively. In these first few stages friction isn't really a concern because input torque is high.

    The next 4 axles use tiny ball bearings I found on amazon. I bought them to fit into my existing design to retrofit plain bearings without really grokking how tiny these are; by far the smallest ball bearings I've ever seen. 3mm OD, 1mmID, 1mm thick. They reduce friction by a lot; hard to quantify without better testing I don't have time for, but a flicked gear spins about 4x longer than in a plain bearing. Friction becomes exponentially relevant at later stages.

    Since the ball bearing ID is smaller than 3/64", I use 1mm stainless steel wire as the axles here. I pull a bit off the wire spool, chuck one end in a drill, and spin it while pulling on the wire with needle-nose pliers. This straightens it, thins the wire a little, and tapers one end for easier assembly.

    Gears are spaced on axles using bushings made from 1mm heat-shrink tubing. Clearance is really important.

  • Externally powering a Casio F-91W

    Ethan • 04/18/2026 at 02:27 • 0 comments

    1. Open watch by unscrewing back panel
    2. Pull electronics assembly out 
    3. Unclip the battery cover (stamped steel) from the screen chassis (white plastic) by lifting the 4 clips around the perimeter
    4. Remove the battery (might be taped onto PCB)
    5. Pull apart the PCB and screen chassis (white plastic)
    6. Remove the negative battery terminal contact spring from the PCB (just pull it off)
    7. Solder thin flexible wires to the terminals as shown
    8. Cover negative solder joint with tape to prevent short
    9. Reattach screen chassis to PCB (line up the alignment pegs and press gently together)
    10. Clip the battery cover back on, making sure you don't press too hard on the bare LCD
    11. I partially reassembled the watch, partially to protect everything, but mostly to make sure I don't lose any more parts. The back cover screws are very long, so if you just partially tighten them the wires stay comfortable.