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Thank you very much for your comment. In this trial and error, the energy efficiency of the escapement was very poor, so I am thinking of improving this first. Because this clock is energy inefficient, the weight is wound up frequently. As a result, the LEGO DC motor broke after about one or two months. This makes it very impractical. Therefore, I am currently thinking of the following. 1. I will try to develop an escapement like the synchronome type. I think this escapement will be much more energy efficient than the current one. In addition, I will be able to utilize some of the know-how of the gravity escapement that I have tried so far. Also, because the time that the pendulum and escapement are in contact is short, it will be possible to reduce escapement error. I think that the Chronobrick-3 is an excellent constant force escapement, but even so, unpredictable changes in the rate occurred. It seems unlikely that the effects of temperature, air flow, or atmospheric pressure were the cause. I was also unable to confirm any wear on the individual parts. Therefore, I think that the escapement error may have caused some problems, resulting in the rate change of the Chronobrick-3. A synchronome escapement might be able to overcome this difficulty. 2. A synchronome escapement originally operates with a pendulum with a high Q value, but I would like to try various variations, such as a low Q value or a pendulum with a short period. Perhaps it would be interesting to combine it with the magnetic pendulum arc error compensation that you invented. It will probably take a lot of time, but I will try new ideas little by little. It would surely be interesting if there were more research into high-precision LEGO pendulum clocks from various angles. In fact, that is the thought behind the name "ChronoBrick-1". I thought it would be wonderful if a new field of LEGO research could be created as a result of this clock. That's why I combined the words chronometer and block and added the number 1 to it. I will let you know if anything interesting happens again.

@@KeiAbeけいけい Thanks for extensive response. Synchronome style escapement is an interesting idea. Some comments: 1. Making pendulum-escapement contact time short is pretty much irrelevant; escapement error does not depend on contact time. Short, strong push may actually make things worse by introducing more vibrations. 2. The escapement error can be made arbitrarily small simply by applying the impulse at 0 phase (when pendulum is exactly vertical). This is what chronometer escapement does. 3. One way to verify if the escapement is the cause of the troubles is to monitor the amplitude. In case the escapement force changes for some reason, amplitude will change accordingly. Of course, the amplitude can also change due to changes of air resistance, but this is very minor effect. Since You mention no noticeable wear on parts, I'm not sure if escapement is truly the cause here. 4. The magnetic system I developed solves a lot of problems because it removes the need to keep the amplitude constant. Thus, we no longer care about escapement error and changes of air resistance. 5. Are you sure that thermal compensation is perfect? Even if its geometry is exact, there may be some friction in the system that prevents reaction to small temperature changes. I encountered this problem with my clock and never solved it completely. 6. Regarding air-related effects, it may be useful to estimate the effect of air buoyancy; Air is about 500 times less dense than Lego, so we have a buoyancy force that is around 0.2% of the pendulum mass. As the air changes density (due to both pressure and temperature), the buoyancy force changes accordingly. Assuming, for example, that air density varies by 10% (quite realistic), we get 0.02% change of the force that acts directly against gravity. This is the same as changing gravity by 0.02%, and that will change the rate by 0.01% or 8.6 seconds/day. Air buoyancy may actually be the biggest limiting factor of precision Lego clocks right now. Well, this became quite a long list :) There is some new research in this field - I have written a book! It is available on Amazon, I put a link in my recent video. Various aspects of clock-related physics are discussed much more extensively than I could do in a RUclips comment.

