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Show HN: Sketch, connect and simulate gears and chains (github.com)
201 points by frankl on July 31, 2013 | hide | past | web | favorite | 58 comments

I've always wondered - Consider the following gear arrangement: http://snag.gy/Tvsgi.jpg

The tiniest push on the gear on the left causes the gear on the right to fly at thousands of RPM. Of course, there would be a ton of friction in the system to overcome. However, what if the left gear was a pinion connected to a rack that was pushed by an extremely powerful, yet slow-moving source, such as a glacier or tectonic plate? With enough gears in this arrangement, an unstoppable force moving just 1mm/year could spin tons of turbines.

Would this work?

Think about how large the forces will be at the first tooth interface at the left (or in the rack). How strong does that tooth need to be?

Alternatively, you can use it the other way. Connect the gear at left to a tectonic plate. Rest your finger on the gear at right. Voila! You can exert a force great enough to stop the tectonic plate's motion. Plausible?

When Archimedes said, "Give me a lever long enough, and a place to stand, and I'll move the Earth.", he actually meant something more like, "Give me a lever long enough, and a place to stand, and I'll change the momentum of the Earth very very very slowly. Unless that lever is incredibly strong and I have access to a considerable source of energy."

"Alternatively, you can use it the other way. Connect the gear at left to a tectonic plate. Rest your finger on the gear at right. Voila! You can exert a force great enough to stop the tectonic plate's motion. Plausible?"

Nope, the question here would be whether the material used to construct the left gear withstand the force that a tectonic plate exerts given that the gear system will not allow it to move. I don't think the mechanics of the tectonic plate exerting force on our gear system and our gear system exerting force on the tectonic plate are symmetrical.

Good point. And even if the gears were made of unobtanium, the whole gearbox would have to be mounted on the opposite tectonic plate on top of breakable rocks.

So the total gear ratio of that gearchain comes out to something like 1119:1, though that's lower than you intended I suspect because you geared it down with a 9:57-or-so ratio on the end. The penultimate axle is geared at 7089:1 with respect to the first axle.

Now while that implies a rotation of one degree of the first axle is accompanied by a rotation of the penultimate axle through 20 or so revolutions, in practice that's not going to happen, because of that ton of friction you pointed out. The friction force acting to stop the last axle turning gets fed back as resistance to your pushing the first wheel, and it gets multiplied back up through the gearchain by the same factor - so the resistance to your turning the first wheel is 7000-times the resistance of turning the last wheel - plus 2000 times the resistance of turning the wheel before it, plus 918 times the resistance of the wheel before that... in total, assuming all friction forces are equal, you're fighting against a force 12000 times the force you need to turn just one gear - just to beat the friction. Okay, so you posit some frictionless maglev bearings in a vacuum, perhaps. But you still want to get these wheels into motion, so then the same multiplier gets applied to the force you need to accelerate the mass of each gear into (rotational) motion in the first place. Getting all those gears spinning requires 12000-times the acceleration to get one of them turning, so 12000 times the force.

And forget about putting a useful load on the end axle - let's put this thing in a car, say, and use it to drive the rear axle. We'll lift up the rear axle and get the engine up to 5000 RPM. Your engine is going to get that axle spinning 7,000 times for every engine RPM - 35 MILLION revs per minute! But when you drop your 1-ton car to get some traction, the engine's going to act like the car weighed 7000 tons...

You could also think of it in terms of energy. If that last gear spins at thousands of RPM, its got a huge amount of kinetic energy from somewhere. It must have come from your 'tiniest push'. Your tiny push has to transfer all that energy - so it can't be that tiny.

tl;dr: no.

So do gears basically help you distribute kinetic energy, or do they serve other purposes?

Gears 'distribute' kinetic energy in that they allow you to take a rotational motion on one axis and generate a rotational motion on a different axis. That can be a parallel, offset axis, as in this case, but it can also be at a different angle, using angled or crown gear teeth. So yes, that's one use, certainly. They let you reverse a rotational direction, too - turning clockwise into anti-clockwise.

But the main thing they do is let you trade angular distance of motion against angular force, or torque - same as a lever does, and much like how a pulley system lets you trade off linear distance of motion against linear force. I can make a gear system that multiplies the effective force I can exert by 50, at the expense of my having to rotate a crank on the input shaft fifty times for every time I want the output shaft to rotate. Or I can use it the opposite way around and make an output shaft spin fifty times for every rotation of my input shaft, at the expense that I have to exert fifty-times the force to overcome any load on the output shaft.

Thanks for coming back to answer. Back to school for me.

There's an art/science experiment piece on display at the Exploratium (unfortunately I can't remember what it's called) that has a similar construction. The gear at one end is turned at a steady pace by an electric motor, and each successive gear attenuates the motion until you get to the last gear, which is set into solid concrete (iirc). If it were free to move, it would take a fantastic span (billions or trillions of years?) to make a full rotation.

