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Thanks! Glad I am not the only one to appreciate a satisfying clunk

This has been a really fun one for me. I hope there will be more contest themes like this.

Can't say I've ever used those hubs, but to me the sliding 8t gears are wonderful and totally irreplaceable. That odd 4L liftarm is sometimes useful. I have a particular soft spot for it because it is used so perfectly in the legendary 8480.

A few more details: The algorithm is basically like the tabular methods at https://en.wikipedia.org/wiki/Determination_of_the_day_of_the_week and physical "perpetual calendars" like this one https://en.wikipedia.org/wiki/Perpetual_calendar#/media/File:50yearcalendar.JPG. However, so far as I am aware, all previous such methods and devices required some sort of manual adjustment for leap years. This device handles leap years automatically. As you can see, the year drum has 14 positions, alternating between leap years and non-leap years, and its motion controls the selector which uncovers different instances of Jan and Feb (other months are not affected). A second innovation is the way exact centuries (1900, 2000, ...) are handled. There is no "00" on the year drum. Instead, these years are formed using the "0" and "000". These are positioned so as to get it right (leap year for a multiple of 400, but not for other multiples of 100). More centuries beyond 1601-2300 could be handled by adding extra entries to the century dial, but I decided this was enough. The day, century and month drums also have 14 positions rather than 7. There is no fundamental need for this, but it simplifies the construction and allows for fewer entries sharing a position (in particular no sharing on the century drum). The output day drum moves by a full 1/7 turn, partly to make it more dramatic and partly to combat gear lash issues. It would be possible to add manual horizontal sliders to the drums so that a single entry could be selected, making it more like a calendar. There is no obstacle to this but I decided it would make it too fussy. Regarding mechanics, it is important that the signals are constantly geared UP, to minimize the effects of gear lash. Gear lash is always a constant fraction of a tooth for every gear meshing (even more for a differential), so each "click" needs to correspond to a big rotation of the shafts, so that the lash remains a small fraction of it. In fact each click corresponds to one rotation for most of the mechanism. Of course there is a balancing act, because gearing up too much would increase resistance. It is also important to minimize the gears. All this ensures that the lash in the final output is fairly small even without the final gravity detent, so then the gravity detent is enough to click it into place. The splat gears are very useful both for their large size (so that they can mesh with an axle that does not intersect the drum) and to get the necessary factor-of-7 gear ratios. The "stickers" are actually not stuck to the drums, but form a tight band around them held in place by friction. This makes adjustment much easier. There are lots of tight clearances everywhere - it feels rather miraculous that everything fits. The drums themselves are quite close to each other; the vertical axle for the leap year selector passes really close to the drums; the taller red window for the day involves some ridiculously small gaps as described above. I'm really happy with how it has turned out. Many of us know that with a model like this there is almost always something that never quite works as well as it should. For once I seem to have escaped that curse!

OK, video is finished!

Elegant!

Looks interesting, would be nice to see it actually driving!

Congratulations - this is a very nice and interesting piece of work. Impressive that you managed to get it so accurate. Some might question the fact that getting on for half the time is spent (auto) winding! But this seems a perfectly reasonable compromise, of the kind that every Lego model inevitably involves.

Sorry that you don't think you'll make the deadline, but I for one very much hope you will continue to pursue this. It looks really interesting, and especially noteworthy that you are aiming for maximum realism.

Thanks everyone! Indeed, you have exactly identified the central challenge here. Due in part to quite a lot of good luck, I think I have managed to solve it...

I think it's finished! Video coming soon...

About the friction from the sliding gear: I think it might be possible to use the very clever method here instead (also check out the linked earlier videos by the same GBC builder). The basic idea is that the two screws (or chains in the earlier version) turn at different speeds in order to control the second degree of motion. I wouldn't want to do it in 2 weeks though!

Final BL order...

What a pity. It's a really interesting idea. I hope you will eventually find a way to make it work even if it's not in time for the competition. So it seems like the horizontal reversing is getting triggered too easily, if I understand correctly? Perhaps it could instead be triggered by physically reaching the end stop?

Thanks! Sorry for all the teasers! Getting the stickers on correctly is a delicate business that requires a fair bit of disassembly...

Working on a taller window for the day drum to display the result more prominently. Some tolerances are incredibly tight, and it is really lucky that they work out. The drum cannot fit beside the middle hole of the thin red left arm - there is only enough room at the two ends. And the clearance between the drum and the grey (soon to be red) engine crank part is so small that the paper sticker cannot go on this bit! Also the liftarm sandwich at the bottom needs a gap to accommodate the crank part.

Right. Everything is now assembled. Not completely surprisingly there was still a bit of a problem with gear lash, meaning that the output day of week indicator would not be reliably centered on the day. Acceptable, but not ideal. I have therefore added a further detent mechanism for the output drum. This one is a much less aggressive gravity driven one, compared with the strong spring driven ones for the inputs. Astonishingly the gear ratios work perfectly for this, and there was just exactly enough space to fit it in, one of many examples of tight tolerances in this model. It turns out to work really well! One drawback is that if you want to calculate the day of the week on the space station, it may not be so reliable! Remaining task is the stickers...

Exciting to see this shaping up!

Yes pneumatics are good. In principle one can use it for arbitrary logic or calculation! One long term goal is a fully pneumatic Babbage difference engine, but using binary rather than decimal. One disadvantage is that constant running tends to dry out the cylinders, so it is not so good for shows. Case in point: https://youtu.be/qsW5xmd9XCY

Thanks! Pity the trans blue is all going to get covered! Many thanks for the encouragement!

Pieces: no idea - maybe 2000? Gold springs https://www.bricklink.com/v2/catalog/catalogitem.page?id=236062&idColor=11&ccName=6472027#T=C&C=11 I'm quite pleased how the colour scheme is turning out. At first I was disappointed that the most neutral colour for the 14t splat gears is medium nougat, but then I realised it is quite a good steampunk colour, especially combined with some pearl gold.

The side panels are really tricky. They need to be strong enough to accommodate the springs for the detent mechanisms, while allowing the various axles and gears to pass through. Curiously, I have not used any frames or panels, and it is likely to stay this way...

It will do Gregorian calendar 1601 - 2399. This could be extended by adding more entries to the century dial.

OK, major updates. I think it is close to being finished apart from the "programming" of the drums. Basically all these bits just need sticking together. It was *much* harder than I anticipated. Getting the necessary bracing to fit around the bulky cylinders was a real challenge. However I am now somewhat confident that it will work, and quite excited!