7 ms·

This one's my favorite (although I haven't read the whole thing): "This movement is designed to double the speed by gears of equal diameters and numbers of tee

by JasuM 7y ago

This one's my favorite (although I haven't read the whole thing): "This movement is designed to double the speed by gears of equal diameters and numbers of teeth—a result once generally supposed to be impossible. Six bevel-gears are employed..." http://507movements.com/mm_226.html http://507movements.com/mm_226.html

JudgeWapner 7y ago
I read and re-read this for a solid 5 minutes and I have no idea how it produces the result. I get that gear D spins orbitally around the left-right axis instead of rotating clockwise, but I can't seem to grok how that would produce 2x rotations.
- ElCapitanMarkla 7y ago
  This is blowing my mind at the mo, I need to see it working...
  - JudgeWapner 7y ago
    I think I got it. The simplest way I can describe it is the gear on the far right is turning the whole square frame on the left because the little shaft turns inside the big shaft. The 2nd gear from the right (that is connected to the big shaft) is turning the "thing-thats-already-turning", so you get 2X rpm.
- neilk 7y ago
  Not a mechanical engineer but I think this is what is happening. Note that Shaft F and shaft D are made to rotate in opposite directions. Then another gear is made to pit those motions against each other, by means of that wacky rotating frame A. To see why let’s unwrap it from a polar coordinate to something more linear. Imagine a wheel with gears resting on a rail with teeth. The wheel has an axle going through it. If you drag the wheel’s axle forward horizontally that’s like what Frame A does to impart 1x rotation. But then the rail is also moving backwards, giving you 2x rotation. I think!
  - Kliment 7y ago
    You're entirely correct - it's a modified differential drive. The two shafts are coaxial to each other and drive their corresponding gears in opposite directions. The frame is fixed relative to one shaft but mobile relative to the other, which is where the extra 1/2 of relative motion comes from. The traditional way to do this was with a crossed belt. This is the higher-friction lower-slippage version of that.
- abdullahkhalids 7y ago
  I think what happens is that E is moving the whole gear D move around. I think you realize this. In other words the motion of E does not change the teeth of E and the teeth of D which are in contact with each other. But then the gear LeftC is making D rotate around the circumference of E i.e. changing the teeth of E and teeth of D which are in contact. Since this is in the same direction as above, you get 2x speed. Essentially imaging you sitting on the edge of a plate. E is making the whole plate spin. And leftC is making you run around the circumference of the plate in the same direction as the direction of rotation. So your angular speed becomes twice as much as the speed of the plate.
  - kd5bjo 7y ago
    E is the output gear, and B is the input. The arrangement on the right is to make the frame A and gear C turn in opposite directions, and D adds the two rotations together again to turn E twice for each revolution of B.
- Animats 7y ago
  A differential is an adder.[1] This is a differential hooked up as a doubler. Mechanical analog computers, especially gun predictors, had lots of setups like that. [1] https://www.youtube.com/watch?v=s1i-dnAH9Y4&t=757 https://www.youtube.com/watch?v=s1i-dnAH9Y4&t=757
  - TeMPOraL 7y ago
    Thanks for that video. Very informative... like many of the videos from that age. There's something about training videos and physics videos from the 50s / 60s that makes them much better than what people produce today; it's hard to say exactly what it is, but they do feel cruft-free.
    - deleted 7y ago
      [deleted]
    - jcims 7y ago
      I wish they would make some for convolutional neural networks.
      - spandexcajun 7y ago
        3blue1brown videos are probably the best equivalent. Maybe a little basic? But really, all his math videos are just ridiculously good quality. https://www.youtube.com/watch?v=aircAruvnKk https://www.youtube.com/watch?v=aircAruvnKk
    - Grustaf 7y ago
      They are not trying too hard to make it fun and entertaining. But it ends up much more entertaining than modern chewing gum tutorial videos.
    - dTal 7y ago
      Not just the 50s/60s - this video explaining differentials is from 1937 and is a marvel of pedagogy: https://www.youtube.com/watch?v=yYAw79386WI https://www.youtube.com/watch?v=yYAw79386WI
abdullahkhalids 7y ago
I wonder if there is some general theorems on what sort of speeds/powers can be achieved given access to some specific types/sizes of gears.
userbinator 7y ago
It's like an automobile differential --- if one wheel stays still, the other wheel turns faster than the input. Hence the warnings to not exceed a certain speed when one wheel is slipping, because the other one turns much faster than what the speedometer indicates.
soulofmischief 7y ago
It took five minutes of re-reading and visualizing but once it clicked there was very much a eureka moment. What a clever little design. Thanks for sharing!

by JasuM 7y ago

JudgeWapner 7y ago

I read and re-read this for a solid 5 minutes and I have no idea how it produces the result. I get that gear D spins orbitally around the left-right axis instead of rotating clockwise, but I can't seem to grok how that would produce 2x rotations.