Edit: Thanks to bockris for pointing out the name. Turns out the last gear rotates once each 13.7 billion years.

One that I've seen in the past is: Machine with Concrete - Arthur Ganson https://www.youtube.com/watch?v=5q-BH-tvxEg

That's the one.

Great arrangement! It will work. Whether it will be financially feasible to construct such a large system of gears, deploy it in extreme weather, keep it well oiled and maintain it, and then transport the generated power to a usable location are entirely different questions.

Hmm... maybe there are more common sources of strong-but-slow power. The heat expansion of bridges? The weight of vehicles sitting idly at a stoplight? The swaying of skyscrapers?

I wonder if you could make a purely mechanical solar panel that way. Get a giant sheet of metal, put it out in the sun, and attach this gear arrangement to it, braced by opposite sides of the expansion. Hmm... I kinda want to make this now.

What you're describing is a move up the Kardashev scale[1]. The Kardashev scale measures how tech-savvy a society is by how they collect and use energy. A Type I society on the scale is able to harness and store all the energy generated on the planet, which we're moving towards now. Regenerative braking and such are definitely progressions in that area, but presumably bigger gains could be had by harnessing the power of tectonic plate movement, volcanic activity, wind, solar, etc.

[1] - http://en.wikipedia.org/wiki/Kardashev_scale

I wonder if we'll be able to harvest all ambient sound one day.

I think the heat expansion of bridges can be put to use to power an interesting gear system art installation at best :-)

Still worth it! I'm gonna try building that mechanical solar panel.

no because speed is nothing without torque.

The right wheel would spin fast, but anything put there to leverage that momentum into energy, be it simple magnetic generator, would be enough to halt the whole system by equalizing the opposing forces, since whatever minimal force it has, will go trhu the same powers that create the initial speed.

It would work, but it would probably not be practical in terms of materials - any significantly huge gear ratio driven from the low-motion side will run into problems with the strength of the gears and the degree of friction involved (and the steady-state static friction pressure & friction loss per second of the fastest gears being sufficiently large to make it impossible to move the slowest gears at all)- and even if you have an impossibly strong frictionless gearbox, the strength of the contact patches with the objects themselves becomes the weak point - the pressure will impress a hole right through the tectonic plates, rock, or glacier you're dealing with, rather than spinning the gears.

Of course it would "work". So would a lever - ask Archimedes:


Well you would need an unrealistically long lever for that. With this gear thing, you could conceivably pack an extremely high gear ratio in a tiny area. I guess gears are just levers in a different form. I was just wondering what the limitations would be in this idea. I guess the construction of the gear system would have to be unrealistically high quality and strong.

1. How is that calculated?

2. Is there a ready way to simulate it?

Great for touchscreen, but tricky with a mouse. I would like to see an option for drawing gears where mouse down sets the center of a new gear and dragging away determines the radius.

Absolutely what I was about to post. For a mouse user, mimicing the circle construction mechanics (with preview!) used in the geometry construction puzzle app that was linked a few weeks back [1] would be the bee's knees.

1: http://www.sciencevsmagic.net/geo/

Totally the first thing I thought of as well. Great idear.

Agreed, and some controls that allow you to specify the radius of a gear instead of drawing it would help, too. I spent a long time trying to draw two gears with the same number of teeth on my ^#$(@#! trackpad. :)

Also, there's a UI limitation with snapping concentric gears together: you can snap a small gear onto a larger one, but not the other way around. This seems to make it impossible to add a pair of concentric gears whose smaller gear is meshed with the edge of an existing gear.

But overall, great project with very pleasant casual interaction. Would be interesting to see what you plan to do with it.

This is really cool!

The ability to save a configuration and share it would be pretty cool, but as well as that, other objects such as sticks which are attached to gears would be a lot of fun. But then I suppose you have to involve gravity :)

Rods and cams would be the next logical step.

This is cool but I'm learning quite quickly that I'm no good at drawing circles with my mouse, perhaps a bit more forgivness when using the gear drawing tool might make life a bit easier?

Overall I'm impressed.

Will probably send a pull request just to be able to draw gears by the diameter or radius instead of the perimeter.

can't even draw a square with the clitmouse...

I have no real use for this, but that didn't stop me from playing with it for 30 minutes!

Love this! It's very intuitive and fun to draw gears of different sizes and hook them together.

I'd love to be able to make more complex gears. I immediately tried to make a compound gear set with three gears and two different bands.

That got me thinking about "Incredible-Machine" puzzle features and how fun it would be to actually try to build working things like clocks, bikes and machines with this.

Really enjoy the different take on the interface.. feel like you might be missing something in having modality though, seems like you could combine the actions for drawing a gear and drawing a belt, which would make it a bit neater.

