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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..).
(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.
If only textbooks could be this good.
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.
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.
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
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. :)
This is an absolutely phenomenal 'explorable explanation'. It methodically layers concepts to foster understanding, deploys interactivity to build intuition, and on top of all that provides crisp, clear narrative on top of all of the amazing visualizations.
If 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/ and https://ciechanow.ski/earth-and-sun/
Earlier quoted context omitted.
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.
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).
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.
Earlier quoted context omitted.
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.
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).
Torque is nothing more than "spinny" force. For example, sometimes you will see the term "generalized force" to mean both force and torque, because it doesn't really matter in some contexts. For example, if I have a robot arm that has some linear joints (like that of a 3D printer) and rotational joints (like that of an arm), you can talk about the generalized forces of each joint. Some of those generalized forces are linear (and people call that "force"), and some of them are rotational (and people call that "torque").
They are exactly analogous to (linear) velocity and _angular_ velocity.
When you talk about force _generating_ a torque, the only thing I can understand is how the linear velocity at a point on a disk (say you blow across its surface) _generates_ an angular velocity.
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
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
Edit: stumbled onto this technique to make 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.