@@davidziemkiewicz1350 Thank you for your valuable opinion. I will get your book and study it. I understand point 2. Point 1 is very interesting. I thought that if the number of contacts between the escapement and the pendulum is reduced, the period during which the pendulum oscillates freely will be longer, and therefore the accuracy will be improved. This is interesting, so I will actually try it out by trial and error. Point 3 did not observe any change in amplitude. I checked the position of the tip of the pendulum with a period of 1.5 seconds in 0.5 mm increments, but no change in the amplitude was observed. I think point 4 is a great idea. Point 5 is not a concern about friction within the system. The earliest prototype pendulum had this problem, but the pendulum I am using now is not a problem. However, if there is a temperature difference between the top and bottom of the pendulum, it cannot be accurately corrected. I was able to confirm this tendency this time. There are several improvement ideas, but I am not sure which is the best. Point 6. The change in the buoyancy of the air is a headache. However, it was not related to the error of Chronobrick-3. (I also measured atmospheric pressure to confirm the trend.) I feel that this concern will not become apparent until I can make a more accurate clock that can run for several months. Actually, I have an idea. I would like to attach a counter float above the center of rotation of the pendulum. This float would cancel out the buoyancy acting on the pendulum, which I think would make it much more accurate. I had this idea before I made Chronobrick-1, but I have not yet been able to test it.

@@KeiAbeけいけい Thanks for the response. 1. Yes, indeed it is a common belief that maximization of time when the pendulum moves freely = better accuracy, but this is not so simple; I'd be very interested in the trial and error results. 2. If there was no change of amplitude, the hypothesis that escapement is the source of problems becomes less likely. In future tests, it may be useful to periodically measure the period of the pendulum with escapement disconnected; that will help to figure out if the escapement is really the problem here. 3. Happy to hear that you could overcome the friction problems in thermal expansion compensation. This issue plagued many "real" clocks as well. 4. If there was no correlation of rate with pressure, then indeed buoyancy may not be a huge issue after all (however, note that buoyancy depends on air pressure, temperature and moisture, so it is pretty hard to confirm its effect or rule it out). Counter float is a brilliant idea; the only problem is that it needs to be airtight and of course it will reduce the Q factor substantially. 5. I wonder if Lego pneumatic cylinder could work in a pressure compensation mechanism?

@@davidziemkiewicz1350 Regarding the fourth point, I think the counter float doesn't have to be an airtight tank, and could just as well be a lump of normal plastic parts. The counter float would be a lump of many plastic parts attached above the pendulum's center of rotation. Metal weights would be attached to the bottom of the pendulum. If that's the case, the pendulum will not look like a simple pendulum, but rather like a rigid pendulum with weights attached above and below the center of rotation. Regarding the fifth point, I once considered the idea of using a pneumatic cylinder. The weights would then move up and down to compensate for changes in atmospheric pressure. However, it may be difficult to realize this since it is affected by temperature changes. I feel like it could be managed if combined with a temperature-compensating pendulum. It's interesting to think about it in various ways. If I had another copy of me, I could try out lots of different things...

Это работа, которую я лично разработал, так что, к сожалению, нет планов по выпуску. Я также хочу, чтобы он был коммерциализирован.

А ты пробовал подавать заявку в Лего? Ведь Аполлон как-то стал официальным набором.

@@Саша11167 Для того, чтобы подать заявку на «LEGO ideas», существует ограничение на общее количество деталей. В моей работе было слишком много частей, поэтому я не смог ее отправить. Другой автор предложил ракету «Союз», но, похоже, она не получила необходимого количества голосов.

Жаль конечно что такой шедевр даже нельзя предложить. Но я всё же надеюсь что ты продолжишь свое творчество и будешь прогрессировать.

Sorry for the late reply. This clock uses a gravity escapement, so it is necessary to reset the position of the gravity arm. In addition, the design has been designed to eliminate parts that generate friction in the gravity arm as much as possible. With this design, there is a risk of malfunction if the gravity arm reset operation is not performed slowly. Therefore, the reset operation is performed slowly using a rotor with wings.

@@KeiAbeけいけい that is very helpful. I was having trouble because my gravity arm reset operation was too fast

Thank you. I haven't given up on my goal to make the most accurate clock possible, running for months. But I've gotten bogged down in the improvement of ChronoBrick1. So I'm going to try this new escapement. I'll give you the technical details later.

@@KeiAbeけいけい Good luck! As you maybe noticed, I recently started an accurate clock project as well, and now I'm getting bogged down with fine tuning. This stuff takes a lot of patience!

