Star Gears
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- เผยแพร่เมื่อ 16 พ.ย. 2024
- More OskarPuzzle at www.youtube.co.... Buy the Gearify software at www.gearifysoft.... Contact Oskar for the gear design drawings at oskarvandevente.... Star Gears is a set of irregular gear, created by unrolling an ellipse. Each of the star-shaped gears has teeth on their teeth in a sort-of fractal way. Surprisingly, these irregularly-looking gears can be used to draw perfect circles. The gears were designed by using the Gearify software by Michael Valle, as demonstrated at the end of the video.
Copyright (c) 2017, M. Oskar van Deventer.
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Would Star Gears be good for a Spirograph? How should it be designed?
whoa.
Misaligning the points.
OskarPuzzle Upon watching the demo, I noticed that you placed the gears so that a big "petal" (not gear tooth) was in the crux between two petals of the other gear. I suppose you could combine the same gears offset from the position described above such as a petal meshing halfway between a petal tip and a gear crux to create a non-circle.
I did immediately think oh wow, a backwards Spirograph! Well I don't know if I have any idea on how best to incorporate it with a Spirograph... But I suspect that the slight differences in circle radius would be related to the computer's numeric approximation of the relationship between the major/minor ellipse radii, and the perimeter of the ellipse. The integration can't actually be solved symbolically for an ellipse perimeter. It needs numeric integration or else one of Ramanujan's approximations. They're symbolic, and very very good, but still only approximate. The Stand-up Maths channel has a great video about the problem here th-cam.com/video/5nW3nJhBHL0/w-d-xo.html
Well, I say it's a great video but really I mean it has some great things in it.
But not the singing. That was a bit... off...
(And he says eclipse a lot without correcting it. And regarding eccentricity he says "up to one" where I would say "towards one". And I don't believe he's proven the accuracy of his own last attempt at a rough approximation, for all eccentricities, as he says, and I'm convinced he got that bit wrong... And when he says that Pi is approximate too, he goes on to claim that Pi is also needed in the power series for an ellipse, which is nonsense because you just omit Pi as an outside factor and the power series that's needed will change -- effectively combining the calculation of Pi with everything else the power series does.)
YOUR attention to detail, however, passes my pedantic standards 😊 Your videos are great enough that I have finally subscribed, to a TH-cam Channel, after many years of refusing to!
In future I'll try to talk about your own video more than someone else's 😂
Apologies in advance if I break your preferred 'netiquette'; I'll try and familiarise myself with the channel a lot more, before I do another ramble!
It appears that the only reason that those gears make different circles is that they are not perfectly precise. The circles are not very different, and they do not seem to have any pattern to their size change. Furthermore, it looks as though the Gearify program only calculates the gears by tracing the path of a base gear, which is not a purely mathematical process. For these reasons, I believe it is completely within the realm of possibility that it is a precision error wither within the program or printer. This is my hypothesis, at least. I love your videos, by the way! You are a mathematical genius. Keep up the good work!
I don't want to spoil Oskar's riddle, but I couldn't help but comment here! I am the creator of the Gearify software program and this comment caught my eye. "it looks as though the Gearify program only calculates the gears by tracing the path of a base gear, which is not a purely mathematical process."
It may appear this way, but the truth is it is an extremely mathematical process being followed here. I won't give away the details, but I can tell you the discrepancy is not due to the software or 3d printer inaccuracies. They exist for a purely mathematical reason. These gears often produce results that defy intuition and that is something that makes them interesting.
Cheers!
-Michael Valle
Michael Valle Good to know! This is my first time ever seeing this application, so that was the best guess I could make without any further knowledge about it. Thank you for your reply. Sorry if I sounded rude or inconsiderate in my first comment.
Not at all, I just have the inside scoop, as the creator, so I was itching to reply! :P
Michael Valle Cheers, mate!
Let's ignore the gears' teeth, because they add constant width to each circle drawn by a pair. If we had circular gears with these gearing ratios (the gearing ratio is simply the quotient of circumferences), they would have the same ratio of radii. Thus, circular gears 1+6 would produce the same circle as 2+5 and 3+4.
The radius of a circle produced by star gears equals r_min(gear A) + r_max(gear B) = r_max(gear A) + r_min(gear B) = 0.5 * [r_max(gear A) + r_min(gear A)] + 0.5 * [r_max(gear B) + r_min(gear B)]
Thus each gear's contribution to the total radius is 0.5 (r_max + r_min). For spherical gears this would be simply r, which is directly proportional to the circumference. However, for a star gear 0.5 (r_max + r_min) isn't proportional to the circumference. Its quotient with the circumference should, however, converge monotonuosly, if my intuition is correct. Therefore gear 1 should be the biggest outlier. That is why gears 2+5 and 3+4 produce almost the same circle already, but 1+6 is noticeably bigger.
easy there einstein
Never would've thought of it like that. Good thinking.
Now say that in English.
I started this video thinking it would be the coolest spirograph. I am now disappointed, but impressed!
