I have heard that it is good practice to always chose the number of teeth of two gears to be relatively prime. This is because there can be impurities in the metal, and if you have a small part of a tooth that is harder than the rest it will erode the opposing gear (there is always some friction going on). By choosing the number of teeth to be relatively prime, the wear and tear is distributed uniformly on the gears, and thus they last longer.
This is an absolutely phenomenal 'explorable explanation'. It methodically layers concepts to foster understanding, deploys interactivity to build intuition, and on top of all that provides crisp, clear narrative on top of all of the amazing visualizations.
If someone ever makes the creation process for this type of visualization accessible to the average university professor, it could blow the lid of the digital textbook market. Most digital textbooks I've seen are basically just putting the text and images on a web page, and maybe integrating multiple choice quizzes. That's seriously under-utilizing the medium. They need to be <i>interactive</i>, and encourage the student to ask questions and run mini experiments.<p>I'm aware this would be extremely difficult; maybe impossible.
I really like this presentation! It’s wonderful.<p>I don’t mean to hijack but I thought this would be an appropriate place to share a photo album of the 3D printed planetary gears in my open source robot:
<a href="https://imgur.com/gallery/GqXD2Zj" rel="nofollow">https://imgur.com/gallery/GqXD2Zj</a><p>I’ve been 3D printing gears for some years now and I want to spread the word that 3D printed gears actually work really well! The gears in the image album above have been operating on that robot for over a year now and they’re showing no real signs of wear.<p>It can be really fun to get a 3D printer and design a little gear assembly. Once you’re comfortable with gears you can use cheap motors to make something that moves. Find a way to drive it with Python from a raspberry pi and you’re on your way to making a robot. :)
The most important section is on involute curves. It's the curve formed by unwinding a string against the circle:<p><a href="https://ciechanow.ski/gears/#strings-attached" rel="nofollow">https://ciechanow.ski/gears/#strings-attached</a><p>It creates a constant angular velocity ratio at all points where the gears mesh (the law of gears).<p>In layman's terms, the tip of the tooth gets thinner so that the angular velocity there is reduced at that larger radius. Otherwise the gears advance/retreat as they rotate, which creates vibration.<p>I think there might be a whole host of curves that work for this, the other main one being a cycloid, which I'm not really familiar with:<p><a href="https://en.wikipedia.org/wiki/Cycloid_gear" rel="nofollow">https://en.wikipedia.org/wiki/Cycloid_gear</a><p>I first learned about involute curves from a cousin that works as a machinist. Mr. Wizard also blew my young mind with noncircular wheels:<p><a href="https://www.youtube.com/watch?v=lg4_Kf9B0MI" rel="nofollow">https://www.youtube.com/watch?v=lg4_Kf9B0MI</a><p>Edit: stumbled onto this technique to make involute gears in CAD:<p><a href="https://www.fictiv.com/blog/posts/creating-involute-gears-in-cad" rel="nofollow">https://www.fictiv.com/blog/posts/creating-involute-gears-in...</a><p>If someone has a simpler method, I'd love to see it.
Wow this is great OP! If you like this check out <a href="http://507movements.com/" rel="nofollow">http://507movements.com/</a> - an animated webpage of 507 mechanical movements with descriptions from a classic book.
Nicely done. Reminds me of <a href="https://geargenerator.com/" rel="nofollow">https://geargenerator.com/</a> which I used to build gear systems for fun.
I didn't know anything about gears until someone filed an issue to tell me that a graphic on the Caddy homepage was wrong: <a href="https://github.com/caddyserver/caddy/issues/2949" rel="nofollow">https://github.com/caddyserver/caddy/issues/2949</a><p>Wish I saw this earlier!
