These interactive animations are so well done.

I think we&#x27;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 &quot;modern web&quot; (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.

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.

Also Matthias Wandel&#x27;s gear generator<a href="https:&#x2F;&#x2F;woodgears.ca&#x2F;gear_cutting&#x2F;index.html" rel="nofollow">https:&#x2F;&#x2F;woodgears.ca&#x2F;gear_cutting&#x2F;index.html</a>

Nicely done. Reminds me of <a href="https:&#x2F;&#x2F;geargenerator.com&#x2F;" rel="nofollow">https:&#x2F;&#x2F;geargenerator.com&#x2F;</a> which I used to build gear systems for fun.

This is very well done. Interactive textbooks should look like this.

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&#x27;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&#x27;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&#x27;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&#x27;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&#x27;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 <a href="https:&#x2F;&#x2F;observablehq.com&#x2F;@redblobgames&#x2F;unwind-circle-example" rel="nofollow">https:&#x2F;&#x2F;observablehq.com&#x2F;@redblobgames&#x2F;unwind-circle-example</a> . It&#x27;s not a lot of code. There&#x27;s a slider, there&#x27;s a loop to generate the lines, and there&#x27;s the output svg. Whenever you move the slider it recalculates the output.I admit that I&#x27;m not using ObservableHQ much for my own projects because I want more of a &quot;hand-written&quot; style. I used d3.js for my older pages and vue.js for my newer pages. Vue&#x27;s reactivity and templates save me probably a factor of 2 or 3 over d3.js.

Writing a small program takes much less effort per line than writing a large program, especially if it doesn&#x27;t have to be maintainable and extensible, especially by other people. <a href="http:&#x2F;&#x2F;canonical.org&#x2F;~kragen&#x2F;sw&#x2F;dev3&#x2F;circlegrid.html" rel="nofollow">http:&#x2F;&#x2F;canonical.org&#x2F;~kragen&#x2F;sw&#x2F;dev3&#x2F;circlegrid.html</a> only took me three hours of JS hacking, and it&#x27;s like 200 lines of code. The simplified version of the basic COCOMO model in David A. Wheeler&#x27;s &quot;SLOCCount&quot; is Person-Months = 2.4 * (KSLOC1.05), which suggests a budget of 0.44 person-months for this code, about two weeks, which is clearly too high; we&#x27;ve all written and debugged a few hundred lines of code in a day on some occasion after getting out of the larval stage. This probably would have been faster if I hadn&#x27;t been so out of practice with DHTML.Another thing, though, is that some things are easier than other things. Usually in a programming job you have to do the easy things and also the hard things. This brings down the average. If you&#x27;re writing a bunch of blog posts for fun, though, you can just publish the ones where good visualizations came out pretty quickly and discard the others that are much more effort for less return.I feel like visualizations using d3.js are still pretty &quot;hand-written&quot;.

&gt; another edit: I also believe one reason that this visualization is good is because there&#x27;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.You can go a step further and reload code without refreshing the page. This makes it even easier to make the sort of fiddly tweaks that visualizations require while avoid change blindness.<a href="https:&#x2F;&#x2F;roadtolarissa.com&#x2F;hot-reload" rel="nofollow">https:&#x2F;&#x2F;roadtolarissa.com&#x2F;hot-reload</a><a href="https:&#x2F;&#x2F;github.com&#x2F;1wheel&#x2F;hot-server" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;1wheel&#x2F;hot-server</a>

This. The time and effort it takes to put such a visualization together for a target audience that might possibly just gloss over the content is immense. Its like making a multi-million dollar movie about people who have no money just to show thier situation. Instead of giving them the money directly. And on top of that you need all the requirements to actually be able to view it in the latest browser.

It is indeed great, and probably one reason you don&#x27;t see it more is that it&#x27;s a ton of work! That&#x27;s 5K lines of hand-written code! (view source and it&#x27;s at the end of the page)<pre><code> $ wc -l gears.js base.js 
 4135 gears.js
 904 base.js
 5039 total
</code></pre>
I&#x27;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&#x27;s 4K lines of code (assuming the base library is reused), it&#x27;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&#x27;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 &quot;hand-written&quot; style (e.g. d3.js, which seems to be on everyone&#x27;s wishlist to learn).My inclination is also to go &quot;hand-written&quot; rather than using a bunch of JS libraries. I think you get a better result that way. It&#x27;s interesting to see that I&#x27;m not totally wrong -- the thing everyone praises ends up being very hand-written. And it&#x27;s smooth and fast, etc.----another edit: I also believe one reason that this visualization is good is because there&#x27;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.