Thanks! A spirograph has typically gears that are mutually prime, so one gets all the parallel spirograph line. For Star Gears, the numbers of teeth are, 11, 22, 33, 44, 55, 66 and 77, all composite and not-mutually prime by design. So I am not sure how Star Gears and Spirograph could be combined.
well maybe if you used a circular gear instead of an oval one, you could use gears that are mutually prime, and make some crazy spirograph stars!
I'll think about that. Thanks for the suggestion, Kai!
there's a direct correlation between the decline of Spirograph and the rise in gang activity. Think about it.
Just like all the other correlations on this page: www.tylervigen.com
E.g. number of people who drowned falling into a pool correlates very well with the number of films Nicolas Cage appeared in
What rise in gang activity?
any pair of properly meshing gears needs to make circle since the axles have to remain a constant distance apart
The amount of points on the star is proportional to the number of teeth on the gear, which is proportional to the circumference, which is proportional to the radius, which is what is considered when adding gears of different sizes.
The definition of gears requires the distance between the centers of two gears to be constant throughout the enter revolution, which explains why circles are drawn.
Indeed!
I think that the cirles have different sizes because of the tooths: to have each time the same circle, you would need a certain perimeter for each gear, meaning a specific ratio between two gear sets. Howewer, you might be not able to respect that ratio, because the perimeter has to be a multiple of a tooth width.
I used to have spirograph, it was amazing all the different patterns you could make
The shapes are not designed to have proportional radii, but proportional perimeters.
Correct!
The higher order the star, the smaller each side becomes. These smaller sides don't go as close to the center point as on a smaller order star. 6+1 makes a bigger circle than 5+2 because the distance between the centers of the 6 and 1 is greater than the distance between the centers of 5 and 2, thus resulting in a larger diameter.
That's really cool, Oskar. It reminds me of a Vsauce video about cycloids, roulettes, and the Brachistochrone curve. Awesome!
this seems like an improvement on a compass. compasses are difficult to use, the dig into the paper and they are easy to move around. you may be able to market this. I think this is genius.
Neebah Cuber - To go full circle one needs to let go of the center gear at some point (or at least move the gear holding finger aside a bit for the pen) More critical though is the highly variable machanical gain which is not useful for drawing circles. Normal circular gears rolling on circular ones work less bad for drawing circles than star gears.
Fester Blats - exactly
To answer the question first I'd have to understand why you'd expect the circles to have the same size in the first place. I may have to think about this some more.
Amazing work Oskar!
My guess is that the different star gears have slightly different sums of teeth due to their irregular shape.
Can you go fractal on these? Make gears with VERY few gears, VERY large teeth, use them as base shape for the next level, and repeat with like twice the tooth count, until you have a reasonable number of teeth.
1:04 I've made a perfsurx tircle.
This is surprisingly amazing
Thank you!
Aren't the circles dependant on the slightly different starting positions? Could you make different circles with the same set of gears?
Isn't the fact that gears make circles in this manner obvious as otherwise they wouldn't be compatible gears (keep their axles at constant distance)?
can this be useful for anything than just fun?
But what if you misaligned the points to be halfway through the spike of a star?
hello! the utility: if you chain them on like the whip, then the resulting Spirograph will be particularly interesting.
But what would happen if you would put the ellipse and one star together like in the video, but would flip the ellipse such that the focal point is on the other side? I can't imagine that this gives a circle as well
Indeed not a circle.
I love getting to watch your vids, thanks, Oskar! (did you change your mic recently?)
Yes, I now use the microphone that you see, that is directly wired to the camera. Why did you ask?
(I got lots of complaints about the sound, so I keep trying and improving)
It sounds a bit... thinnner? than the old mic. Like there's less on the low end...
I have tried a lot. No clue how to get that aspect better.
manufacturing tolerance?
Good video !
You need to give us the answers to your questions
Does it sound to anyone else like he says, "I'm Oskar from Dave Hunter"?
geez i cant figure it out
We need to start a gofundme to get oskar a high quality 3d printer like the ones shapeways uses :)
Thank you for that suggestion. Of course your generous donation of such printer to me would be highly appreciated. But could that donation also include the funding of an underpayed unskilled worker who operates the machine, takes care of cleaning the 3D-printed part and handles all the maintenance issues? (See also oskarvandeventer.nl/FAQ.html.) :-) :-)
🎵star gears, wear made to turr-er-er-ern🎵
Wait why was this just announced when it's a few months old
few months old? are you living in the future?
Oskar privatizes these videos until their release date. They're often viewable on his shapeways site before they're public on youtube.
they are different sizes.
Eddie Stauber it's twisting around the pen differently
why this video isn't 50 fps?
Why should it?
Don’t you mean an oval
Here is my answer to the question: They all equal 7.
your neck seems more elongated in this video...
ZEKLUSE What an odd remark!
ZEKLUSE lol
Sweetbutterflykripperino i dont think you understand my profile pic...
gear gears...
Es genial lo amo¡
Thank you!
Wat
kirby ❤️
Whitchcraft!
early?!