For me, nothing beats the mechanical calculator used to calculate torpedo firing solutions in WWII. It was a sophisticated differential equation solver that kept a real-time updated firing solution using ... gears.<p>There's a whole maintenance and operations manual beautifully scanned here[1]. I've wanted to build one forever, but lack the time and expertise.<p>1. <a href="https://maritime.org/tech/tdc.htm" rel="nofollow">https://maritime.org/tech/tdc.htm</a>
In college, one of my lab courses required us to learn manufacturing techniques. We covered a wide range of methods for machining and shaping things, all out of metal.<p>Making gears was interesting, we had to first turn a rough blank of metal on a lathe to make a steel gear blank (about 12cm in diameter and 2cm thick) then drill out the center and broach a keyway for the axle that would go through the gear. This was all pretty straightforward, but the final piece of work was more difficult, it was cutting the teeth of the gear. The teeth of a properly made gear require complex shapes.<p>There are, as I recall, two ways to cut the teeth. Hobbing uses a helical cutting head turning on an axis that is roughly perpendicular to the axis of the gear. The cutting head and gear turn at the same time in a synchronized manner and the teeth are eventually cut out by the cutting head. See [1] for a video of a large complex gear being made this way.<p>The other method, broaching, uses a straight bar of tool steel that has thick straight across cutting teeth. The bar is pushed past the disk shaped gear blank. The cutting bar moves in a straight line parallel to the axis of the gear blank. Repeated passes over the gear blank cuts out the spaces between the gears teeth.<p>Master machinists taught us how to make these kinds of projects. They would produce a finished gear in about 15 minutes of instruction; then we would have something like two weeks to make the gear. They made everything look easy; it definitely wasn’t easy for me.<p>[1] <a href="https://www.youtube.com/watch?v=0rnTh6c19HM&feature=share" rel="nofollow">https://www.youtube.com/watch?v=0rnTh6c19HM&feature=share</a>
I'm going to add very little to this discussion, but it's the second article from this blog I've seen here, and - like the other one, about the Earth and the Sun - it's absolutely amazing. This is some of the finest work in "explorable explanations". I'm going to save the copy of both just to be sure to show them to my kid in a couple of years; this beats any educational material on the topic I've been exposed to before.
This was simply wonderful, and hidden at the bottom was a link to an insect named "Issus coleoptratus"[1] which evolved something like a biological gear for synchronizing its legs.<p>As an almost complete aside, in Terry Pratchett's "Last Continent" there is a God of Evolution that comments on how difficult it is design a biological wheel.<p>“It’s very hard to design an organic wheel, you know,” said the god reproachfully. “They’re little masterpieces.”<p>“You don’t think just, you know, moving the legs about would be simpler?”<p>“Oh, we’d never get anywhere if I just copied earlier ideas,” said the god. “Diversify and fill all niches, that’s the ticket.”<p>“But is lying on your side in a mud hole with your wheels spinning a very important niche?” said Ponder.<p>[1] <a href="https://en.wikipedia.org/wiki/Issus_coleoptratus" rel="nofollow">https://en.wikipedia.org/wiki/Issus_coleoptratus</a>
You may find yourself wondering: what would happen if the gears are not circular?<p>The answer is then they can implement a wide range of mathematical functions like reciprocal, tangent, square etc. and you will get a kick out watching an hour long video about a mechanical "computer" with cams building up differential calculations:
<a href="https://www.youtube.com/watch?v=s1i-dnAH9Y4" rel="nofollow">https://www.youtube.com/watch?v=s1i-dnAH9Y4</a><p>Enjoy!
A very cool style gear is a harmonic drive. It has a somewhat flexible inner gear driven by a cam which engages it to the outer gear. It allows for extreme gear ratios with high torque in very small packages (think helicopter pitch control).<p><a href="https://en.wikipedia.org/wiki/Harmonic_drive" rel="nofollow">https://en.wikipedia.org/wiki/Harmonic_drive</a>
Really great interactivity and visualizations on this blog. Check out the other posts too: <a href="https://ciechanow.ski/archives/" rel="nofollow">https://ciechanow.ski/archives/</a>
Cool, really cool. I really wish I could've seen that as a kid. Not asking, but logical next step is to go 3-D with straight-cut gears & helical-cut &c &c.<p>Anyone else play Gizmos & Gadgets as a kid? I can't help but flash back; I feel like that's how I learned "gearing" (and magnets, and maybe more..).