In addition, his page lead me here <a href="http:&#x2F;&#x2F;archive.is&#x2F;S01gX" rel="nofollow">http:&#x2F;&#x2F;archive.is&#x2F;S01gX</a> 
Start at &quot;The little gears that couldn&#x27;t.&quot; sectionPS: had to archive the link because of SSL errors prevent direct access. my guess - my browser had old number of gears :P

I can&#x27;t quite remember what the software was, but I vaguely recall something in school that we used to explore various topics in physics which used an approach very similar to this. Literate text with interactive diagrams and input variables.It wasn&#x27;t web delivered and was a Windows, perhaps Win 3.1 application. This was in mid 90s

I&#x27;m going to add very little to this discussion, but it&#x27;s the second article from this blog I&#x27;ve seen here, and - like the other one, about the Earth and the Sun - it&#x27;s absolutely amazing. This is some of the finest work in &quot;explorable explanations&quot;. I&#x27;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&#x27;ve been exposed to before.

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:&#x2F;&#x2F;www.tec-science.com&#x2F;mechanical-power-transmission&#x2F;gear-types&#x2F;cylindrical-gears&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.tec-science.com&#x2F;mechanical-power-transmission&#x2F;ge...</a>

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.

It&#x27;s really funny you mentioned the other discussion because that&#x27;s what I immediately thought when I looked at this page: that&#x27;s a great use of SVG animations.It&#x27;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):
&quot;There are whole worlds of use-cases outside the very restricted design paradigm you&#x27;re describing.&quot;

&gt; I personally disagree with people who disable JS and expect the web to continue working as expectedIn a general sense, I agree with you.But pages that are generally static, like a blog or news article, should still work.I think it&#x27;s completely reasonable that the animations in the linked article break with JS disabled. Could they have been done differently and had graceful degradation? Yeah, I suppose. But I think it&#x27;s fine as-is.

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. <a href="https:&#x2F;&#x2F;proxx.app&#x2F;" rel="nofollow">https:&#x2F;&#x2F;proxx.app&#x2F;</a>), but I imagine that a11y animated SVGs would be a better approach here (if they were easier to create).

Can you explain what is it that you win? Because the current state where it takes a talented programmer + mathematician + designer to create this kind of content is loss for everyone.No, SMIL on its own cannot replicate these illustrations. I hope that some future standard for declarative reactive graphics will be able to.

&gt; The author is not to blame here, as we lack decent tools for declarative graphics&#x2F;animations.Please show me the pure SMIL declaration for a pixel-exact replica of the example from the wonderful article: number and size of teeth on a spinning gear scales based on the horizontal position of a draggable slider.On a related note: this wonderful article is an article. The next time an HN article about web complexity triggers another HTML Class of 4.01 Reunion, it would be great if admirers of this article would post the link and force them to reveal the true depths of their asceticism.I think I win either way. If there really is an SMIL solution then then the 4.01 grumps would be forced to backport declarative graphics&#x2F;animation into their nostalgia. If not, then my point stands.

It&#x27;s easy to lose track of in the face of scene graph vector formats like svg but you have to remember canvas + javascript can be thought of as a procedural cad system, that is, the epitome of drawing tools.The svg is a static weak alternative to true procedural generation.For reference the postscript language is the same way. hand written procedural postscript is an amazing drawing tool.

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 &#x27;inspect&#x27; 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&#x27;t see what&#x27;s driving the animation (also JS), so that could still be improved using SMIL, but there is obvious benefit for using SVG here.Don&#x27;t take me wrong, it is really a nice article with very pleasant and clear animations. I&#x27;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&#x2F;animations.¹ <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=22297461" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=22297461</a>
² <a href="https:&#x2F;&#x2F;www.opencrux.com&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.opencrux.com&#x2F;</a>

Really great interactivity and visualizations on this blog. Check out the other posts too: <a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;archives&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;archives&#x2F;</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&#x27;s columns from IEEE CG&amp;A.  Really delightful work (in both cases).