​@@davidziemkiewicz1350 I look forward to seeing your work! It really does take patience. I've been trying and failing for years to make an accurate clock, but I still have errors that I don't understand. I think it's relatively easy to achieve a daily difference of about 30 seconds. If you want to achieve a daily difference of less than a few seconds and a monthly difference of less than 30 seconds, there are many difficulties ahead. The most mentally painful thing is that it takes a long time to run the device. For example, even if it seems to work perfectly for the first week, it may become unstable from the second week. What's more, there are times when it's difficult to find an easy-to-explain reason for it, such as wear and tear.

@@KeiAbeけいけい Precisely. You are right, I'm at around 30 second/day rate right now and going below that is painful - right now it is "losing stability after 6 hours of perfect running". The prospect of getting instability after one week terrifies me. Recently I found a paper about some very simple photogate assembly with no microcontroller (signal is going directly to PC microphone input, sampled at 44 kHz). This will hopefully aid me in fine tuning. I'll report results on youtube. If you are interested in that, google "Sub-$10 sound card photogate variants"

Let me explain the technical details. This escapement was inspired by and developed from the Arnfield escapement. The goal is to completely separate the pendulum motion from the drive torque, even at the expense of energy efficiency. In order to achieve the above separation, I am working on the following two ideas. 1) About how to lift the gravity arm. The Arnfield escapement uses the rotation of the escape wheel to lift the gravity arm. However, because LEGO bearings have a large amount of play, the height at which the gravity arm can be lifted is affected by the driving torque. I was troubled by this drawback when I prototyped an Arnfield escapement several years ago. Therefore, in this escapement, the mechanism that lifts the gravity arm has been modified. 2) About unlocking the escape wheel The Arnfield escapement unlocks the escape wheel by movement of the gravity arm. However, with that method, the motion of the pendulum is indirectly affected by the driving torque. Therefore, a special mechanism was inserted between the gravity arm and the escape wheel lock. This mechanism was born from research on ChronoBrick2. ChronoBrick2 did not produce satisfactory results, so it is only available to the public on a limited basis.

In this video, knife-edge support is used for the gravity arm bearing, not the pendulum bearing. The pendulum bearing uses a cylindrical rolling bearing, similar to ChronoBrick1. As you say, this bearing is difficult to adjust. The following phenomena may occur. 1) If the shaft of the cylinder is slightly off horizontal, the pendulum will drift to one side. If the pendulum were to come into contact with the structure supporting the cylinder, the accuracy would immediately deteriorate. 2) How much does the cylinder shaft bend due to the weight of the pendulum? If the center is at its lowest point, the pendulum is stable. However, with the goal of operating for many months, and considering the durability of the cylindrical shaft, it is desirable to have less deflection. (In other words, the shorter the cylinder shaft, the better) If you use a short cylindrical shaft, the pendulum will sometimes be stable and sometimes not, depending on the slight distortion in its shape. If the pendulum is not stable, the result may be the same as in 1), or there may be cases where the pendulum moves in a twisted manner, as if shaking its head. Even with the drawbacks mentioned above, this mechanism exhibits excellent low friction and high durability.

@@KeiAbeけいけい Thank you very much for extensive explanations. 1. I was troubled by inconsistent lifting position of the Arnfield escapement as well, this is a brilliant way of solving this issue. 2. Escape wheel unlocking mechanism is also great. In principle, for perfectly built Arnfield escapement, gravity arm stops completely when impacting locking arm (ellastic collision), immediately detaching itself from pendulum. Unfortunately reality is not perfect, so this is a very good solution of fixing the problems here. 3. Regarding the cylinder - yes, it wants to wander to side, especially with light pendulum. I usually use 4 studs long cylinder, allowing it to bend quite a bit under the weight of the pendulum. Good for fixing it in place, but no idea if the bend increases over time (plastic parts under stress tend to slowly creep, even when plastic deformation threshold is not exceeded). In my recent tests with heavy pendulum (~1.5 kg), cylinder suspension was only ~20% worse than knife edge. Good tradeoff for much better durability.