Slightly off topic but it has long bothered me that racing simulations let you pick arbitrary gear ratios in the tranissions and differentials. Real life has two restrictions, you can't have half teeth, and you can't have huge teeth count. A 3.00 ratio sure, 12:36 but a 3.01? No car differential can fit a 100:301 ratio gearset and 10:30.1 just won't turn past the broken tooth.
There should be some tool to make such nice animations easily. Not just gears, but any other illustrations with moving parts with the ability to have a zoomed in detail beside the animation, etc.
Well illustrated and explained.<p>For some interesting, less conventional gears that surprisingly still function, checkout out <i>How To Make Organically-Shaped Gears</i>:<p><a href="https://www.youtube.com/watch?v=3LdlSAN1yks" rel="nofollow">https://www.youtube.com/watch?v=3LdlSAN1yks</a>
I have a dumb question about this. Under the header 'Torque', where the wrench is introduced the first time, the length of vector F is non-linear with the position of the slider; in other words, the curve you see (that of the length of F) is not straight. Why is that? Torque is distance times force, where is the non-linear component? The article goes on to talk about the angle of the force, but that isn't relevant in that graph yet, is it? (meaning, that graphic seems to suggest we're talking only about a force perpendicular to the wrench?)
I am learning about car mechanics as a hobby. How a car works is a nice learning site. [1]<p>Just learned about starter motors today. I didn't know it has gears too, in particular the planetary gear system, which is not mentioned in this tutorial. (I quickly skimmed through)<p>[1] <a href="https://www.youtube.com/watch?v=VRe_hKxzKUg&t=1094s" rel="nofollow">https://www.youtube.com/watch?v=VRe_hKxzKUg&t=1094s</a>
<a href="https://www.howacarworks.com/" rel="nofollow">https://www.howacarworks.com/</a>
If you're interested in the machining/making of gears there's a youtube channel where a person makes clocks and other timekeeping devices (some of ancient designs). It's fascinating to watch, and makes me want to get a metal lathe/mill someday.<p><a href="https://www.youtube.com/channel/UCworsKCR-Sx6R6-BnIjS2MA" rel="nofollow">https://www.youtube.com/channel/UCworsKCR-Sx6R6-BnIjS2MA</a>
This is a great learning resource. I just found tec-science the other day and I agree with the author that it is worth to take a look, as they have some excellent visualisations.
<a href="https://www.tec-science.com/mechanical-power-transmission/gear-types/cylindrical-gears/" rel="nofollow">https://www.tec-science.com/mechanical-power-transmission/ge...</a>
This is wonderful and I can't wait to go through his other articles.<p>It reminded me a lot of: <a href="https://acko.net/blog/animate-your-way-to-glory/" rel="nofollow">https://acko.net/blog/animate-your-way-to-glory/</a>
Nicely done! It kind of reminds me of this old video: How Differential Steering Works (1937)<p><a href="https://www.youtube.com/watch?v=yYAw79386WI&t=209" rel="nofollow">https://www.youtube.com/watch?v=yYAw79386WI&t=209</a>
This may be a stupid question, but it is something I always wondered.<p>Torque is effective due to the mass of the lever having a force applied to it, right? Is the length of the lever being used as a stand-in for the mass being affected (a longer lever would necessarily have more mass)? If the lever had no mass, would there be no torque? If the lever did not have a uniform mass distribution, would the difference in applied torque differ based on where on the lever you applied the force (is the derivative of torque with respect to mass not constant for a non-uniform mass distribution)?
Seymour Papert writes in the introduction Mindstorms about he was fascinated by gears as a child and spent much time playing with them, and what he learnt through play provided a valuable intellectual foundation for learning many elementary and advanced ideas in mathematics.<p><a href="http://www.papert.org/articles/GearsOfMyChildhood.html" rel="nofollow">http://www.papert.org/articles/GearsOfMyChildhood.html</a>
I am super impressed by the smooth animation and the graphic design of the elements.<p>I wish this were all open source so I could just copy it in to a project I’m in the middle of.<p>Very inspiring.