Seymour Papert&#x27;s childhood (cf. &quot;Mindstorms&quot; [1] introduction) obsession with gears sprung to mind.[1] <a href="http:&#x2F;&#x2F;worrydream.com&#x2F;refs&#x2F;Papert%20-%20Mindstorms%201st%20ed.pdf" rel="nofollow">http:&#x2F;&#x2F;worrydream.com&#x2F;refs&#x2F;Papert%20-%20Mindstorms%201st%20e...</a>

The minute hand rotates at 1 revolution per hour ;)

The minute hand would be one revolution an hour.

&gt; Hour hand: 2RPDJoke&#x27;s on you, I have a 24 hour clock!<a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;GreatGadgets-1858-24-Hour-Clock&#x2F;dp&#x2F;B01N91DQ7G" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;GreatGadgets-1858-24-Hour-Clock&#x2F;dp&#x2F;B0...</a>

Second hand: 1RPMMinute hand: 1RPHHour hand: 2RPD

&gt; Almost by definition, the second hand of a clock rotates at 1 rpmMinute hand, surely ;)

I think you missed the &#x27;easily&#x27;.

You&#x27;re in luck, such a tool exists! It&#x27;s HTML and JavaScript. :)

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.

I&#x27;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&#x27;s levers all the way down.

Wow this is great OP! If you like this check out <a href="http:&#x2F;&#x2F;507movements.com&#x2F;" rel="nofollow">http:&#x2F;&#x2F;507movements.com&#x2F;</a> - an animated webpage of 507 mechanical movements with descriptions from a classic book.

It&#x27;s been posted on HN a few times too, although without much discussion.

sighIf I don&#x27;t post it someone else will. Here&#x27;s the spinning levers video you&#x27;ve all already seen a million times:<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=JOLtS4VUcvQ" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=JOLtS4VUcvQ</a>

This is wonderful and I can&#x27;t wait to go through his other articles.It reminded me a lot of: <a href="https:&#x2F;&#x2F;acko.net&#x2F;blog&#x2F;animate-your-way-to-glory&#x2F;" rel="nofollow">https:&#x2F;&#x2F;acko.net&#x2F;blog&#x2F;animate-your-way-to-glory&#x2F;</a>

I was on a Chromebook with a touchscreen. Maybe you do &quot;platform detection&quot; and don&#x27;t register touch handlers on laptops. I haven&#x27;t looked at your code (I didn&#x27;t see a repository link and I didn&#x27;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.

Curious: does something not work for you? If so, what platform are you using? Asking because it works perfectly for me on mobile...

For the author: adding support for touch events, or using normal HTML sliders would be helpful.

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).

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.

I think that the only role the mass of a lever would play in contributing to torque is through inertia.

Nope, the mass of the lever doesn&#x27;t play in to the torque that is applied at all. All that matters is that the force be transmitted via atom-to-atom motion. It&#x27;s the rigidity of the wrench that mediates that, not its mass.Of course, to create rigid objects, practically speaking they need to be made of something that will have mass. So the rigidity and the mass are related in a very loose sense. In any case, from a Newtonian physics perspective, you&#x27;ll see none of those terms in there - neither a &quot;rigidity&quot; nor a mass. The torque is simply the length of the wrench multiplied by the magnitude of the force.In a more detailed analysis, you might consider the flexure of the wrench by analyzing the stress and strain inside the wrench. That would no longer treat the wrench as a perfect idealized body that is completely rigid, but rather a body that can stretch based on the internal compressive or tensile forces that arise inside of it. Sometimes we don&#x27;t think of metals as being stretchy, but with enough force, they&#x27;re not so different from a rubber band.With all that said, once you consider the _dynamics_ of the situation - how the forces applied give rise to motion - then mass does come into play. If you apply torque to a wheel, that will cause an angular acceleration proportional to the mass of the wheel. If you were using a wrench to spin a gear, then the mass of the gear decides how fast it will start to spin. Also, the mass of the wrench matters here, since presumably it will be spinning too: some of your effort has to go into angularly rotating the wrench. So it would have a &quot;parasitic&quot; effect on how fast you could get your gear spinning.

The mass of the lever just adds or subtracts from any other external force(s) applied to the lever - depending on the direction of the external force relative to the direction of gravity.So a heavy wrench is helpful when pushing down, while loosening a rusty nut. But a light carbon fibre wrench would be better when pulling up.How much torque gravity adds or subtracts in that case is also dependent on the distribution of mass along the length of the lever.And to add to the fun, the mass of the leaver does add momentum into the equation, which comes into play as extra work required when changing speed of the rotation (e.g. starting, stopping the turn). And how much momentum also depends on the distribution of mass along the length of the lever.

