19 ms·

Gears

• boynoob 7y ago
  Hi guy so thx
• bcheung 7y ago
  If only textbooks could be this good.
  • julienchastang 7y ago
    Exactly. Or put another way, why is there not more pedagogic material like this on the web? We have Jupyter notebooks in many different academic subjects but so many of them are half-baked. This website serves as an example of how good web-based teaching material can truly be.
    • sbarre 7y ago
      Lack of incentive to create it?
    • gugagore 7y ago
      I think we'll get there. Part of the problem has been ensuring that the content keeps working. There has been so much educational content produced on Flash, Java Applets, and other platforms that currently have no support. But the "modern web" (HTML5 and javascript) seem likely to last a long time and be supported on many, many platforms. So now we need better authoring tools, because as another comment suggests, not everyone is up for writing 4K lines of code.
      • kragen 7y ago
        That's what I thought, but now more and more features are being disabled either entirely (as with the SQLite interface in WebKit) or for unencrypted sites, which — correct me if I'm wrong here — includes web pages you've archived on your local filesystem. Maybe <canvas> will survive that, despite its use in browser fingerprinting, but camera access and appcache are already nuked, and the only interface that let you do custom realtime DSP on audio streams from an unencrypted origin is deprecated.
• whalesalad 7y ago
  These interactive animations are so well done.
• subinsebastien 7y ago
  Nicely done. Reminds me of https://geargenerator.com/ https://geargenerator.com/ which I used to build gear systems for fun.
  • ohazi 7y ago
    Also Matthias Wandel's gear generator https://woodgears.ca/gear_cutting/index.html https://woodgears.ca/gear_cutting/index.html
• tartoran 7y ago
  This is very well done. Interactive textbooks should look like this.
• TeMPOraL 7y ago
  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.
  • chubot 7y ago
    It is indeed great, and probably one reason you don't see it more is that it's a ton of work! That's 5K lines of hand-written code! (view source and it's at the end of the page) $ wc -l gears.js base.js 4135 gears.js 904 base.js 5039 total I've wanted to make visualizations like this for my blog. Writing a blog post takes me around 10 hours, which is a fair amount of effort. I believe that the visualizations will take more time than writing in general -- i.e. it would be more like 20 hours, bringing the total to 30. If you consider that it's 4K lines of code (assuming the base library is reused), it's very easy to see that it could take 20+ hours. Probably more like 40-80 to be honest. I guess there is that other thread that says people only write 10 lines of code a day, which would make it 400 hours ;) I don't think that applies here but it could be closer to 400 than 10 or 20. ---- I also wonder if you can save time by using a less "hand-written" style (e.g. d3.js, which seems to be on everyone's wishlist to learn). My inclination is also to go "hand-written" rather than using a bunch of JS libraries. I think you get a better result that way. It's interesting to see that I'm not totally wrong -- the thing everyone praises ends up being very hand-written. And it's smooth and fast, etc. ---- another edit: I also believe one reason that this visualization is good is because there's no build process in the JS. The author clearly just edits the code and refreshes the browser. You need that kind of fast edit-view loop to make good visualizations. IOW, consider using plain JS for blog posts. They are documents and not apps.
    • amitp 7y ago
      Having been down this road, yes, it does take time, but you can save some time by using SVG and some DOM library. Although canvas is faster, most diagrams don't really need it, so I use SVG unless I really need to switch to canvas. SVG also adjusts for screen dpi automatically. The things I like: 1. Reactivity (ObservableHQ, Vue.js, hyperactiv.js, etc.). There's usually some underlying data and then a corresponding visualization. These reactive systems let you modify the underlying data and then the visualization updates automatically. You don't have to figure out which diagrams to update when. Even easier: just redraw everything every time you change anything. 2. Some easier way to write the DOM (d3.js, jsx, vue, lit-html, etc.). Since I'm writing a blog post with html, I usually prefer writing my js-in-html (vue) rather than html-in-js (jsx) but try both directions and see which you prefer. 3. No build step. This is especially important when I want to update a page years later and don't want to figure out which build tools I was using in 1997 or 2007 or 2017. I want my pages to last for decades, and I still update my pages from 25 years ago. I tried recreating one of the gear page diagrams in ObservableHQ https://observablehq.com/@redblobgames/unwind-circle-example https://observablehq.com/@redblobgames/unwind-circle-example . It's not a lot of code. There's a slider, there's a loop to generate the lines, and there's the output svg. Whenever you move the slider it recalculates the output. I admit that I'm not using ObservableHQ much for my own projects because I want more of a "hand-written" style. I used d3.js for my older pages and vue.js for my newer pages. Vue's reactivity and templates save me probably a factor of 2 or 3 over d3.js.
