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So, I recently watched a video by the Brick Experiment Channel about building a 1 Googol:1 reduction gearbox, which at the time of writing this question, is at #44 on Youtube Trending. At the end of the video, it makes the claim that the final gear will rotate once every 10^93 years. This seems unlikely to me; it seems much more likely that energy losses due to friction along the mass of gears will reduce the amount of energy it's receiving to 0, so it will never spin on it axis, at least as a result of this machine.

However, I'm left wondering where exactly this in the contraption energy is lost, and how much of it is lost to heat and how much is lost to noise. How efficient are LEGO Technic gears, when mounted on their standard X-shaped axles through the holes in standard LEGO Technic bricks?

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    If the gear at the start is turning, then there are only 2 options: the gear at the end will turn, or a piece somewhere in the middle will deform / break. – Chronocidal May 19 at 8:36
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    "How efficient are Lego Technic gears, when mounted on their standard X-shaped axles through the holes in standard Lego Technic bricks?" I don't think this question is answerable, as it depends on many factors, like the age and wear of the axle and the hole, the radial load on the axle, the materials of the surfaces (usually ABS, but polycarbonate for the transparent parts), the sizes and shapes of the meshing gears, the forces that push the gears together, etc. Granted, most of these are only small factors, but given there are many, the resulting uncertainty is large enough to be significant. – zovits May 19 at 9:26
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    @Chronocidal First the wheel at the beginning has to turn a lot (since the gears are discreet for a long time even a gear only 30 gears away from the start won't turn for an appreciable amount of time, you can even see it in the video) but second I'm guessing what you will actually get is a broken motor rather than anything else. Once it starts actually moving too many gears it will grind to a halt through friction. – DRF May 19 at 11:41
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    @DRF A broken motor falls under "the gear at the start is not turning" :P Yes, it may take a (very) long time - but, so long as the first gear keeps turning, eventually one of the two outcomes I gave will occur – Chronocidal May 19 at 12:02
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Nice find. First of all, it is interesting to see the various techniques they use.

The short answer to your question would be: It doesn't matter. Each gear, axle and all other components bend, stretch and absorb energy. This means that even for normal large LEGO Technic sets, such as the 42055, you have to build carefully and avoid too much pressure to reduce friction.

When it comes to Googol, it will take years to move most of the gears above their tolerance of, say, 0.1 mm. This is why they put the motor to the beginning of each section to show that it works in principle.

So, starting the whole thing will increase tension and some eruptive movements of the gears in the middle will follow. But the gears further down the line will never move.

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The slower a gear moves the less power (energy per unit time) is lost.

So while each stage of the gearing does lose some power this is more than made up for by the gear ratio. There should still be plenty left to drive the final stage.

A bigger problem is whether the mechanism will actually survive for 1093 years of continuous turning or whether a combination of natural degradation of the plastic and wear from continuous turning will destroy it first. I would bet on the latter.

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