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In my late-Victorian-based world, mechanical contraptions are incredibly advanced due to the early discovery and quick popularisation of mechanical computation.

The science of writing instructions for such machinery has allowed an effective AI ruler to come to power.

The insecurity I now face is how compact the parts required can be produced and assembled.

The parts used would probably be akin to those in this training video on a US-Navy mechanical computer.

What is the smallest I can possibly make a simple, 16-toothed gear wheel?

If you have any concerns towards possible problems of having such small machinery, such as lubrication or friction, please feel free to voice them.

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    $\begingroup$ This sounds like a plain history question: which was the smallest watch mechanism during the Victorian period? $\endgroup$
    – L.Dutch ♦
    Commented Jun 6, 2019 at 14:04
  • $\begingroup$ @L.Dutch Not necessarily, since it may have been possible to produce even smaller mechanisms, but it simply wasn't worth the cost in time or money to produce impractically small mechanisms. $\endgroup$
    – A Lambent Eye
    Commented Jun 7, 2019 at 7:22
  • $\begingroup$ I'd propose that if they'd set their mind to it, the Victorians would have only been limited by the resolution of their optics, which was in turn limited by the wavelength of visible light. This is not to say the cogs would have been on the order of 1 um, but the smallest features would not be smaller, i.e. the axle, or the points of a single cog. This would make the cogs on the order of 100 um (1/10th mm) As the number of cogs grows with the cube of their smallness, the QA process would be a sight to behold... (does your mechanical AI have sight?) $\endgroup$
    – bukwyrm
    Commented Jun 7, 2019 at 14:40
  • $\begingroup$ @bukwyrm No, she doesn't have sight, but the engineers do. $\endgroup$
    – A Lambent Eye
    Commented Jun 7, 2019 at 16:22
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    $\begingroup$ You may be interested in Marine chronometers which were produced on a large scale for the navy and was probably close to limit a of what a human could make by hand without optics. They also work without oil so that's a bonus. $\endgroup$
    – John
    Commented Jun 7, 2019 at 20:13

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In the 19th century, watchmakers were producing watches small enough for ladies to wear on their wrists. These would have included tiny gear wheels, including escapement wheels with more than sixteen teeth less than an eighth inch across, and actual gears significantly smaller than that. Screws as small as 0000 size (approximately .02" diameter) could be produced by automatic machines by the end of the 19th century. The original Babbage Engine was large and heavy, but could have been reduced by more than half with the best machining techniques of fifty to sixty years later.

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  • $\begingroup$ Which of Babbage's engines are you referring to? The Difference Engine 0 or a later development? $\endgroup$
    – A Lambent Eye
    Commented Jun 7, 2019 at 14:19
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    $\begingroup$ I was actually remembering the one that was reproduced recently -- I don't recall if it was the Difference Engine or based on the partially completed Analytical Engine prototype. And reducing by half is a very conservative estimate; watchmaking techniques could probably put the complete Engine as it was built in the last couple decades into a case comparable to a tower desktop computer (with functionality roughly like an Altair 8080 machine from the 1970s, only slower). It'd be a major pain to maintain and repair, though... $\endgroup$
    – Zeiss Ikon
    Commented Jun 7, 2019 at 14:30
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Through the use of a Precision or Micro Pantograph, which was used for detailed inscribing in the 1800's, gears of microscopic size could have been produced. The problem with such small gears is the microscopic nature of the surface of metals at the microscopic level. The jagged or even leafy surface of metals would make them poor gears.

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There is a crusty old joke, which I'm sure predates even the Victorian era. Two teams (since the cold war, these are often depicted as US and Russia, but it could be any competing teams) are challenged with making the smallest possible pipe.

Team A gets their best scientists and engineers together, and creates a tube of gold with microscopic dimensions, some crazy fraction of a human hair.

They send it to team B, who sends it back. Team A says "but you just sent our own tube back: where's yours?". Team B tells them to look inside the Team A tube, where they find a sheaf of seven of Team B's tubes, made of glass.

If you're familiar with the principle of Rock Candy, you'll understand the principle here. You can make any shape, stretch it out, and it becomes thinner while retaining its shape.

That means there's no mechanically-limited constraint to the size of the thing. You can make a glass gear at the finest resolution of your tooling, then stretch it and the diameter will reduce as the inverse square of the length.

So, I don't think generating gears smaller than they could machine would be an issue for them. Affixing those gears might, though.

But the biggest issues, as others have intimated, would be wear and maintenance.

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  • $\begingroup$ What would you suggest to improve maintainability? $\endgroup$
    – A Lambent Eye
    Commented Jun 7, 2019 at 21:54
  • $\begingroup$ @ALambentEye Well... solid state stuff, basically. Mechanical stuff will always wear, though perhaps a hard glass might wear more slowly than steel? Failing that, error detection and regular replacement, as we have with datacenter hard drives even today. $\endgroup$
    – Dewi Morgan
    Commented Jun 8, 2019 at 23:09
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    $\begingroup$ snopes.com/fact-check/drilled-wire $\endgroup$
    – armb
    Commented Jul 4, 2019 at 16:25

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