• n3uromancer 7y ago
  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. https://www.tec-science.com/mechanical-power-transmission/gear-types/cylindrical-gears/ https://www.tec-science.com/mechanical-power-transmission/ge...
• ultrasounder 7y ago
  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.
• jmiskovic 7y ago
  The illustrations are what draws attention and they are very nice and informative. 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. 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. 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. ¹ https://news.ycombinator.com/item?id=22297461 https://news.ycombinator.com/item?id=22297461 ² https://www.opencrux.com/ https://www.opencrux.com/
  • dekhn 7y ago
    It's really funny you mentioned the other discussion because that's what I immediately thought when I looked at this page: that's a great use of SVG animations. It's why I made this comment in response to a UX designer (many people on the thread seem to think that SVG animations are mainly for animating UX components): "There are whole worlds of use-cases outside the very restricted design paradigm you're describing."
  • nerdkid93 7y ago
    I personally disagree with people who disable JS and expect the web to continue working as expected, but one of the other downsides of using Canvas for such animations is that there is no good way of exposing that animation to screen readers. Some projects get around this by having an accessibility layer in DOM that overlays the Canvas which renders the actual animations (e.g. https://proxx.app/ https://proxx.app/), but I imagine that a11y animated SVGs would be a better approach here (if they were easier to create).
• amitp 7y ago
  Really great interactivity and visualizations on this blog. Check out the other posts too: https://ciechanow.ski/archives/ https://ciechanow.ski/archives/
• visitect 7y ago
  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).
• 9214 7y ago
  Seymour Papert's childhood (cf. "Mindstorms" [1] introduction) obsession with gears sprung to mind. [1] http://worrydream.com/refs/Papert%20-%20Mindstorms%201st%20ed.pdf http://worrydream.com/refs/Papert%20-%20Mindstorms%201st%20e...
• nimish 7y ago
  > Almost by definition, the second hand of a clock rotates at 1 rpm Minute hand, surely ;)
  • cbsks 7y ago
    The minute hand rotates at 1 revolution per hour ;)
  • jentulman 7y ago
    The minute hand would be one revolution an hour.
    • nimish 7y ago
      Hoist by my own petard!
  • function_seven 7y ago
    Second hand: 1RPM Minute hand: 1RPH Hour hand: 2RPD
    • Sohcahtoa82 7y ago
      > Hour hand: 2RPD Joke's on you, I have a 24 hour clock! https://www.amazon.com/GreatGadgets-1858-24-Hour-Clock/dp/B01N91DQ7G https://www.amazon.com/GreatGadgets-1858-24-Hour-Clock/dp/B0...
• dmortin 7y ago
  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.
  • mottosso 7y ago
    You're in luck, such a tool exists! It's HTML and JavaScript. :)
    • lsorber 7y ago
      I think you missed the 'easily'.
• dsalzman 7y ago
  Wow this is great OP! If you like this check out http://507movements.com/ http://507movements.com/ - an animated webpage of 507 mechanical movements with descriptions from a classic book.
  • defulmere 7y ago
    Came here to post that link :)
  • Rapzid 7y ago
    I'm sad to say it took so long to occur to me, but I believe 507 was what introduced me to the concept that it's levers all the way down.