No, torque has nothing to do with mass. Even making the level &quot;massless&quot; would not change the applied torque one bit.

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)?

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&#x27;t all about the gears, but I would love to get more insight into it

I love this video. It&#x27;s such a great visualization, simple and clear, and gets the point across while being entertaining.And it&#x27;s from 1937! We have so many video editing and effects tools today, but sometimes simpler is best.

Nicely done! It kind of reminds me of this old video: How Differential Steering Works (1937)<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=yYAw79386WI&amp;t=209" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=yYAw79386WI&amp;t=209</a>

i&#x27;m so happy for the global pause button in this article

The interactivity also reminded me of this post from Bret Victor: <a href="http:&#x2F;&#x2F;worrydream.com&#x2F;LadderOfAbstraction&#x2F;" rel="nofollow">http:&#x2F;&#x2F;worrydream.com&#x2F;LadderOfAbstraction&#x2F;</a>

Or have a look at all his interesting articles here: <a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;archives&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;archives&#x2F;</a>

If you enjoyed the article, check out others by the same author which are done in a similar way. For example <a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;color-spaces&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;color-spaces&#x2F;</a> and <a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;earth-and-sun&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;earth-and-sun&#x2F;</a>

Yeah this is amazing. Interactive learning can be super powerful for a number of topics.

Explorable Explanations is the term AFAIK. Nicky Case has a whole page of resources on the topic: <a href="https:&#x2F;&#x2F;explorabl.es&#x2F;" rel="nofollow">https:&#x2F;&#x2F;explorabl.es&#x2F;</a>

Is there a widely known name for these types of &#x27;explorable explanations&#x27;?

What is your point?  Are you saying that it&#x27;s bad he didn&#x27;t tidy up the source?

We are all sitting here in collective awe, and the JS source contains this header:&gt; &#x2F;* Dear explorer, this code works, but is by no means of high quality. Once a post is written I don&#x27;t go back to the source code again and the formatting, robustness, DRYness and abstraction choices reflect that. *&#x2F;<a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;gears.js" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;gears.js</a>

I wish I had sites or visualizations like this when I had to do maths, I mean for example I&#x27;ve had to use sin&#x2F;cos&#x2F;tan in all kinds of calculations without ever being explained what they actually are, and the formulas without being explained what they&#x27;re good for.

I&#x27;m sure a lot of users on HN are angry that this site requires JavaScript and demand it to be accessible on a text based browser.

Drives me crazy that if I suggest diagrams like this might be useful on wikipedia or documentation I mostly get downvoted into oblivion.

This is an absolutely phenomenal &#x27;explorable explanation&#x27;. 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.

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!

Why is it ironic? The target audience clearly is not mechanics and engineers who actually use gears.

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&#x27;s an insight to be gained regarding helical gears, but it was never discussed.<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Gear#Helical" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Gear#Helical</a>

I&#x27;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.

While I appreciate the beauty this piece, I can&#x27;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.

Must have been an insane amount of work to put this together - well done!

Bravo for the author for such a captivating interactive blog post. Works great on mobile!

Well illustrated and explained.For some interesting, less conventional gears that surprisingly still function, checkout out How To Make Organically-Shaped Gears:<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=3LdlSAN1yks" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=3LdlSAN1yks</a>

This is incredible, and apparently every other post on that site is too.

There are 30(!) different animations on this one blog post alone.The work he put into this is admirable. A great education tool.

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.

Clickspring&#x27;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&#x27;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<a href="https:&#x2F;&#x2F;youtu.be&#x2F;v19cu2hj2Ms" rel="nofollow">https:&#x2F;&#x2F;youtu.be&#x2F;v19cu2hj2Ms</a>

If you&#x27;re interested in the machining&#x2F;making of gears there&#x27;s a youtube channel where a person makes clocks and other timekeeping devices (some of ancient designs). It&#x27;s fascinating to watch, and makes me want to get a metal lathe&#x2F;mill someday.<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;channel&#x2F;UCworsKCR-Sx6R6-BnIjS2MA" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;channel&#x2F;UCworsKCR-Sx6R6-BnIjS2MA</a>

In case anyone else couldn&#x27;t tell from the image and didn&#x27;t want to read all of the history:&gt; 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.