@@KeiAbeけいけい By the way, I have some ideas on improving Arnfield escapement, but in a different way. It is well known that the impact of the push applied to the pendulum on the rate depends on the timing of the push, and is close to 0 when the push occurs when pendulum is exactly in the middle (has maximum speed). This is premise behind chronometer escapement. Arnfield is bad in this regard because the pendulum picks the gravity arm and carries it all the way to max amplitude. My concept is to (somehow) modify the gravity arm so that: 1. At upper position, pushing force is close to 0 (so small inconsistencies in upper position don't matter) 2. The force exerted by the gravity arm is at maximum when the pendulum is in lowest position 3. Gravity arm follows the pendulum to the other side of swing, gradually reducing the force, so that force vs angle relation is symmetrical around 0, same as with chronometer escapement 4. The detachment of gravity arm occurs when pushing force is near 0, so inconsistencies here also don't matter.

@@davidziemkiewicz1350 Thank you very much. It's difficult to visualize everything with just words, but I feel like I've managed to understand the main points. I thought it was an interesting idea. I can't think of a mechanism to make this happen even if I think about it a little.

どうも，ベルナールジトン氏のアイディアをもとに東北大学で作ったもののようですね． www.sci.tohoku.ac.jp/mediaoffice/second/event-report4.html

Thank you for your comments! As for the inefficiency, it is probably due to the excessive energy consumed by the vertical motion of the gravity arm pushing the pendulum. On the other hand, as you mentioned, the friction of the trigger part of the gravity arm ((1) between the pendulum and the trigger, (2) between the trigger and the gravity arm, and (3) on the trigger's rotating axis) seems to have a negative effect on accuracy. The above parts seem to be prone to wear, and their effect on accuracy changes over time. While (3) is easy to improve, (1) and (2) are more difficult to solve. I am currently working on a prototype of an improved clock. my goal is to maintain accuracy close to that of a quartz clock for at least three months, but we are having a hard time achieving it.

@@KeiAbeけいけい I guess it's no easy task! What you are achieving is amazing, it would be great even outside the limitations of Lego!

Thank you for your interest in my clock. Sorry for the delay in replying to your comment. The power supply by overhang is a good idea. Under the condition that the motor is used to reset the clock in a short time, I think it can be assembled with LEGO without any difficulty. You are also right about the transmission efficiency of gears. However, the efficiency of the gravity escapement of my clock is low, and this is the main cause of its low efficiency. The efficiency of the gravity escapement is considered to be low to begin with, but in my clock, the efficiency is even lower because of the emphasis on accuracy. Therefore, I have to accept a certain degree of inefficiency...

It would have been interesting if the pendulum controlled the flow of water, but this pendulum seems to be purely decorative. However, I think it is a very beautiful clock :-)

Hello. Thank you for your comment :-) Here are the design parameters for the use of copper wire. Please refer to 6:53 of the video. The length of the pendulum from the support point to the lower end is about 73 cm. The distance from the center of rotation of the link to the center of gravity of the bob is about 11 cm. The distance from the center of rotation of the link to the point where the wire is connected is about 2.5 cm. The wire is approximately 50 cm long, folded in half, and connected to the pendulum rod at the center and to the left and right links at the ends. If metals other than copper are used, the design should be reviewed by comparing the coefficient of linear expansion. When making a pendulum with an oscillation period of 2 seconds, the pendulum will be long, and temperature compensation errors may occur due to temperature differences caused by the height of the room. I am currently working on an improved version.

Hello:-) Thank you for your comment. Can you message me on Twitter or Flickr? I can then use that message to give you my email address. Twitter:twitter.com/Kei_Kei_Twi Flickr:www.flickr.com/photos/91934169@N08/albums

He should put this on lego ideas

Thanks for the comment! That is a very fascinating possibility ... However, this is my impression from actually running the watch, and it seems to me that the error depicted in the graph is due to slight wear and dust on the escapement parts. Someday, I would like to build a clock that can see the effect of the moon's gravitational pull, and run it for months.