• dsfyu404ed 7y ago
  sigh If I don't post it someone else will. Here's the spinning levers video you've all already seen a million times: https://www.youtube.com/watch?v=JOLtS4VUcvQ https://www.youtube.com/watch?v=JOLtS4VUcvQ
  • userbinator 7y ago
    It's been posted on HN a few times too, although without much discussion.
• pmilla1606 7y ago
  This is wonderful and I can't wait to go through his other articles. It reminded me a lot of: https://acko.net/blog/animate-your-way-to-glory/ https://acko.net/blog/animate-your-way-to-glory/
• microcolonel 7y ago
  For the author: adding support for touch events, or using normal HTML sliders would be helpful.
  • Drdrdrq 7y ago
    Curious: does something not work for you? If so, what platform are you using? Asking because it works perfectly for me on mobile...
    • microcolonel 7y ago
      I was on a Chromebook with a touchscreen. Maybe you do "platform detection" and don't register touch handlers on laptops. I haven't looked at your code (I didn't see a repository link and I didn't bother looking further). Cheers on the cool demos, I think it could be the start of a great resource for elementary school teachers introducing machines. I know this sort of thing would have been great when I was in grade 3.
      • Drdrdrq 7y ago
        Sorry, I didn't mean to imply I was the author - I was just curious what failed. Thank you for the explanation! I agree that OP made cool demos. :)
• andonisus 7y ago
  This may be a stupid question, but it is something I always wondered. 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)?
  • fsh 7y ago
    No, the mass of the object that has a force applied to it has absolutely nothing to do with the torque. Here is how Wikipedia defines the torque caused by a force acting on an object with a rotation axis: Torque is the product of the magnitude of the force and the perpendicular distance of the line of action of force from the axis of rotation.
    • andonisus 7y ago
      So the force generated by the torque is completely unaffected by the mass of the lever? Then, why does applying the force on a longer portion of the lever create more torque? I had thought it was because there is more mass acting on the point of rotation (longer lever = more mass).
      • buckminster 7y ago
        It's the distance that matters. If you push a car it will speed up. If you push it twice as far it will speed up more. If you apply the same force using a longer lever then the end of the lever moves further (it follows a bigger circle) so you are applying the same force over a bigger distance.
      • kragen 7y ago
        > So the force generated by the torque is completely unaffected by the mass of the lever? Yes, that's right. > Then, why does applying the force on a longer portion of the lever create more torque? Most of the answers to this question reduce, upon examination, to "that's how we define torque". We define the torque of 100 newtons at a lever distance of one meter as the product of 100 newtons and a meter, which we can call 100 newton-meters, which is equal to 1000 newtons at a lever distance of 0.1 meters. But that doesn't really answer the question, which becomes, why is torque defined in this way an interesting thing to think about? And the answer is that if the lever is a rigid body free to rotate around a fulcrum, then 100 newtons at one meter in one direction will make it start to rotate, while 1000 newtons at 0.1 meters in the opposite direction will precisely cancel that "moment", as we call it, and there will be no tendency to start rotating. It's about what forces are needed to cancel each other. Well, but, why should that be? Why does it take exactly 1000 newtons and not, say, 316.2 newtons? And I don't think I have a really good answer for that question. In the case of an elastic solid body it falls out of Hooke's law and the geometry of the situation, which you can reduce to two long, skinny triangles sharing a common side bisected by the fulcrum. But it seems to be much more general than that. > I had thought it was because there is more mass acting on the point of rotation (longer lever = more mass). Nope. You can try using a pair of scissors or a folding ladder as a lever, or pull in different directions on the end of a fixed-geometry lever. The lever's mass doesn't change, but the leverage certainly does.
• deleted 7y ago
  [deleted]
• omgneering 7y ago
  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
• milansuk 7y ago
  Nicely done! It kind of reminds me of this old video: How Differential Steering Works (1937) https://www.youtube.com/watch?v=yYAw79386WI&t=209 https://www.youtube.com/watch?v=yYAw79386WI&t=209
  • joaomacp 7y ago
    I love this video. It's such a great visualization, simple and clear, and gets the point across while being entertaining. And it's from 1937! We have so many video editing and effects tools today, but sometimes simpler is best.
