Davidz90

I'm proud to present a strong contender to the title of the most accurate Lego clock in the world. It all started from a stable base: Lego tower sandwiched between wooden boards and the base contains ~15 kg granite slab. This sort of extreme build was needed to keep structure vibrations in check with ~1 kg swinging pendulum. The final (for now...) clock is here: Just now, I finished a 23 hour measurement of clock accuracy. The pendulum is intended to have 2 seconds period. Here's how it actually is: period_24h by David_Z1, on Flickr basically 2 seconds +-300 microseconds. However, what we care about is the total error of the clock (how much it is early/late), which is a sum of the errors of all periods: error_24h by David_Z1, on Flickr The clock started on time, at ~2 hours it was 0.6 seconds early, near 9 hours it was 0.8 seconds late. Less than 1 second error in 24 hours is a Rolex-level accuracy (in fact, a little better than any mechanical watch). And now some technical details: The key component of the clock is grasshopper escapement (invented by John Harrison, it is one of the most accurate clock mechanisms). It's characteristic feature is that within some limits, clock speed is independent of amplitude. Due to the technical limitations of Lego (too much friction), I couldn't get that - the clock speed depended on amplitude/driving force, which is always a little variable due to friction. In order to combat this, I devised a magnetic compensation system - two magnets on the sides of the pendulum, pulling it away from center. As the amplitude increases, the distance between magnets at the pendulum at full swing decreases. By pulling the pendulum away from center, the magnets fight the gravity, and thus slow the pendulum down. The slowdown depends on magnet distance, so it is a function of pendulum amplitude. This amplitude-dependent slowdown counters the amplitude-dependent speedup of the mechanism. With this system in place, the clock speed looks like this: mag_s4 by David_Z1, on Flickr Clock rate is the standard way of measuring speed - rate of 1 seconds/day means that after 1 day of working, clock will be 1 second early or late. You can see that near 4 degree amplitude, rate is not changing much at all. This is astonishing stability - 1 second/day means 1/(24*3600) = 1/86400 - about 10 parts per million! Second key component is the compensation of thermal expansion - as it gets hotter, pendulum expands and clock slows down. This is especially bad with ABS plastic. I fixed this by hanging the pendulum weight on steel wires, and then using the expansion of bricks to compensate the smaller expansion of wires. The system is described in the video and currently is over 90% efficient (the dependence on temperature is decreased 11 times).

Thank you!

I have the CADA orrery. Instructions indeed had some minor issues. Specifically the order some pieces are added seemed a little random at times and not like a sensible person would do. As if the instruction creation was at least partially automated.

90 m/s is very impressive! In fact, this may be one of the fastest shooting Lego thing ever. How did you measure the speed? With a chronograph?

I think that in the instructions, only the earth axis is lined up more or less properly, with proper seasons and equinoxes. I haven't checked but I believe that the initial moon position was whatever. In general, the set would benefit from some slip clutches allowing for easy correction of the relative positions.

One error in my previous post: everything is sidereal (rotations relative to fixed base), moon too. This means that we need the sidereal lunar month which is 27.32 days. So 27 is remarkably accurate after all! Now if we want some serious accuracy, I've done some more calculations and here are the results: calculations by David_Z1, on Flickr

Actually, I did XD In fairness, it is quite a bit more convoluted and makes use of multiple differentials, but for me that's a plus. The, moon is the most puzzling - a simple 1:28 would be better. I'l definitely make a mod implementing better gear ratios & limiting the color vomit on the model.

I got the set. Very pleasant build. Unfortunately, my Earth prints are also slightly displaced, Africa experienced catastrophic tectonic shift. After studying the gearing, I can confirm the earlier findings about gear ratios: 1 lunar month = 27 days (should be 29.53059 solar days) 1 sun rotation = 27 days (technically OK, some parts of the sun rotate at this speed) 1 hand crank rotation = 3 days Regarding the year, earth is atached in such a way that without input, it will remain stationary in relation to the base (not the arm). So it will gain an extra solar day throughout the year (from the perspective of earth, sun will do 1 full rotation). This means that the year length is 364.5 sidereal days (2:729 gear ratio, rotations in relation to fixed base/stars) + 1 solar day. Since the earth rotations are in relation to the fixed base, all the days in calculations are sidereal days, which are shorter than solar days (they are 23 hours, 56 minutes long, so approx. 0.997222 of a solar day). Therefore, the final periods, in solar days, are: 1 lunar month = 26.9249 days (should be 29.53059 days) 1 year = 364.4874 days (should be 365.2425 days) In short, year length is a little worse than the earlier calculations.

This one is truly jaw-dropping. Absolutely brilliant engineering.

A working calendar. The first obstacle was devising way to encode the length of the months. My "eureka" moment was using a days dial with 32 positions and a hand that skips 1-5 days at the end depending on the month. A 12-sided cam with 5 possible heights turned out to be quite doable and compact.

Amazing!

Indeed, the orbit eccentricity of Earth is less than 2% so including that would be just extra complexity with no visible difference. For moon, on the other hand, it would make more sense to add eccentricity, which is not that complicated mechanically. The comment about inaccurate sun size was hilarious; it should be about 100 times bigger than earth, good luck doing that (still simpler than realistic distances, would be a few kilometer radius lol).

Ok, here's a decently working stepper mechanism with 8t gear, now properly aligned with beams: I'm not 100% satisfied with the reliability, but the idea seems viable.

Yes, I understand, valid point. I'll try a few things tomorrow.

Here's my quick and dirty prototype. Works just fine in one direction, adding second pallet below is problematic.