That gif at the top reminds me of an IQ test I took in 6th grade. There was an entire section where they would show you a sequence of gears and tell you what direction one of them was spinning. Then they would ask you what direction some other gear was spinning.<p>They all looked like that first gif (but not animated of course).
Maybe I’m misremembering but isn’t torque usually expressed as a cross product of force and radius?<p>(Making pound-feet the pedantic but correct phrasing of the colloquial “foot-pounds”)<p>That way the torque vector points in the direction that a screw would move if you turned it in the direction it’s being forced.
This is Also a very helpful GIF how a gearbox in a car works<p><a href="https://mobile.twitter.com/moo9000/status/1210190630040821760" rel="nofollow">https://mobile.twitter.com/moo9000/status/121019063004082176...</a>
This is great! The visual representation of rotation speed at each point makes a confusing subject much clearer. Is anyone familiar with the gear wars? I know it wasn't all about the gears, but I would love to get more insight into it
A fun one to watch afterwards:
<a href="https://www.youtube.com/watch?v=5q-BH-tvxEg&feature=emb_title" rel="nofollow">https://www.youtube.com/watch?v=5q-BH-tvxEg&feature=emb_titl...</a>
I would need additional proof that gears were designed with many of these mathematical considerations in mind and didn't just arise out of trial and error by the machinists
Wow!. I always blank out when my MEs talk to me about Gear ratios and TOrque when designing Electro mechanical systems. This is really helpful. Thanks for making this.
This is a really awesome article and brought me back to intro physics class, saving it and will return to it in the evening so I can fully digest :) Thanks!
Very nice!<p>These animations are running in a <canvas>.<p>Any idea what the author used? Is everything produced with math (eg: a gear solver, etc)?
> The considerations behind real world gears are much more complicated than what I’ve presented<p>Nah... Nah I would say you pretty much nailed it in this blog post! Incredible. HN Gold right here.
The illustrations are what draws attention and they are very nice and informative.<p>In context of parallel HN discussion¹ on merits of animated SVG, I consider it a loss for open standards that these animations are not made in SVG. If you try to inspect this page, the design and animation is hidden behind canvas and some (nicely written BTW) imperative javascript. It is hard to replicate, and hard to compose with other elements. The illustrations are completely white when disabling JS, which is less than ideal graceful degradation. Some people would argue that executing custom scripts should not be required to show animated graphics, even if it includes basic interactivity.<p>For comparison, visit this page² and try to 'inspect' animated graphics. Observe the SVG element in DOM and see how it changes when you scroll. Just by spending few minutes exploring you could probably recreate them, or at least reuse them somewhere else. We still don't see what's driving the animation (also JS), so that could still be improved using SMIL, but there is obvious benefit for using SVG here.<p>Don't take me wrong, it is really a nice article with very pleasant and clear animations. I'm merely speaking from perspective of open standards, and technology stack that provides good foundation for building complex illustrations. The author is not to blame here, as we lack decent tools for declarative graphics/animations.<p>¹ <a href="https://news.ycombinator.com/item?id=22297461" rel="nofollow">https://news.ycombinator.com/item?id=22297461</a>
² <a href="https://www.opencrux.com/" rel="nofollow">https://www.opencrux.com/</a>
The diversity of topics, hand-crafted graphics, and quality of explanation on all the posts on this blog remind me a lot of Andrew Glassner's columns from IEEE CG&A. Really delightful work (in both cases).
This is awesome. I wonder if the author could be convinced to participate in a similar discourse on the subject of gears, as they relate to audio synthesisers?<p>Pretty much all the modern synths these days have infinitely lubricated gears and pulleys in them, pushing those speaker cones/amp inputs ..
While I appreciate the beauty this piece, I can't help but think of the irony of such a complicated piece to explain something which mechanics and engineers, who actually use gears, understand completely intuitively.
<i>sigh</i><p>If I don't post it someone else will. Here's the spinning levers video you've all already seen a million times:<p><a href="https://www.youtube.com/watch?v=JOLtS4VUcvQ" rel="nofollow">https://www.youtube.com/watch?v=JOLtS4VUcvQ</a>