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That's a lovely machine! I have been experimenting with various designs for large wheels for some time. I am surprised by how sturdy these appear to be. Great work!

In addition to the Power Functions components, there is a wide variety of other Lego motors, most of them no longer in production. You can find very detailed information about them on Philo's page. All are "compatible" in the sense that they use standard lego attachments (studs or axle holes) and standard lego axles.

Many thanks for the further data, Blakbird. I have been away for a while, so have not been able to experiment further. I suspect that the "prying apart" of the wheels may well be the major reason for the difference between your picture and mine. I am using relatively rough "art paper", and you say your paper is quite "sticky". Sticky paper could easily result in more prying apart. It would certainly by worth a try going back to the knobbly motorcycle tires. The "prying" and "squishing" effects might be less. The knobbly tires are very slightly thicker (in the direction along the axle), so with the half-bush spacing there is a bit of a danger that they might rub on the structure. I need to check this. Another potential solution would be to use a much bigger wheel such as 88516, and mount it much further out (more than a stud further in this case). I'm less keen on this as it would require major redesign and might cause other problems. I would also like to see how much of the inaccuracy can be "hidden" by staring from the center of the curve, as I did. (I may try a simulation for that). Again, I want to find the best possible set-up, so that it can be incorporated into the final instructions!

Hi all, Just over a year ago I presented version 1 of this MOC. It is a purely mechanical device that draws a fractal curve - I believe it is the first time such a thing has ever been done, in Lego or otherwise. It uses a single L-motor, a series of Geneva mechanisms, and a stepped transmission mechanism to draw a Heighway twin-dragon, a space-filling curve that never intersects itself. (No Mindstorms here!) One problem with version 1 was that the final curve was huge - about 2m by 3m. Consequently I never found a big enough piece of paper and enough space to run it to completion - it just wasn't practical. In the new version I have managed to solve this problem. I filled the one remaining space with an add-subtract mechanism comprising two differentials. The previous version made a 90 degree turn by turning one wheel by a full turn while holding the other fixed. In the new version, one wheel makes 2/3 of a turn while the other makes 1/3 of a turn in the opposite direction. Consequently, the final drawing is 3 times smaller, about 0.7m by 1m. In addition, I redesigned almost every part of the mechanism, and made it far more robust and reliable. I think it is now at a stage where it would be reasonable of other people to make it - I am working on an LDraw file... The full drawing takes 256 turns and just over an hour to complete. It is accurate enough that the curve never intersects itself, and is within a few cm of joining up to itself at the end. Not bad for pure mechanical dead-reckoning! Here is the actual drawing, compared with a mathematically perfect computer generated version. More pictures and LDraw file on brickshelf and bricksafe

Hm - I am also a bit surprised that Blakbird's version didn't quite join up right, and I don't have a good explanation at the moment. As I mentioned, I fine-tuned the wheel spacing by trail and error. After doing a rough version of your calculation, I just got it to do a bunch of left turns in succession, and adjusted until the angle was right. This test was done on a wooden floor with no paper and no pen, whereas the final run was done on fairly rough paper, so I'd be surprised if the paper is responsible for the difference (but it's possible). It might help to start in the center of the curve rather than the corner. I did this partly because I wasn't sure of the exact size and orientation, to maximize the chances of it staying on the paper. Many thanks for the instructions! I am aware of a few issues, and I'm keen to make them perfect. I have already started making a few improvements, both in the stepping and, in one case, to the actual build, to make it easier to put together. I would like to know exactly what issues you had - I'll PM you... One thing I found is that uneven floor can have a big effect. It did not work so well on a hardwood floor, which has some imperfections. The video is from a tiled kitchen floor (with thick paper), which is also not perfect, but flatter than the wood floor. It looks like you are using a wooden table, which ought to be very flat. It also looks as if your wheels and casters have gone of the edge of the paper at times. That caused alot of trouble for me, because the casters can get stuck under the edge of the paper. It's possible that caused some inaccruacy.

Wow - Akiyuky proves he is a genius yet again. If there is a better use for the red sliding 8t gear, I have yet to see it! At first I thought the video must be speeded up, but no; it is just insanely fast! And making the sorting arm push the release mechanisms is pure comic gold (as well as very ingenious).

Stunning model and very imaginative back story! I only wish it was all motorized. I do realize that would be very very difficult...

Cute! Keep up the good work.

Now that is one strange looking vehicle! You might want to try reinforcing the chassis and the mechanisms a bit...

There might be other ways. Combining a diff with a continuously variable transmission would do it in principle...

Even though it may not be the best for vehicle transmissions, I'm a big fan of this one: - the spur gears on the housing are great for add subtract mechanisms and their many variants...

Nice work! it reminds me a little of Il Tempo Gigante

Well, no wonder your motor is working hard with the additional weight of an orange 6L thin liftarm AS WELL as a 7L black one, and a 3/4 pin to connect them Great work - the orange looks awesome! Indeed, there is not that much torque to spare when it comes to making a turn. Of course, all the mechanisms do have quite a bit of friction (the worms, the differentials, the armatron). I did find that things improved after a careful going over all the mechanisms looking for slightly bent axles and rough gears (in particular I find that the double bevels sometimes have rough spots on the sides). One more technical point to record about this model (if anyone cares!) The 3x3-quarter-circle-liftarm catch that releases the armatron mechanism in response to a command from the brain required quite a few designs (even though the final solution is very simple). It is really crucial that the liftarms have a perfectly circular shape (and this is the first time I have ever used this fact in a model). That way, there is no possibility of the armatron forcing the catch out of the way when there is no command from the brain, yet it requires relatively little force to drag the catch out of the way to give a command (you only have to overcome the friction).

