This seems like a solution that has not found its problem yet.

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.

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.

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!

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?

This tickles a part of my brain that not many things do. Nice work.

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.

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...

I'm always amazed at what you come up with

It is very refreshing to see new engineering from people like you. Oh, the wonders of computer aided drafting and 3-D printing.

I really sat here and watched a 7 minute explanation of gear mechanisms, with zero prior interest in the topic. Your videos are great!

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

Wow, I'm impressed by the KZfaq 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.

the puzzle potential is exciting!

So satisfying! Do you think you could make a version of that design that is in the shape of an infinity symbol?

Every engineer watching this is letting out a satisfied sigh right now.

How about the lock mechanism from this video: kzfaq.info/get/bejne/pct7gZp53Z6shn0.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.

These models are so beautiful!

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.

the algorithm has blessed me with another channel that displays interesting and intriguing items

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.

Babe wake up, new Henry Sagerman video just dropped

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

I like how you can explore diferente way, out of the box... it's very interesting....

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.

The last design is so marvelous!! I have no idea sticks and gears mixed up and do well.

the first clip makes me happy

Great work! That didn't feel like 7 minutes, the time passed very quickly. Great video very informative, glad the algorithm brought me here.

im not too savy on mechanical engineering despite my fascination with them, but this was a fantastic breakdown of these sorts of mechanisms.

Triple-helix was awesome

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.

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.

It would be interesting to see the strength and benefits between each of these gears to see which would be better used for certain scenarios.

정말이지 놀라운 3d 프린팅 공예실력이지 아니할수가 없지 아니한 그런 영상인거 같다 태엽의 간격이 정말이지 완벽히 일치하고 설계를 제대로 하여 매끄럽게 태엽이 서로 상호작용 하면서 돌아가는 모습이 정말이지 아름답다.

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.

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..

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.

I dont know how I ened up on a video about gears and screws...but good stuff. Well deserved like.

In this age of information technology, I never expected to be surprised by good ol' mechanics!

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!

Lovely as always Mr. Segerman!

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. :)

Bro that is the most absurd way to present pasta I have to give props to that.

The Boreman racks remind me of a 50's mechanical naval firing computer. Looks like a coordinate system

This one’s a real beaut. And it’s fun to compare with the “ancient”, discolored triple-gears from the distant past. 😉

There is a kind of a metal lathe 3-jaw chuck which uses similar racks to sunchronise its jaws.

It is really hard to find real life scenarios that can implimet this type of gear.

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

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.

That mechanism is smooth as butter, Id love to know how you printed it.

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.

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 ❤

Mesmerizing and fascinating. Subbed, sir.

You can make really cool artistic elevators with these mechanisms

ngl that looks like a steampunk biblically accurate angel

I have been thinking about a mechanism that could move like this, and now you have bring it to reality

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.

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.

6:41 "I imagine that could be a fun research project" that could probably be a masters thesis

I am convinced that biblically accurate angles are just drones that had these kind of gears.

Very nice! As a retired engineer my recommendation is that you patent that t-t gear set immediately. Good luck.

That looks very satisfying

Mans voice is like Qui Gon Gin without the urgency. Just the calm.

1:20 thanks for the advice, wife says shes pretty impressed

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?

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 tickles my brain in all the right ways

Insane levels of thinking involved as always!!

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.

As a carpenter, I used to use a Yankee screwdriver which has some complex gearing.

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.

Deserves a Thumbs Up and a comment. Nice work.

With this, You can open wine bottle behind the corner🎉

the biblically accurate gear mechanism

Biblically accurate gear mechanism

you could totally extend the length of those twisting gears around into circles themselves and make some interesting (and artistic) gear linkage

Biblically accurate gearbox.

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.

When I first saw the thumbnail for this video I thought you had created a replica of DNA Helicase. Fascinating mechanism!

Hello, Mr. Segerman, I'd like to propose a fishing rod with a spinner bait as a popular screw-screw translation. Here is why, When you reel in a fishing line, the reel spins and bobs up and down, winding up the line while maintaining an even spool of line. This is the first screw motion. it is oscillating linear, and constant rotational As the line reels in, the lure's spinner will also cause the the lure to travel in a corkscrew motion, spinning as the line is reeled in. This is the second screw motion. It is constant linear and constant rotational. I hope this fits the bill, it certainly seems to fit to me.

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.

I momentarily got worried when you said "ill just use my hand" with the corkscrew in your hand.

Very impressive, congratulations!

While I can't confirm if it was a screw-screw mechanism, my drafting teacher in highschool had a special adjustable squaring tool for faster square plotting that had a screw as at least part of it as you would rotate a knob and the x and y axis would create distance or close it at the exact same time, assuring you were tracing a square. He said it was a novelty antique he found back in the '70s. But it was less practical than the ruler built into a drafting bench for a multitude of reasons.

I wonder what next level genius is going to do with this.

I'm, many times, watching this kind of smart stuff with shame, because i feel so, so stupid. Subscribed.

these look like the mechanisms you would need for the traps in video game dungeons

For a moment I thought it is one of those "biblically accurate angels" videos.

I’d be super surprised if I ever see one in a real world situation. Really neat though, I appreciate the brain power behind it 👍

First thought: “What in the actual f@$k?” Second thought, “That is amazing that can actually exit!” Very cool!

How on earth do you come up with these endless fantastical contraptions...

i only saw the thumbnail for a moment, and i had no idea what i was supposed to be looking at. i thought it was supposed to be a biblically accurate angel

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.

Fascinating presentation -- informative and mesmerizing!

There is yet another tool, that fits the rotate/translate box as well as the translate/screw box, depending on which of its elements you fix in your hands. The _Archimedes drill_ a bit outmoded, but still available!

This is epic bro you are a Genius it seems.

As always, well done, Sir!