Exploring gears with different kinds of motion. You can buy a copy of the screw/screw gearing model from Shapeways at shpws.me/Ts69 You can also try printing out your own. You can download the files from www.printables.com/model/5191...
@@henryseg I have a folder on my computer titled "Solutions in search of problems." I think this sort of engineering is good practice and frees your brain up for lateral thinking once the real problems come along. One of the files in this folder was a spherical gear, which I never figured out but these smarties did: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-hhDdfiRCQS4.html What would this be an example of? Rotation-rotation-rotation?
In kinematics, when you choose a different part of the mechanism for the 'grounded' part (you called it the frame), it is called a kinematic inversion.
The "two ordinary racks" from 5:45 remind me of a safety feature in railway rolling stock, where they add large rack-like panels to stop relative motion along a vertical axis in colliding vehicles. That prevents a situation where one vehicle's frame could slide on top of the other frame and crush everything in the passengers' space.
Ive seen these on thise little cargo wagon deal, basically a skin made of teeth that fit to the cart, then you could lever the teeth up to keep it rolling.
I love 'periodic tables' like this. Some are just done stupidly, but when you decompose the the space into orthogonal attributes, you get an amazing pointer to possibly undiscovered items. Your table here shows this ( labeling "screw" with an additional "rotate+translate" label adds a bit of insight ) But it also shows that you have not yet identified all the axes. Look at the rotate/rotate box where you have at least 3 different mechanisms that fit into the same grid location. I think the missing axis ( or axes ?) is angle between the two planes of motion (??) with values 'planar', 'bent', 'yawed' and 'pitched'' If you added another 3 layers to this grid, and added the 'useless configurations ( like your locked up racks ) you'll possibly get a complete set of mechanisms. Color coding 'part A' and 'Part B' might make things clearer. The 'plane of engagement' is another possible axis. Some missing items: in rotate/rotate: you have pane of motion values 'planar', bent and pitched, but are missing yawed the spur/screw item engages on the 'bent 90 degrees' plane, but could engage at 45 degrees bent ( would lock up) or planar ( the spur would have rack holes and the screw would be lozenge shaped) the 3 item screw is probably two items together with left and right chirality somehow, which hints at another axis in rotate/translate: there is a missing rack/pinion where the 'rack' translates up out of the page, and one where it translates away from the pinion in rotate/screw: the handle of the corkscrew could emerge from the screen and twist the handle axis could be an axle aligned top/bottom of screen and used to roll the cork remover to the right I am probably missing some, and I feel I have mistakes above because I probably haven't characterized all the orthogonal attributes correctly.
interesting idea, although in practice combinations of any of these and bevel gears can change the axis we're working around. however, a few additions just for thought: a spiral gear would be a good example of a rack and pinion-esque gearing that pushes the rack away from the gear a rack and pinion moving up out of the page could be filled by a worm gear moving a rack, which is yet another way that the adjustable wrench can fit into the diagram, if you look at it from above constant gear ratio, whether or not it can be worked infinitely, and different possible frames of reference are all other possible things to explore, I feel this is a discussion that can very easily get very complex
The translate-translate gear is *almost* a pair of opposed mechanum wheels, if you were to bend one of the translate gears around so that it loops back on itself. The action of the rollers is as if the floor had teeth at 45 degrees to the plane of rotation.
i dont really think i've had much of a previous interest in gears, but the way you explain everything with examples in a calm voice kept me engaged the entire time lol. love it!
Translate-translate gear is actually used in garage door locks, it has irregular teeth on both key and lock if they match it slides freely, if not it binds.
Henry, have you considered attempting to build a pliable/flexible version of that mechanism, such that the helical racks conjoined to form a figure eight?
@@punpundit5590 I'm definitely not an expert on this but my intuition tells me that if they are both Möbius strips then there should be no need for that intermediate spur
The Museum Of Science And Industry in Chicago has a staircase of mechanical movements. I have been fascinated by that staircase since I was a child. I am glad to see people appreciating these topics again...
How about the lock mechanism from this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-oeKN7Hx8HVI.html as an example of a translate/translate mechanism. The door is the "frame" part, and the key and the locking bar are the parts moving relative to the frame.