Thanks for your comments! I considered using an L-shaped gravity arm, but in order for the gravity arm to reset after it completely leaves the pendulum (i.e., for the torque of the gears and the force pushing the pendulum to be completely independent), I needed to use the method shown in this video. The rotation axis of the wheel, which is in contact with the tip of the gravity arm and the pendulum, is made of thread and can rotate almost freely. After about a month of continuous operation, there seems to be no deterioration in the thread. I wondered if it would be possible to use the repulsive force of a magnet instead of the wheel, but it seems to be difficult...

@@KeiAbeけいけい I see. Yes, the need to completely leave the pendulum before reset complicates things. Still, as long as the gravity arm pivot and pendulum pivot are not exactly the same, there will be some mismatch in trajectories that allows for detachment, just the margin of error in position may be small. The thread axis is an interesting solution. I don't know how magnets would perform. On one hand, it would be completely frictionless. On the other hand, they would interact with each other all the time, transforming a simple push into continous, variable force.

Thanks for your comment! The fly fan is interesting to watch in action :-)

@@KeiAbeけいけい i have a BrickLink Studio file of my fly designs, which i would like to share with you. i tried to post the link, but my comment was filtered. if you like, you can post a comment on one of my videos, then i can post the link to you in my reply, without fear of the comment being filtered. KEvron

Thank you for your comment :-) I started by improving the Galileo escapement, and after more than a year of trial and error, I developed a prototype of this clock.

Thanks for the comment! :-) I think your point is probably correct. Through repeated experimentation, I knew empirically that wear on the gravity arm unlocking mechanism would affect the accuracy of the clock. To solve this problem, I am testing a way to drastically reduce the wear of the unlocking mechanism. In the past, I have considered using the slave pendulum that you suggested, but it would require a major redesign, and if I were to prototype it, it would have to be after the next prototype. I also tried Arnfield's escapement, but it seemed to have an effect on the period depending on the rotational torque.

@@KeiAbeけいけい A bit late reply: Arnfield is completely free from torque variations only when 3 conditions are met: 1. gravity arm is always fully lifted, with no variation in height 2. gravity arm and locking arm have equal masses - so that when the gravity arm impacts the locking arm, it stops completely and immediately detaches itself from the pendulum, while the locking arm takes all momentum and unlocks. 3. locking arm always stops at the same point, so that the point where gravity arm impacts it and stops is constant By the way, thanks again for inspiring me to do some in-depth calculations; now they are available as a research paper: arxiv.org/pdf/2103.14947.pdf and right now I'm polishing it for a peer-reviewed journal.

Hello! I posted an improved version of the gravity escapement :-) ruclips.net/video/kFMCaekb744/видео.html

Thank you! This is very interesting. I'm busy with work, so I'll watch your videos carefully on my days off. Your theoretical analysis skills are amazing. I made a clock with a simple theory and countless trial and error. There were many things that seemed to work but did not, and I could not explain why.

Thank you for your comment! Inspired by the precedents of the wonderful LEGO clocks around the world, I have finally achieved this accuracy. It took an incredible amount of trial and error, and a lot of hard work.

Thanks for the comment! :-) Your insight is correct. I did some simple calculations and found that the support point of the pendulum moves slightly, so depending on the swing angle, a pendulum similar to a cycloid pendulum can be realized. However, the pendulum requires a very large swing angle, so I haven't been able to take advantage of its characteristics in this prototype.

*"It may actually correct the circular error!"* i suspect you've already covered this in one of your videos, but what the what? does this have something to do with the center of oscillation? surely, the two radii are factors. KEvron

@@KEvronista I have not covered it yet but I plan to do some calculations. Indeed, the two radii are factors there. However, as Kei Abe said, I suspect that a very large swinging arc is needed to make any difference here.

@@davidziemkiewicz1350 *"I suspect that a very large swinging arc is needed to make any difference here."* if that's the case, then i might have to work it into my own designs. my only concern with it is that its geometry might not work well with my galileo (boomer!) escapements. ....and all this time, i've been sitting on a new knife edge design. can you imagine my discomfort? KEvron

@@KEvronista I can definitely feel that. I'm in the middle of rebuilding my grandfather clock with this suspension and grasshopper escapement of all things.