It&#x27;s funny how often that happens. A favorite example: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Two_pounds_(British_coin)#Design" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Two_pounds_(British_coin)#Desi...</a>

I didn&#x27;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:&#x2F;&#x2F;github.com&#x2F;caddyserver&#x2F;caddy&#x2F;issues&#x2F;2949" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;caddyserver&#x2F;caddy&#x2F;issues&#x2F;2949</a>Wish I saw this earlier!

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&#x2F;amp inputs ..

I am interested in differential analyzers too, especially after the anecdotes in Richard Hamming&#x27;s Learning to Learn (aka Hamming on Hamming)[1] about re-purposing &quot;gun directors&quot; to solve engineering problems.Some of the mechanisms involved are really elegant, like the torque amplifier[2] which wasn&#x27;t invented until the 1920s. A tabletop demo of one is on my to-do list.[1] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;playlist?list=PL2FF649D0C4407B30" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;playlist?list=PL2FF649D0C4407B30</a>[2] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Torque_amplifier" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Torque_amplifier</a>

The same sorts of things were built using analog electronics.And even these have fallen by the wayside to digital electronics.

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&#x27;s a whole maintenance and operations manual beautifully scanned here[1]. I&#x27;ve wanted to build one forever, but lack the time and expertise.1. <a href="https:&#x2F;&#x2F;maritime.org&#x2F;tech&#x2F;tdc.htm" rel="nofollow">https:&#x2F;&#x2F;maritime.org&#x2F;tech&#x2F;tdc.htm</a>

Cool, really cool. I really wish I could&#x27;ve seen that as a kid. Not asking, but logical next step is to go 3-D with straight-cut gears &amp; helical-cut &amp;c &amp;c.Anyone else play Gizmos &amp; Gadgets as a kid? I can&#x27;t help but flash back; I feel like that&#x27;s how I learned &quot;gearing&quot; (and magnets, and maybe more..).

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&#x27;s not wrong.

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.

PETG. Specifically it would either be Hatchbox PETG or PushPlastic PETG.

Which material are you using the print the gears?

Thank you! It’s certainly an involved project. I recommend starting by building one motor and gearbox assembly and getting control working from python. If you can get that far you can build the rest!And the website you linked looks nice. There is also hackster.io and hackaday.io. While those sites are fine, it becomes one more thing to update. I prefer imgur for simple photo albums as that integrates well with reddit, my primary promotional place. Imgur actually works really well for me there. And then my real build updates are on my YouTube channel. And I have my own website where I try to throw everything.So I end up trying to funnel people to my website and just using whatever media hosting makes sense for that particular media.

That project looks great! I&#x27;m very tempted to start building this because of how good it looks, but I know it would take lots of time and effort, even with the designs already available.As an aside, would something like <a href="https:&#x2F;&#x2F;www.makerfol.io&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.makerfol.io&#x2F;</a> be useful for your build log? I see many people using imgur for this but it&#x27;s always struck me as suboptimal.

Thanks! I’ve used helical gears in some of my projects. i didn’t have a specific rationale for not using them in Rover, except it’s more CAD work in my particular CAD program. But they can be nice! Rovers gears certainly do make some noise.

Hey, nice project :)A few friends were experimenting with 3D-printed gears for their robots, I&#x27;ve advised to switch to helical gears as these should make less noise, and less prone to wear (since the load never happens on a single teeth, but is transfered progressively). Of course, that creates axial load, which might or might not be an issue (and countered with a second cog), and complexify assembly, especially for planetary gears. But if you try (or already have) them out, let me know.On our part, the test have proved successful, but we&#x27;re not looking at tens of kilometers, and mostly print PLA.To clarify why they aren&#x27;t used more, their production process is traditionally more complex, but that doesn&#x27;t happen with additive manufacturing. I&#x27;d also guess that the teeth shape makes them more robust than conventional filling, and more evenly distributes force on the layer joints.

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:
<a href="https:&#x2F;&#x2F;imgur.com&#x2F;gallery&#x2F;GqXD2Zj" rel="nofollow">https:&#x2F;&#x2F;imgur.com&#x2F;gallery&#x2F;GqXD2Zj</a>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. :)

Imagine if we could revamp the textbook industry so articles like this have a fighting chance of being included.