• cpdean 7y ago
  i'm so happy for the global pause button in this article
• ftio 7y ago
  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.
  • jakub_g 7y ago
    If you enjoyed the article, check out others by the same author which are done in a similar way. For example https://ciechanow.ski/color-spaces/ https://ciechanow.ski/color-spaces/ and https://ciechanow.ski/earth-and-sun/ https://ciechanow.ski/earth-and-sun/
    • RickS 7y ago
      The interactivity also reminded me of this post from Bret Victor: http://worrydream.com/LadderOfAbstraction/ http://worrydream.com/LadderOfAbstraction/
    • lobo_tuerto 7y ago
      Or have a look at all his interesting articles here: https://ciechanow.ski/archives/ https://ciechanow.ski/archives/
      • Bendingo 7y ago
        Excellent - thx !
  • pier25 7y ago
    Yeah this is amazing. Interactive learning can be super powerful for a number of topics.
  • joshdance 7y ago
    Is there a widely known name for these types of 'explorable explanations'?
    • 7y ago
• holler 7y ago
  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!
• globular-toast 7y ago
  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.
  • anamexis 7y ago
    Why is it ironic? The target audience clearly is not mechanics and engineers who actually use gears.
  • learn_more 7y ago
    I had the same feeling, hoping to receive an epiphany, perhaps on the bevel of the gear teeth, but nope. Then I thought, ok, surely there's an insight to be gained regarding helical gears, but it was never discussed. https://en.wikipedia.org/wiki/Gear#Helical https://en.wikipedia.org/wiki/Gear#Helical
  • thrower123 7y ago
    I'm not sure this is intuitive for many mechanics. I can remember studying for the ASVABs in high school (it has, or at least it did, have a whole section on spatial orientation and gears and pulleys), and it was pretty common for people to be flummoxed by the questions about picking which direction a gear in a set would turn when another was rotated. And this was with a set of people that tended to tinker on cars and snowmobiles all the time for fun.
• IshKebab 7y ago
  Must have been an insane amount of work to put this together - well done!
• warpech 7y ago
  Bravo for the author for such a captivating interactive blog post. Works great on mobile!
• kjhughes 7y ago
  Well illustrated and explained. For some interesting, less conventional gears that surprisingly still function, checkout out How To Make Organically-Shaped Gears: https://www.youtube.com/watch?v=3LdlSAN1yks https://www.youtube.com/watch?v=3LdlSAN1yks
• drcongo 7y ago
  This is incredible, and apparently every other post on that site is too.
• codewritinfool 7y ago
  Incredible. Thanks for posting this.
• whiddershins 7y ago
  I am super impressed by the smooth animation and the graphic design of the elements. I wish this were all open source so I could just copy it in to a project I’m in the middle of. Very inspiring.
  • dmix 7y ago
    There are 30(!) different animations on this one blog post alone. The work he put into this is admirable. A great education tool.
• NegativeLatency 7y ago
  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. https://www.youtube.com/channel/UCworsKCR-Sx6R6-BnIjS2MA https://www.youtube.com/channel/UCworsKCR-Sx6R6-BnIjS2MA
  • falcolas 7y ago
    Clickspring's work on the Antikithra mechanism (and the Pateron exclusive Byzantine Sundial) is particularly interesting, because not all of the movements created by gears are circular or even. The input can be purely rotational, but the output is not. For example on the Antikithra mechanism, it has to account for the procession of the moon's orbit which causes an uneven time to complete one orbit. To properly simulate this, a pin-and-slot system is combined with an offset pivot to turn the rotation of gears into a movement that lags behind and then speeds ahead, mirroring the actual orbital period. I worded that poorly; the video does a better job of explaining it (within the first minute), and the rest of the video shows the gear train coming together https://youtu.be/v19cu2hj2Ms https://youtu.be/v19cu2hj2Ms
• mholt 7y ago
  I didn't know anything about gears until someone filed an issue to tell me that a graphic on the Caddy homepage was wrong: https://github.com/caddyserver/caddy/issues/2949 https://github.com/caddyserver/caddy/issues/2949 Wish I saw this earlier!