Industrial grippers have translate/ translate mechanisms. An air cylinder moves 90 degrees to two jaws causing them to open or close some of Schunk's grippers are made this way.
Wow, I'm impressed by the RU-vid algorithm. I had been googling for a helical gear to support at idea level the design of a track for simultaneous translating and rotating camera motion, and that happens to match your last design if we put a regular gear in place of the other helix.
For the bottle opener, The screw forces caused by the cork screw are translating the cork screw, and that translation is moving the gears, not a screw motion through the gears. It's the same gearing in both action. Just because it's spinning in the gears, doens't mean it's moving by screw gearing, which is why it works in both directions as translation..
There was a video circulating a while back showing a door latch that uses the translate translate arrangement. I can't find the original video on its own, but the Maker's Muse youtube channel has a video about/including it you can find searching "Rack Lock". Apparently they are known as реечный замок and we're fairly common in Russia. There are quite a few videos in Russian of commercial реечный замок but most of them show more enclosed factory made units, I haven't found any that show the mechanism as well as the clip in the Maker's Muse video.
Beautiful gears. it's pretty wild to think how many unimagined mechanisms could be out there. Seems like the variations could be infinite. I imagine interlocking sets of lattices which interact together in beautiful but horrifying complexity There's a purity to the physical representation of relationships between objects and systems, vs proxies through abstractions
As for the tranlation/translation mechanism in the real world - there are locks with the key in the form of a rod with the inclined grooves and two parallel latches with the same type of grooves in the lock itself. Pushing the key in between the latches you make them move and unlock the door. In our country such locks have been used in garage doors mainly some time ago but not any more as I can tell
2:10 the translate gear thingy - I found a similar thing the other day when fixing a pair of binoculars that has this zoom thing and you control it with an arm around one of the eye pieces. A thin piece of metal moves along and the same motion is replicated on the other eye piece. It’s so clever, I’d never come across it before and was why I bought the broken binos from the charity shop.
I know there are locks that use a design similar to the borromean racks, but they only use two pieces and a frame. You push one of the racks into the key hole and the corresponding motion on the other rack lifts the latch on the door. The teeth on the racks are irregularly spaced so each key is unique.
I love the idea of someone randomly coming across this & suddenly understanding (Eureka!!!) what they need to do in order to get the idea that they've been mulling over to work.
Damn that was really enjoyable to watch 😄 Very clear and concise explaining and awesome visualisation with the Models and real-life examples in tools! I subscribe right away ❤
I have no idea what i'm going to do with this information, but i enjoyed this video nonetheless. You have a pleasant voice and way of explaining things. Thank you for the video, and I wish you a good rest of your day!
Corkscrew is a mix of screw and rack and pinion. Screw motion moves the rack, that rotates the pinion. Theer is no direct interaction of screw and pinion.
A related excerpt from HG Wells, “The War of the Worlds”: “And of their appliances, perhaps nothing is more wonderful to a man than the curious fact that what is the dominant feature of almost all human devices in mechanism is absent-the wheel is absent; among all the things they brought to earth there is no trace or suggestion of their use of wheels. Almost all the joints of the machinery present a complicated system of sliding parts moving over small but beautifully curved friction bearings….”
This is the time when learning becomes an adventure again. Let us not forget the AMOUNT of equations, differential equations, that these things have. Inverse kinematics is rigid body mechanics hence classical symplectic groups. The amount of knowledge required for these is fascinating. Lagrange equations, Lagrange Kane equations, Hamilton equations, Hamilton Jacobi principle, Poisson Brackets and Lagrange Brackets. Classical mechanics never stops being fascinating. These videos makes the analysis explicit and understandable.
OMG HOLY SHIT, GOD OF GRARS, OMG, THAT FIRST MOVEMENT WAS SMOOTH AND PRECISELY MEASURED AND SHAPED, WITH A MATHEMATICAL SOLUTION FOR ITS MATERIAL AND MEASUREMENTS
You could make them elastic and turn them into a circle like screw and screw forever. Maybe the circle is big but I think it would work when you use a few more frames arranged in a tetraeder way and the circles will rotate themselves around their centerline instead of them rotating 90° relative to the frame in the center and crash into each other. :)
I remember seeing a video of a weird lock that was a rack and rack mechanism, the key was one rack, with irregular tooth spacing at a 45 degree angle and the lock had a bolt with the complimentary tooth spacing. I was unable to find the original, but Maker's Muse did a video on it in 2019.