The whole blog, really. Someone throw money at this person to write science texts full time.

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<pre><code> t = np.linspace(0, 1); (1 - 1j*t) * np.exp(t * 1j)
</code></pre>
And that gives you almost a radian of the involute, unless I&#x27;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 <a href="https:&#x2F;&#x2F;forum.freecadweb.org&#x2F;viewtopic.php?t=27866" rel="nofollow">https:&#x2F;&#x2F;forum.freecadweb.org&#x2F;viewtopic.php?t=27866</a> Draft.makeBSpline will apparently do the job. Blender should be similar.To me this sounds simpler.

Geartrax software, it will draw perfect involute splines.

I wrote a CAD package in Go that has a function for it.<a href="https:&#x2F;&#x2F;github.com&#x2F;deadsy&#x2F;sdfx" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;deadsy&#x2F;sdfx</a><pre><code> func InvoluteGear(
 numberTeeth int, &#x2F;&#x2F; number of gear teeth
 gearModule float64, &#x2F;&#x2F; pitch circle diameter &#x2F; number of gear teeth
 pressureAngle float64, &#x2F;&#x2F; gear pressure angle (radians)
 backlash float64, &#x2F;&#x2F; backlash expressed as per-tooth distance at pitch circumference
 clearance float64, &#x2F;&#x2F; additional root clearance
 ringWidth float64, &#x2F;&#x2F; width of ring wall (from root circle)
 facets int, &#x2F;&#x2F; number of facets for involute flank
 )</code></pre>

Cycloid gears are used in roots-style superchargers. I learned about the shape back in college when I thought I was going to build one from scratch.<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Roots-type_supercharger" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Roots-type_supercharger</a>

The most important section is on involute curves. It&#x27;s the curve formed by unwinding a string against the circle:<a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;gears&#x2F;#strings-attached" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;gears&#x2F;#strings-attached</a>It creates a constant angular velocity ratio at all points where the gears mesh (the law of gears).In layman&#x27;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&#x2F;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&#x27;m not really familiar with:<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Cycloid_gear" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Cycloid_gear</a>I first learned about involute curves from a cousin that works as a machinist. Mr. Wizard also blew my young mind with noncircular wheels:<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=lg4_Kf9B0MI" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=lg4_Kf9B0MI</a>Edit: stumbled onto this technique to make involute gears in CAD:<a href="https:&#x2F;&#x2F;www.fictiv.com&#x2F;blog&#x2F;posts&#x2F;creating-involute-gears-in-cad" rel="nofollow">https:&#x2F;&#x2F;www.fictiv.com&#x2F;blog&#x2F;posts&#x2F;creating-involute-gears-in...</a>If someone has a simpler method, I&#x27;d love to see it.

Yes, relatively prime means coprime means gcd=1

This is what is commonly meant by ‘relatively prime’, yes. Also referred to as being coprime.Defn: a &amp; b are coprime&#x2F; relatively prime iff GCD(a,b) = 1

By relatively prime, do you mean the largest denominator == 1? Or in other words, 15 and 22 should be relatively prime?

<pre><code> That&#x27;s also what I was taught as a best practice, but it&#x27;s not always possible.
</code></pre>
Well of course it&#x27;s possible -there are infinitely many sets of coprime numbers! Silly engineers

That&#x27;s also what I was taught as a best practice, but it&#x27;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&#x27;s bound to happen sometime for maintenance), you can make sure it&#x27;s reassembled so that the same teeth will continue to mesh, preserving the wear pattern. Otherwise, wear is substantially increased.

This is a similar problem to riding a fixed gear bike. When using skidding as a braking technique, specific areas of the tyre will wear faster unless you select a gear (front chainring and rear sprocket) combo with a large amount of skid patches. This is due to the rider always engaging in a skid with their crankset in a specific position - either left or right foot at 90 degrees, and the other at 270 degrees.Here&#x27;s a fun calculator for it: <a href="https:&#x2F;&#x2F;www.surplace.fr&#x2F;ffgc&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.surplace.fr&#x2F;ffgc&#x2F;</a>Notice that a very common gear combo, 44&#x2F;16 only gives 4 skid patches, so if you&#x27;re after longer lasting tyres avoid this setup.

I second TOT, his videos are just fun to watch.  Plus, you learn something.