  • jcl 7y ago
    It's funny how often that happens. A favorite example: https://en.wikipedia.org/wiki/Two_pounds_(British_coin)#Design https://en.wikipedia.org/wiki/Two_pounds_(British_coin)#Desi...
    • nitrogen 7y ago
      In case anyone else couldn't tell from the image and didn't want to read all of the history: > An oddity of the design is that it depicts nineteen interlocking gears. Because there is an odd number of them, the mechanism could not actually turn.
      • rezgi 7y ago
        That's not the case for the two pounds though. In the coin's situation, it's because the three gears at the top are interlocked and jammed.
• fit2rule 7y ago
  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? Pretty much all the modern synths these days have infinitely lubricated gears and pulleys in them, pushing those speaker cones/amp inputs ..
• jvanderbot 7y ago
  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. 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. 1. https://maritime.org/tech/tdc.htm https://maritime.org/tech/tdc.htm
  • bacon_waffle 7y ago
    I am interested in differential analyzers too, especially after the anecdotes in Richard Hamming's Learning to Learn (aka Hamming on Hamming)[1] about re-purposing "gun directors" to solve engineering problems. Some of the mechanisms involved are really elegant, like the torque amplifier[2] which wasn't invented until the 1920s. A tabletop demo of one is on my to-do list. [1] https://www.youtube.com/playlist?list=PL2FF649D0C4407B30 https://www.youtube.com/playlist?list=PL2FF649D0C4407B30 [2] https://en.wikipedia.org/wiki/Torque_amplifier https://en.wikipedia.org/wiki/Torque_amplifier
  • WalterBright 7y ago
    The same sorts of things were built using analog electronics. And even these have fallen by the wayside to digital electronics.
• otto_ortega 7y ago
  Lovely work, thanks!
• arh68 7y ago
  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. 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..).
  • joshdance 7y ago
    I played Gizoms and Gadgets. Fun game.
• frankus 7y ago
  Maybe I’m misremembering but isn’t torque usually expressed as a cross product of force and radius? (Making pound-feet the pedantic but correct phrasing of the colloquial “foot-pounds”) 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.
  • catblast 7y ago
    That is the correct way to express torque with vectors. The definitions in the blog post are not vectors, they are scalars and the dot is not a dot product, just multiplication. (F_t there is what is commonly notated as F_perpendicular). I agree it is confusing to those of us used to seeing bold letters usually used for vectors (and I would argue that using more conventional notation at even a basic level is better), but it's not wrong.
• TaylorAlexander 7y ago
  I really like this presentation! It’s wonderful. 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: https://imgur.com/gallery/GqXD2Zj https://imgur.com/gallery/GqXD2Zj 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. 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. :)
  • outworlder 7y ago
    Which material are you using the print the gears?
    • TaylorAlexander 7y ago
      PETG. Specifically it would either be Hatchbox PETG or PushPlastic PETG.
      • djmips 7y ago
        Have you considered fibre reinforced plastic? I'm not an expert but I'm curious if that's a good option.
        • TaylorAlexander 7y ago
          I’ve seen fiberglass reinforced nylon gears used with success in commercial injection molded gearboxes. It can definitely help by increasing gear stiffness. However 3D printing with fiberglass causes rapid nozzle wear, and recently people are saying that fiberglass reinforced 3D printing filaments represent a human hazard. Since I’ve managed to get my gears to work without reinforcement, I’ve not tried it. One thing I do with printed gears is make the gear teeth much larger than would be strictly needed in an injection molded solution. This lets me deal with reduced material performance compared to injection molding.
• anigbrowl 7y ago
  The whole blog, really. Someone throw money at this person to write science texts full time.
  • divbzero 7y ago
    Imagine if we could revamp the textbook industry so articles like this have a fighting chance of being included.
