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Gears

ciechanow.ski

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Re: Gears

#111

Post by WalterBright »

jvanderbot wrote: post #69

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

The same sorts of things were built using analog electronics.

And even these have fallen by the wayside to digital electronics.

Re: Gears

#114

Post by kragen »

zackmorris wrote: post #79

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 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…

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 Draft.makeBSpline will apparently do the job. Blender should be similar.

To me this sounds simpler.

Re: Gears

#115

Post by roel_v »

pavpanchekha wrote: post #94
anderspitman wrote: post #84

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 t…

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!)

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/great illustrations/great interactive charts to an existing work?

I know (really, like, I know) how detrimental this would be to anyone's career, and I'm not saying this as a moral condemnation of what you're doing - just curious, as I'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.

Re: Gears

#116

Post by roel_v »

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?)

Re: Gears

#117

Post by adossi »

roel_v wrote: post #116

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…

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

Re: Gears

#118

Post by progval »

roel_v wrote: post #116

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…

Torque = distance×force, so force = torque/distance, so force is linear in 1/distance.

Re: Gears

#119

Post by boznz »

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

Re: Gears

#120

Post by kragen »

saltcured wrote: post #98
kragen wrote: post #76

Earlier quoted context omitted.

> 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…

A generalization which applies to levers, pulleys, and hydraulics is mechanical advantage while conserving energy. You have a system with input work and output work (energy) that are the same, ignoring frictional losses. Recall that work is force over distance. The mechanical system relates the input and output distances by a scalar coefficient. Since the working distances are related by a ratio, the working forces a…

Yes, that's an excellent point, but I think the lever law is more general than that. For example, it continues to apply when the lever in question is stationary, even though no value of the forces involved would violate conservation. In fact, it holds to higher precision in that situation because your measurements aren't confounded by vibration and accelerating masses.

Maybe you can derive it from some kind of generalization of Hooke’s Law to cover nonlinear stress–strain relationships, elastic hysteresis, anisotropy, viscoelastic behavior, and so on, but it's not obvious to me what that would be. Also, I feel like the concept of angular moments acting to produce angular acceleration is simpler and more general than all that stuff, but I'm not sure if conservation of energy and geometry alone are sufficient to derive it.

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