Thanks - these pictures are very helpful. Quite a masterpiece. Where do you get the sails? Indeed. I remember reading somewhere that for many years the only way for a human to travel over 100mph was in an ice-yacht.

The sailboat is amazing! I'd like to see more details... For those who don't like mixing PF with water, another possibility that I've always wanted to try is a land-yacht:

The GBC speedometer is fantastic work. Really innovative use of the differential! (And the ball pump is pretty nice too). When it bottoms out at "Min", what stops the paddle wheel from turning backwards? Just carefully balanced friction in the friction pin versus the clutch wheel? To be picky, I think it does not genuinely give a reading of speed or flow (in balls per minute). Assuming a constant flow of balls, I think it will drift all the way to "Min" if the flow is less than some critical threshold, or drift all the way to "Max" if the flow is greater than the same threshold. Nevertheless, I still say it's awesome! I wonder if there is any way to genuinely get a reading of balls per minute by mechanical means?

Without question, it was this compound of five tetrahedra. Even with a computer model on the screen it is very hard to work out how to interleave them.

That's a lovely MOC. Wonderful mechanics for such a small space!

Actually, there is even more to be said on this point. It is equally important that the upper "brain" does not operate too SLOWLY relative to the lower "drive module". If it did, the drive module could complete its turn WHILE a rocker arm was lifted by one cam. Then it would receive a second turn instruction from the same lifting of the rocker arm, which of course is no good. So the relative speeds of the two halves need to be just right. The time for the drive module to complete a turn needs to be longer than the time that the rocker arm is lifted by a cam, but less than that time plus the "down time" between one rocker actuation and the next. And of course, all these things are not completely deterministic, but subject to some variation, so extra safety margins need to be built in. In fact, this issue is only really important for the earlier cams in the sequence, especially the first one. The later ones move very quickly from one position to the next, as a result of the backlash in the Geneva mechanisms combined with the weight of the rockers acting as a detente mechanism. All this is part of the reason for choosing "sharp" cams (1x3 liftarms) for the earlier Geneva axles. (But "blunt" ones later because of the low torque available). This issue caused a lot of trouble in earlier versions of the machine, when the drive modules were not 100% reliable. Also, I've made a slightly nicer (color coded) version of the "road map" here.

That's a very funny and clever creation! I so wish TLG would do more dinosaurs along the lines of 4958...

Wow, thanks Philo, that was FAST! And great work on the PDF, Blackbird. I really need to learn LPub...

Here ya go!

I'm not sure I want to try calculating that! Building time maybe half a day per week for a year? But it's very hard to estimate the amount of thinking time... Surely nonsense I don't know anything about your job, but your Lego creations are simply stunning! If Lego building was my job I would probably be fired - it takes me forever to get anything finished, and many aspects of it I approach in inefficient and illogical ways (e.g. I'd never heard of condition number, although the basic idea sounds easy and natural).

I would welcome Blakbird or others improving the Ldraw file / instructions. I basically did the minimum to make it buildable. If you compare the knobbly tires with those of your 8422, I think you'll find there is no detectable difference in diameter. However, there are some other confounding factors here: 1. The positioning of the wheels in the file may not quite match reality (and I did not try that hard). 2. The tires squish a bit when there is weight on them, changing the diameter. 3. The diameter is only an approximation to what you want - when the vehicle makes a turn, the tires interact with the floor in complicated ways involving friction and deformation of the rubber. (It's possible that THIS part is different with the smooth/knobbly tires). I believe experiment is the only way to get the turn angle exactly right. This is what I did - I kept adjusting the wheel spacing on the real model until I got turns of 90 degrees (as measured by the cumulative effect of several consecutive turns). Then tried to find a combination of pieces to enforce that wheel spacing as best I could. That's right. I toyed with this idea (after the Pendragon 1) but decided it was too difficult, and besides, an add-sub mechanism makes it cooler! I like the current size of the drawing. It's big enough to look impressive, and big enough that it could not easily be drawn by hand, but not so big as to be impractical (like version 1). Quite right. Thanks for the clarification. The earlier post contains a deep link. But brickshelf seems a bit unreliable these days, so here it is in bricksafe too.

It looks as if I got myself confused about this. What I said earlier about it being insensitive to initial conditions was not correct. As you say, the initial set-up in the LDraw file does not match anything in the schematic list of diagrams, and is NOT the correct way to set it up. One possible correct initial setting is to have the cams on one side pointing towards each other in pairs. I will edit the LDraw file to reflect this. Other initial settings will produce DIFFERENT patterns, generally less interesting than the dragon, but also quite nice. E.g. the incorrect set-up in the file (all cams pointing one way on one side) gives a space-filling curve that fills a diamond shape (according to my computer program). Edit: I think the LDraw should be correct now!