Any plans to add more complicated gear types? Would love to see something like this enabling easy explanations of watches and the like..

In case you're interested, here are two of the best video's I've seen describing how a watch works ( http://www.youtube.com/watch?v=OiCPu0SjEW4 ) and how a differential works ( http://www.youtube.com/watch?v=K4JhruinbWc&t=1m50s )

Don't let their old school-ness throw you off. They are both extremely well done and demonstrate in clear and simple language from first principles to finished object.

Hah, the first thing I did was build a going train. I had to use belts for the second, third, and fourth wheels because the planarity was difficult or impossible to manage.

It was of course more like an electronmechanical clock since there isn't a way to build a balancewheel and escapement, but since I had to eyeball the gear sizes and draw them with my mouse anyway, it now appears to be approximately 0:65:101am.

Cool! Something like this is the first thought I had when I saw the old book "507 Mechanical Movements in Dynamics, Hydraulics, Hydrostatics, Pneumatics, Steam Engines, Mill and Other Gearing" on HN a few months ago[1].

1. https://news.ycombinator.com/item?id=5660770

Very fun!


- draw involute teeth forms

- allow non circular gears

- add other linkages

- plot force (torque) and velocity (rotational velocity) against time or position

That would be a pretty slick tool for some quick back of the envelope type calculations.

Reminds me of Mindstorms:


In the intro of the book Seymour A. Papert describes how gears provided an early concrete framework that made understanding abstract mathematical concepts presented at a later point much easier to visualize and apply.

Very good experience on the latest iPad. I wish there was a way to delete gears though.

Also having the play button toggle pause/play would be nice.

Drawing a slash through a gear seems to delete it. I'm not sure whether or not that is intentional

draw a slash though the gear to delete.

I learned a bunch by watching the demo (big ? on the right)

This is really cool. I could definitely use something like this when testing gear functionality on a bot I'm making.

I don't have my tablet with me but I'm eager to try it. Have you tested on Android?

I tested it on my 2010 android phone and it just barely works on that. More recent android tablets should be able to run it quite smoothly.

I've played a bit on my desktop browser and it's fun! Can't wait to show it to my kids. I've looked for similar things a long time ago and only found Java apps/applets. I like that this is browser based.

Do you have a TODO features list? I don't know Coffeescript but this would be a good learning experience for me. I can think of at least one feature I would like to add.

Currently there's no todo list with features like other types of gears, more easily creating gears of specific sizes and the like, but I would very much welcome contributions of that type. I ported this version from the original in java, to make it usable on mobile devices, because they are much more widely available than e.g. wacom tablets.

I'm using the GearSketch environment in my PhD research to study different forms of support for learning about gears. For instance, I created a puzzle generator that creates concrete gear configurations based on abstract descriptions (e.g. there are two unmovable gears, one larger than the other; goal: connect them in such a way that the large gear will turn faster than the small gear). Using each student's solutions to earlier puzzles, the software tried to model their individual understanding of the gears domain and create new puzzles based on that. Turns out accurately modeling student knowledge is hard. ;)

The students using GearSketch are 10-11 years old, and understanding the interactions between the normal gears and chains is already quite challenging for this group, so my current focus is not on adding more elements. But like I said: I'd love to see others working on it and would be available to help.

I just tried it on Chrome on desktop and it is usable. I think the touch just makes the experience better.

Please add a permalink feature.

This is pretty neat. I've been doing a similar thing lately (rendering arbitrary-sized bicycle chainrings in SVG), so I have gears on the brain.

I'm surprised this one uses canvas instead of SVG, actually. Compatibility reasons?

very nice. very smart how it won't let you put gears together that will violate their rotation. would be wicked if you could right click (or otherwise select) a gear and edit its radius and/or tooth count.

At last, I have found the true purpose of my GNote II. Things get a lot more complex when you realize you can drag gears around with chains attatched after you place them...

reminds me of Arthur Ganson, artist who sometimes makes homemade gears. Has fun with gear ratios too (I think the machine with concrete will spin 1 revolution in 10000yrs if I remember correctly).


I was a museum gaurd at an art museum that had his work last century. He now has a permanent home at the MIT Museum.

Impossible to add the chains with a touchpad.

Using it with a touchpad is far from ideal, but you should be able to manage it by drawing the chain very widely around the gears. The chain will be tightened automatically.

You need to create two gears, a big one and a small one, then place the small one directly in the center of the big one. You can then attach a chain around a gear. Took me forever.

Same problem on my Galaxy Nexus, I tried all combinations of placing a belt, and it just wouldn't work.

Uncaught TypeError: Type error - gearsketch_main.js:53

Am I the only one getting this? Chrome 28; Windows 7.

My (almost) 4-year-old has a new favorite activity. Thanks!

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