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Is it possible to create a gear train whose average speed is fixed, but whose speed constantly fluctuates? I'm imagining something that would ideally always complete a single revolution in fixed time, but move irregularly along the way.

My interest in this problem is from the writings of Terry Pratchett, whose character Lord Vetinari has a clock which ticks irregularly, but keeps correct time. Numerous versions of this clock have been made using electronic control, but I'm interested in the mechanical possibilities of it.

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    $\begingroup$ See youtube.com/watch?v=WYcqJ5HdxA4 for some ideas. $\endgroup$ – Transistor Sep 19 '19 at 21:31
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    $\begingroup$ Irregular ticking but ultimately keeping the correct time is a different problem. Eccentric gears are certainly a thing, but driving an escapement with eccentric gears wouldn't do what you wanted. OTOH, if you could build an escapement that only "ticks" (and takes energy from the clockspring) when the pendulum swing has diminished below a certain point, then you could use that in conjunction with irregular gears driving the escapement to get irregular ticking. And in centuries of clock-making, such escapements have probably been made. $\endgroup$ – TimWescott Sep 20 '19 at 0:11
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    $\begingroup$ And note that it wouldn't keep as good of time as a regularly-ticking clock: a driven pendulum is oh-so-slightly faster than an undriven one. Having an irregular impetus to the pendulum can't be good for accuracy. $\endgroup$ – TimWescott Sep 20 '19 at 0:13
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    $\begingroup$ This is literally the Corpus Clock in Cambridge, UK. The mechanical clock is only accurate every five minutes (by design). In between, it erratically goes faster or slower: "this erratic motion reflects life's 'irregularity'". Maybe there's a description of that clock somewhere. $\endgroup$ – Wasabi♦ Sep 20 '19 at 2:04
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So you could design an escape wheel with varying spaces between the teeth but a fixed total duration.

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  • $\begingroup$ I started with that idea, but I was wondering if there might be something that would allow a bit more perceived randomness. Simply varying the tooth spacing on the escape wheel would create a pattern of short and long "seconds", wouldn't it? That would be the easiest to retrofit into an existing clock movement, though, so if it could be done with a repetition period greater than would be a noticeable pattern, it would be fantastic! Ideally the pattern, if there must be one, would be such that it would precess around the clock, to avoid being able to notice "16 sec past is always long". $\endgroup$ – sehrgut Sep 19 '19 at 21:17

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