Anyone that is fascinated by gears owes themselves a visit to This Old Tony&#x27;s video on YouTube titled &quot;Gears! - But Were Afraid To Ask&quot;<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=Q-XOM4E4RZQ" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=Q-XOM4E4RZQ</a>He goes into the nerdy depths of gear make-up, metallurgy, meshing, machining and mistakes as he manufactured metal gears on a mini-lathe.

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.

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&#x27;s very different work, that professors aren&#x27;t trained for. Again, it&#x27;s not easy, maybe impossible. But if it could be done...PS - I see you&#x27;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&#x27;d be interested in talking more about this.

Not to dismiss your work, but do you think the best investment of your time is to write another textbook (assuming this is an undergraduate level book in a relatively well-explored field), or in adding detail&#x2F;great illustrations&#x2F;great interactive charts to an existing work?I know (really, like, I know) how detrimental this would be to anyone&#x27;s career, and I&#x27;m not saying this as a moral condemnation of what you&#x27;re doing - just curious, as I&#x27;ve found myself that there are many cases in these circumstances where the interests of the author do not align with those of the audience. Just wondering if you feel the same way.

I&#x27;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&#x27;m thinking about it!)

I suspect the optimum balance would still be somewhat technical. Maybe something on the level of a spreadsheet. It takes some specific knowledge to use effectively, but is still fundamentally a simple and intuitive tool.

I developed some widgets for interactive books in primary and secondary education. We had different quiz widgets (multiple choice, etc) but also drag and drop stuff and other types of widgets. The people in editorial producing the books configured the widgets using custom HTML tags. It worked very well. As long as they knew HTML they could configure these widgets.The problem is that anything that is easy to produce and configure with a set of options is going to be very limited.It is certainly possible to create an environment for producing mechanical and physical simulations with visual tools but it would not be trivial to develop.

Whoa, some of those interactive tutorials are really impressive.

I&#x27;ve always been partial to this TAM 212 online reference from UIUC. I don&#x27;t know what the professor used to generate it but many of the diagrams are interactive and help build intuitive understanding of the material.<a href="http:&#x2F;&#x2F;dynref.engr.illinois.edu&#x2F;ref.html" rel="nofollow">http:&#x2F;&#x2F;dynref.engr.illinois.edu&#x2F;ref.html</a>

This sort of interactivity would be perfect for Wikipedia.

There is a research area called &quot;Empirical Modelling&quot; which was trying to create these tools but not sure of the progress.<a href="https:&#x2F;&#x2F;warwick.ac.uk&#x2F;fac&#x2F;sci&#x2F;dcs&#x2F;research&#x2F;em" rel="nofollow">https:&#x2F;&#x2F;warwick.ac.uk&#x2F;fac&#x2F;sci&#x2F;dcs&#x2F;research&#x2F;em</a>

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&#x27;ve seen are basically just putting the text and images on a web page, and maybe integrating multiple choice quizzes. That&#x27;s seriously under-utilizing the medium. They need to be interactive, and encourage the student to ask questions and run mini experiments.I&#x27;m aware this would be extremely difficult; maybe impossible.

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: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Digital_scent_technology" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Digital_scent_technology</a>

Nicely made. And as soon as the fan appeared my cpu fan started to spin like crazy. It felt real

That diagram with the wrench and force increasing as the radius decreases should be linear.

This is beautiful. Great explanations, and a really powerful interactive website. A really impressive and engaging page to pull it all together.

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).

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:<a href="https:&#x2F;&#x2F;imgur.com&#x2F;jFpN0f3.jpg" rel="nofollow">https:&#x2F;&#x2F;imgur.com&#x2F;jFpN0f3.jpg</a>

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]: <a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;base.js" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;base.js</a>[2]: <a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;gears.js" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;gears.js</a>[3]: <a href="https:&#x2F;&#x2F;github.com&#x2F;Ciechan?tab=repositories" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;Ciechan?tab=repositories</a>(P.S. &lt;canvas&gt; is an interesting choice, I had expected &lt;svg&gt; before opening the page inspector. Separately, I love the creative use of TLD in the domain name.)

Very nice!These animations are running in a &lt;canvas&gt;.Any idea what the author used? Is everything produced with math (eg: a gear solver, etc)?

I remember learning gear size ratios in sixth grade math class with special LEGO sets.