ElCapitanMarkla 7y ago
This is blowing my mind at the mo, I need to see it working...
- JudgeWapner 7y ago
  I think I got it. The simplest way I can describe it is the gear on the far right is turning the whole square frame on the left because the little shaft turns inside the big shaft. The 2nd gear from the right (that is connected to the big shaft) is turning the "thing-thats-already-turning", so you get 2X rpm.
neilk 7y ago
Not a mechanical engineer but I think this is what is happening. Note that Shaft F and shaft D are made to rotate in opposite directions. Then another gear is made to pit those motions against each other, by means of that wacky rotating frame A. To see why let’s unwrap it from a polar coordinate to something more linear. Imagine a wheel with gears resting on a rail with teeth. The wheel has an axle going through it. If you drag the wheel’s axle forward horizontally that’s like what Frame A does to impart 1x rotation. But then the rail is also moving backwards, giving you 2x rotation. I think!
- Kliment 7y ago
  You're entirely correct - it's a modified differential drive. The two shafts are coaxial to each other and drive their corresponding gears in opposite directions. The frame is fixed relative to one shaft but mobile relative to the other, which is where the extra 1/2 of relative motion comes from. The traditional way to do this was with a crossed belt. This is the higher-friction lower-slippage version of that.
abdullahkhalids 7y ago
I think what happens is that E is moving the whole gear D move around. I think you realize this. In other words the motion of E does not change the teeth of E and the teeth of D which are in contact with each other. But then the gear LeftC is making D rotate around the circumference of E i.e. changing the teeth of E and teeth of D which are in contact. Since this is in the same direction as above, you get 2x speed. Essentially imaging you sitting on the edge of a plate. E is making the whole plate spin. And leftC is making you run around the circumference of the plate in the same direction as the direction of rotation. So your angular speed becomes twice as much as the speed of the plate.
- kd5bjo 7y ago
  E is the output gear, and B is the input. The arrangement on the right is to make the frame A and gear C turn in opposite directions, and D adds the two rotations together again to turn E twice for each revolution of B.
Animats 7y ago
A differential is an adder.[1] This is a differential hooked up as a doubler. Mechanical analog computers, especially gun predictors, had lots of setups like that. [1] https://www.youtube.com/watch?v=s1i-dnAH9Y4&t=757 https://www.youtube.com/watch?v=s1i-dnAH9Y4&t=757
- TeMPOraL 7y ago
  Thanks for that video. Very informative... like many of the videos from that age. There's something about training videos and physics videos from the 50s / 60s that makes them much better than what people produce today; it's hard to say exactly what it is, but they do feel cruft-free.
  - deleted 7y ago
    [deleted]
  - jcims 7y ago
    I wish they would make some for convolutional neural networks.
    - spandexcajun 7y ago
      3blue1brown videos are probably the best equivalent. Maybe a little basic? But really, all his math videos are just ridiculously good quality. https://www.youtube.com/watch?v=aircAruvnKk https://www.youtube.com/watch?v=aircAruvnKk
  - Grustaf 7y ago
    They are not trying too hard to make it fun and entertaining. But it ends up much more entertaining than modern chewing gum tutorial videos.
  - dTal 7y ago
    Not just the 50s/60s - this video explaining differentials is from 1937 and is a marvel of pedagogy: https://www.youtube.com/watch?v=yYAw79386WI https://www.youtube.com/watch?v=yYAw79386WI

abdullahkhalids 7y ago

I wonder if there is some general theorems on what sort of speeds/powers can be achieved given access to some specific types/sizes of gears.

userbinator 7y ago

It's like an automobile differential --- if one wheel stays still, the other wheel turns faster than the input. Hence the warnings to not exceed a certain speed when one wheel is slipping, because the other one turns much faster than what the speedometer indicates.

soulofmischief 7y ago

It took five minutes of re-reading and visualizing but once it clicked there was very much a eureka moment. What a clever little design. Thanks for sharing!