The screw-screw contraption is like most advanced mathematics. There maybe some practical application in the future somewhere but if we are honest we must admit that we mostly do it for the fun.
There was a Russian lock design for keyed gates that was a translate/translate gear set. The key was one rack and the latch was the other rack and the door was the frame.
Couldn't a "screw - screw" combo be as simple as a screw and the the nut or hole it is threaded into? The perpendicular screw - screw model you made is pretty cool.
I would imagine the optimal shape would still be close to the circle involute, but then perhaps bevelled following another involute perpendicular to it? Not really sure. You're right that would make an interesting project particularly if this mechanism saw an industrial application.
I can imagine the screw/screw mechanism being used as a regulatory mechanism to ensure 2 angled planes move in a rocking motion at a locked speed ratio and only one of them is powered. There is probably a much simpler way of doing it too.
This reminds me of Polhems Mechanical Alphabeth, a 17th century effort of making a library of mechanisms to translate every motion to every other motion. Although I don't think he saw "screw" as a motion.
Here's a guess: If you take a typical leadscrew, but call the "screw-shaped" (rotational) part "frame" what previously was the "frame" becomes a rotational part, and what was the nut (translational) part becomes a screw (movement) part. Alternatively, If we define the part that was the nut (translational) part to be the "frame", the screw-shaped part becomes a screw-movement part, and what was the "frame" becomes a translational part. These are all equivalent functionally, but what we call the frame changes our perspective, and thus the relative motion of the other parts becomes different. I think that it's interesting that this means that when we change the "perspective", it changes what classification can be applied to the system. For example, if we take a typical set of bevel gears, and name one gear the "frame", the frame becomes a rotational part, but the other bevel gear becomes something entirely new that moves in two rotational axis. The system still has one degree of freedom, but the part moves in multiple different ways (this is because the axis of rotation changes throughout the cycle, namely, the axis of rotation rotates along with the part previously called a frame.) This concept, and the fact that "screw" motion appears to be a combination of rotational and translational motion, leads me to believe that this would generalize to a wide variety of different types of motion, but perhaps we can classify those motions as compositions of simpler types of motion. Some combinations (like in screw motion) might be commutative, but others (like the mentioned double rotation) might not. I wonder what relationships these types of motion might have? Could we come up with a useful notation for how mechanical machines work as a result?
Ooh, you noticed that property of changing perspectives. Shall I point out that if you change your perspective to that of the worm gear on the spanner, the jaw becomes screw movement, and the handle becomes rotational movement? It's basically an example of an applied leadscrew though, (but using a rack instead of a nut) so I guess it's not surprising it has the same properties.
i dont know about screw-rotation (maybe just a wrench looked at from the right direction?), but a tool i use a fair bit is the micrometer. while it doesn't have any mechanisms per se, it nevertheless is used to convert screw motion into precise linear motion, for the sake of precision measurement. the thimble moves in a screw motion relative to the frame while the spindle moves-in practice-linearly.
The screw/screw functionally works like a set of bevel gears sliding 2 racks, but are much more elegant. If ever there's a need to both slide and rotate elements in 3 axes, there it is!
If we think about rotation of a verrry big wheel around a very faraway axis, then in the limit we get translation. So the rack and pinion is a limit of the gear-gear link (with either the parallel or intersecting axes). At which point I thought of the rack and rack, which of course you finally got around to at 5:45.
It would be fun to see if you can get different gearing ratios for the screw:screw device. perhaps it could be used in some sort of pantograph type application.
Translate-translate is used in some garage locks in Russia. It is a very old design, but it is still manufactured. The key is pushed (or inserted sideways, rotated and pulled) through a hole and the "teeth" on the key interact with the "teeth" on the springloaded locking bolts, retracring them. Secrecy is achieved by the angle and positions of the teeth.
Actually a screw screw would be awesome for a lower weight safe locking mechanism. Extension and rotation can make a better lock than just translation from rotation. Similar to the force as rotation and lock mechanism works on modern rifles.