Very cool! It looks like the output shaft has quite a bit of lateral movement, perhaps something like a Schmidt coupling (<a href="https:&#x2F;&#x2F;www.thingiverse.com&#x2F;thing:233667" rel="nofollow">https:&#x2F;&#x2F;www.thingiverse.com&#x2F;thing:233667</a>) 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.

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).<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Harmonic_drive" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Harmonic_drive</a>

This is Also a very helpful GIF how a gearbox in a car works<a href="https:&#x2F;&#x2F;mobile.twitter.com&#x2F;moo9000&#x2F;status&#x2F;1210190630040821760" rel="nofollow">https:&#x2F;&#x2F;mobile.twitter.com&#x2F;moo9000&#x2F;status&#x2F;121019063004082176...</a>

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&#x27;s not.

Loosening a bolt gets easier as you turn the wrench, no? I assumed thats what the diagram was showcasing

Thanks, that makes sense. Once you start thinking about it, it&#x27;s obvious (e.g. F can never go to 0), turns out I&#x27;ve always had a wrong mental model of how the length of a lever influences the torque (beyond &#x27;longer lever = more torque&#x27; of course).

Torque = distance×force, so force = torque&#x2F;distance, so force is linear in 1&#x2F;distance.

I have a dumb question about this. Under the header &#x27;Torque&#x27;, 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&#x27;t relevant in that graph yet, is it? (meaning, that graphic seems to suggest we&#x27;re talking only about a force perpendicular to the wrench?)

Works fine with noscript and ublock active.. wish all sites played this well

A fun one to watch afterwards:
 <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=5q-BH-tvxEg&amp;feature=emb_title" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=5q-BH-tvxEg&amp;feature=emb_titl...</a>

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&#x27;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.

I&#x27;m not a car guy, and I don&#x27;t know about the differentials, but don&#x27;t continuously variable transmissions allow for this? I&#x27;m guessing they&#x27;re not in common use on race cars, but in principle, shouldn&#x27;t they allow for a 3.01 ratio?

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&#x27;t have half teeth, and you can&#x27;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&#x27;t turn past the broken tooth.

This looks pretty fantastic on mobile. Nice and responsive. Great animations. Good job!

Absolutely, they even work for a while.The Youtube channel &quot;Gear Down for What?&quot; has some pretty cool planetary designs.<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;c&#x2F;GearDownForWhat" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;c&#x2F;GearDownForWhat</a>

This was simply wonderful, and hidden at the bottom was a link to an insect named &quot;Issus coleoptratus&quot;[1] which evolved something like a biological gear for synchronizing its legs.As an almost complete aside, in Terry Pratchett&#x27;s &quot;Last Continent&quot; 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] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Issus_coleoptratus" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Issus_coleoptratus</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.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] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=0rnTh6c19HM&amp;feature=share" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=0rnTh6c19HM&amp;feature=share</a>

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&#x27;t know it has gears too, in particular the planetary gear system, which is not mentioned in this tutorial. (I quickly skimmed through)[1] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=VRe_hKxzKUg&amp;t=1094s" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=VRe_hKxzKUg&amp;t=1094s</a> 
<a href="https:&#x2F;&#x2F;www.howacarworks.com&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.howacarworks.com&#x2F;</a>

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.<a href="http:&#x2F;&#x2F;www.papert.org&#x2F;articles&#x2F;GearsOfMyChildhood.html" rel="nofollow">http:&#x2F;&#x2F;www.papert.org&#x2F;articles&#x2F;GearsOfMyChildhood.html</a>

Oh my! These animations are sooooooo satisfying to look at!

Great article. How did you make those images with sliders? Any tool or library you used?

<a href="https:&#x2F;&#x2F;youtu.be&#x2F;Q-XOM4E4RZQ" rel="nofollow">https:&#x2F;&#x2F;youtu.be&#x2F;Q-XOM4E4RZQ</a> An awesome video on making gears.

&gt; The considerations behind real world gears are much more complicated than what I’ve presentedNah... Nah I would say you pretty much nailed it in this blog post! Incredible. HN Gold right here.

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 &quot;computer&quot; with cams building up differential calculations:
<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=s1i-dnAH9Y4" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=s1i-dnAH9Y4</a>Enjoy!

I would need additional proof that gears were designed with many of these mathematical considerations in mind and didn&#x27;t just arise out of trial and error by the machinists

The writing and interactive examples are really amazing. Would deffo read the entire series of articles. Gonna bookmark it.