• zackmorris 7y ago
  The most important section is on involute curves. It's the curve formed by unwinding a string against the circle: https://ciechanow.ski/gears/#strings-attached https://ciechanow.ski/gears/#strings-attached It creates a constant angular velocity ratio at all points where the gears mesh (the law of gears). 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. 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: https://en.wikipedia.org/wiki/Cycloid_gear https://en.wikipedia.org/wiki/Cycloid_gear I first learned about involute curves from a cousin that works as a machinist. Mr. Wizard also blew my young mind with noncircular wheels: https://www.youtube.com/watch?v=lg4_Kf9B0MI https://www.youtube.com/watch?v=lg4_Kf9B0MI Edit: stumbled onto this technique to make involute gears in CAD: https://www.fictiv.com/blog/posts/creating-involute-gears-in-cad https://www.fictiv.com/blog/posts/creating-involute-gears-in... If someone has a simpler method, I'd love to see it.
  • kragen 7y ago
    Well, I think the parametric formula for the involute of a circle is (1-it) exp(it). If you pop open Python with Numpy you can say t = np.linspace(0, 1); (1 - 1j*t) * np.exp(t * 1j) And that gives you almost a radian of the involute, unless I've screwed something up. You can evaluate that at the desired number of points, clipped to the desired range of radii, export the coordinates to CSV if necessary, and import them into your CAD program as a smooth polyline. For example, with FreeCAD, you can directly script it in Python and https://forum.freecadweb.org/viewtopic.php?t=27866 https://forum.freecadweb.org/viewtopic.php?t=27866 Draft.makeBSpline will apparently do the job. Blender should be similar. To me this sounds simpler.
  • double0jimb0 7y ago
    Geartrax software, it will draw perfect involute splines.
  • deadsy 7y ago
    I wrote a CAD package in Go that has a function for it. https://github.com/deadsy/sdfx https://github.com/deadsy/sdfx func InvoluteGear( numberTeeth int, // number of gear teeth gearModule float64, // pitch circle diameter / number of gear teeth pressureAngle float64, // gear pressure angle (radians) backlash float64, // backlash expressed as per-tooth distance at pitch circumference clearance float64, // additional root clearance ringWidth float64, // width of ring wall (from root circle) facets int, // number of facets for involute flank )
• deleted 7y ago
  [deleted]
• alphaBetaGamma 7y ago
  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.
  • Aperocky 7y ago
    By relatively prime, do you mean the largest denominator == 1? Or in other words, 15 and 22 should be relatively prime?
    • dan-robertson 7y ago
      Yes, relatively prime means coprime means gcd=1
    • graphpapa 7y ago
      This is what is commonly meant by ‘relatively prime’, yes. Also referred to as being coprime. Defn: a & b are coprime/ relatively prime iff GCD(a,b) = 1
  • nbadg 7y ago
    That's also what I was taught as a best practice, but it's not always possible. Otherwise, best practice is to index the gears (ie mark a specific tooth on each). That way, when you disassemble the gearbox (it's bound to happen sometime for maintenance), you can make sure it's reassembled so that the same teeth will continue to mesh, preserving the wear pattern. Otherwise, wear is substantially increased.
    • fermenflo 7y ago
      That's also what I was taught as a best practice, but it's not always possible. Well of course it's possible -there are infinitely many sets of coprime numbers! Silly engineers
• anderspitman 7y ago
  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 interactive, and encourage the student to ask questions and run mini experiments. I'm aware this would be extremely difficult; maybe impossible.
  • pavpanchekha 7y ago
    I'm a professor currently writing an online textbook. I can assure you that writing a textbook, without anything interactive, is extremely challenging. I find it hard to imagine a time when my book will be good enough that adding interactive explorables will be the best educational return on time invested. (Though I'm thinking about it!)
    • anderspitman 7y ago
      I think it definitely is more appropriate in some domains than others. Sometimes you can replace 1000 words with a picture, 100 pictures with a video, and 10 videos with an interactive visualization. In that case, it might not actually be more work. I think the problem is that it's very different work, that professors aren't trained for. Again, it's not easy, maybe impossible. But if it could be done... PS - I see you're at U as well. I work on a datavis team (iobio) in the genetics department (Steph says hi!). If you ever want to meet up I'd be interested in talking more about this.
      • rolandog 7y ago
        Bear in mind that some people are more visual, so I think the interactive visualization should serve as a complement to the 100-1000 words that describe it, not an in-place substitution... (Also, let's not forget about the visually impaired, which need the interface to be accessible).
        • 7y ago
• yread 7y ago
  Nicely made. And as soon as the fan appeared my cpu fan started to spin like crazy. It felt real
  • jansan 7y ago
    Now it needs to be 3D and a smell generator that emits grease odor and you will have a full 5D experience! Digital scent technology: https://en.wikipedia.org/wiki/Digital_scent_technology https://en.wikipedia.org/wiki/Digital_scent_technology
• max_ 7y ago
  How are these animations implimented?
• polishdude20 7y ago
  That diagram with the wrench and force increasing as the radius decreases should be linear.
• zyngaro 7y ago
  Amazing work!
• retrobox 7y ago
  This is beautiful. Great explanations, and a really powerful interactive website. A really impressive and engaging page to pull it all together.
• jedberg 7y ago
  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. They all looked like that first gif (but not animated of course).
• pier25 7y ago
  Very nice! These animations are running in a <canvas>. Any idea what the author used? Is everything produced with math (eg: a gear solver, etc)?
  • divbzero 7y ago
    I was wondering the same! The author appears to be using his own functions written in vanilla JS. The Gears page loads a custom Canvas library base.js [1] plus an page-specific gears.js [2]. iOS graphics appears to be an area of expertise [3] for the author. [1]: https://ciechanow.ski/js/base.js https://ciechanow.ski/js/base.js [2]: https://ciechanow.ski/js/gears.js https://ciechanow.ski/js/gears.js [3]: https://github.com/Ciechan?tab=repositories https://github.com/Ciechan?tab=repositories (P.S. <canvas> is an interesting choice, I had expected <svg> before opening the page inspector. Separately, I love the creative use of TLD in the domain name.)
    • pier25 7y ago
      Thanks for the JS files. Would be nice to know about his process. Here it appears he is importing the graphics from somewhere else converted to imperative drawing code: https://imgur.com/jFpN0f3.jpg https://imgur.com/jFpN0f3.jpg
      • bestest 7y ago
        That's just a function that draws a spanner.
        • pier25 7y ago
          Obviously, but my point is that if you look at the coordinates these do not seem to have been handwritten.
• hkiely 7y ago
  I remember learning gear size ratios in sixth grade math class with special LEGO sets.
• roland35 7y ago
  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). https://en.wikipedia.org/wiki/Harmonic_drive https://en.wikipedia.org/wiki/Harmonic_drive
  • abraae 7y ago
    Very cool! It looks like the output shaft has quite a bit of lateral movement, perhaps something like a Schmidt coupling (https://www.thingiverse.com/thing:233667 https://www.thingiverse.com/thing:233667) could be used to remove that movement and allow a fixed output shaft. I last saw one of these inside an IBM 3890 check reader machine.
• miohtama 7y ago
  This is Also a very helpful GIF how a gearbox in a car works https://mobile.twitter.com/moo9000/status/1210190630040821760 https://mobile.twitter.com/moo9000/status/121019063004082176...
• roel_v 7y ago
  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?)
  • adossi 7y ago
    Loosening a bolt gets easier as you turn the wrench, no? I assumed thats what the diagram was showcasing
    • roel_v 7y ago
      Yes, but my idea was that pushing the wrench at distance x is double as hard as pushing it at distance x * 2; my understanding of the diagram is that it's not.
  • progval 7y ago
    Torque = distance×force, so force = torque/distance, so force is linear in 1/distance.
    • roel_v 7y ago
      Thanks, that makes sense. Once you start thinking about it, it's obvious (e.g. F can never go to 0), turns out I've always had a wrong mental model of how the length of a lever influences the torque (beyond 'longer lever = more torque' of course).
• boznz 7y ago
  Works fine with noscript and ublock active.. wish all sites played this well
• nicpottier 7y ago
  A fun one to watch afterwards: https://www.youtube.com/watch?v=5q-BH-tvxEg&feature=emb_title https://www.youtube.com/watch?v=5q-BH-tvxEg&feature=emb_titl...
• mtreis86 7y ago
  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.
  • SummerlyMars 7y ago
    I'm not a car guy, and I don't know about the differentials, but don't continuously variable transmissions allow for this? I'm guessing they're not in common use on race cars, but in principle, shouldn't they allow for a 3.01 ratio?
    • mtreis86 7y ago
      Yes, a CVT uses a steel belt around two cones, and can have any ratio between them. Most race cars use mechanical transmissions with automatic controls as that's the most robust design. Some stunt vehicles use automatics or CVT as landing with the wheels at different speeds than the vehicle causes a massive shock through the drivetrain. In a manual that shock goes right to the engine, in automatics there is usually some amount of absorption of rotational shocks due to the less rigid coupling. Diffs are almost always a ring and pinion gear.
• salvagedcircuit 7y ago
  This looks pretty fantastic on mobile. Nice and responsive. Great animations. Good job!
• person_of_color 7y ago
  Can you 3d print gears?
  • Ardren 7y ago
    Absolutely, they even work for a while. The Youtube channel "Gear Down for What?" has some pretty cool planetary designs. https://www.youtube.com/c/GearDownForWhat https://www.youtube.com/c/GearDownForWhat
    • person_of_color 7y ago
      Why only for a while?
• salgernon 7y ago
  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. 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. “It’s very hard to design an organic wheel, you know,” said the god reproachfully. “They’re little masterpieces.” “You don’t think just, you know, moving the legs about would be simpler?” “Oh, we’d never get anywhere if I just copied earlier ideas,” said the god. “Diversify and fill all niches, that’s the ticket.” “But is lying on your side in a mud hole with your wheels spinning a very important niche?” said Ponder. [1] https://en.wikipedia.org/wiki/Issus_coleoptratus https://en.wikipedia.org/wiki/Issus_coleoptratus
• tomger 7y ago
  This is a beautiful article.
• known 7y ago
  Cute explanation; Thank you;
• Jahak 7y ago
  This is a beautiful article
• todd8 7y ago
  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. 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. 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. 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. 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. [1] https://www.youtube.com/watch?v=0rnTh6c19HM&feature=share https://www.youtube.com/watch?v=0rnTh6c19HM&feature=share
• smnplk 7y ago
  I am learning about car mechanics as a hobby. How a car works is a nice learning site. [1] 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) [1] https://www.youtube.com/watch?v=VRe_hKxzKUg&t=1094s https://www.youtube.com/watch?v=VRe_hKxzKUg&t=1094s https://www.howacarworks.com/ https://www.howacarworks.com/
• chewyandjedi 7y ago
  https://youtu.be/jMAjWOiqx-g https://youtu.be/jMAjWOiqx-g
• kuu 7y ago
  High quality content. Thanks OP!
• chalst 7y ago
  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. http://www.papert.org/articles/GearsOfMyChildhood.html http://www.papert.org/articles/GearsOfMyChildhood.html
• atregir 7y ago
  Oh my! These animations are sooooooo satisfying to look at!
• rampatra 7y ago
  Great article. How did you make those images with sliders? Any tool or library you used?
• deleted 7y ago
  [deleted]
• arein2 7y ago
  https://youtu.be/Q-XOM4E4RZQ https://youtu.be/Q-XOM4E4RZQ An awesome video on making gears.
• bilekas 7y ago
  > The considerations behind real world gears are much more complicated than what I’ve presented Nah... Nah I would say you pretty much nailed it in this blog post! Incredible. HN Gold right here.
• daralthus 7y ago
  You may find yourself wondering: what would happen if the gears are not circular? 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: https://www.youtube.com/watch?v=s1i-dnAH9Y4 https://www.youtube.com/watch?v=s1i-dnAH9Y4 Enjoy!
• yachtman 7y ago
  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
• nojvek 7y ago
  The writing and interactive examples are really amazing. Would deffo read the entire series of articles. Gonna bookmark it.