Utterly fascinating to see how very simple mechanical devices, like differing gear ratios, can be used to calculate things like logarithms.
For example, could an electrical analog system be a way of carrying out large-time molecular dynamics simulations? With proper tuning of the material, might you be able to create arbitrary potentials between the electrons within it so that they would interact roughly like atoms in an MD simulation? Or, perhaps you could create an analog chip where the electrons would 'naturally' solve various NP-hard problems, effectively by brute force?
For a completely different portrayal of futuristic mechanical computers, check out Neal Stephenson's story The Diamond Age. It's set in an era of nanotech, and the computers are nanoscale clockwork computers.
This is cool, because the Hubbard model is a simple and displays interesting phenomena, but understanding it is a hard problem. The Hamiltonian (that is to say, the energy) consists only of a kinetic energy plus an interaction between the spin up and spin down particles on the same site (e.g. if I have two spin up bosons and four spin down bosons, the interaction contribution to the energy is 8 U, where U is a constant parameter---the strength of the interaction.) Depending on this interaction strength U, the system might behave either like a conductor or an insulator.
The problem is hard to deal with analytically (for reasons I can't say I understand) and, as I understand it, the space of possible states is so huge that the numerics become computationally intractible at about a lattice 5 sites x 5 sites x 5 sites. So being able to see the phase transition happen is very neat, and exactly what you expect from an "analog quantum computer": simulating with cold atoms a system that we can't really simulate with ordinary computers.
Musicians are still using them. Modular synthesizers are the bomb.
Guns, not missiles. At 0:50, the narrator refers to "initial shell velocity."
They were last used in combat in the 1990s, when the Iowa-class battleships fired their 16-inch guns at Iraqi positions in Kuwait. The Navy never bothered to replace them with digital computers, because they were already accurate enough for the guns they controlled.
This 1937 video about differentials is also enlightening:
Why is it that old tutorial videos are so thorough and informative?
Highly worth a visit if you're interested in this sort of mechanical computing stuff…
 So far I saw : analog target computations, wheel differentials, wave diffusion
 Is what I know as a Geneva Drive. Back before we had fancy alloy springs and were forced to use Steel as the material for mainsprings because that's all we knew, watches had problems where a freshly wound watch would run fast and a watch that hasn't been wound for a day or so would start to run slow, as the strength of the spring tapered off. The Geneva Drive was a solution, though it's more of a hack, to only let the spring release power inside the middle of it's power arc, by preventing the watch from unwinding past a certain low point and preventing the user from winding the spring up to it's strongest point.
 This is a simple Heart Cam. Mechanical Chronographs (Stopwatches) use these to reset the chronograph runner to zero. A hammer, represented as the horizontal pin, is released from a caught position with spring tension on it, which slams into the heart cam and forces it to reset to a predetermined position. Incredibly simple design. No matter where the hammer slams down on the cam, it is guaranteed to reset to the same place. (It's also a golden ratio)
 This is basically the design of a modern instantaneous date wheel. The snail-cam ("D" looking thing) is generally affixed loosely on the gear. The worm gear drives the flat gear, naturally, which catches the snail-cam and drives it forward. As the cam rotates, it slowly raises up the hammer, which has tension provided by the spring. At a defined point, the hammer reaches the apex of the snail-cam and (since the cam is affixed loosely and is allowed some circular freedom) slams forward "instantaneously". The cam will usually have a finger that then flicks forward a date wheel.
 Fusee Chain. Similarly to the reasons behind the Geneva cross (loss of power as a spring unwinds), we developed the Fusee chain to compensate for the loss of power by acting like a transmission in a car. As the spring unwinds, it uncoils the chain from the spiral wheel, which in turn will have a high-torque output at first (~ 1:1 ratio), and slowly increase revolution while decreasing power. These were highly present in English watches, but are no longer produced (as we have fancy alloys that alleviate all of the necessity of these things)
 A Verge Escapement. Another long-forgotten mechanism. Escapements are the things that regulate the output of circular motion. It's basically a ratchet-and-pawl mechanism. You'll generally have an oscillator (like a pendulum) attached to the lateral verge which rocks the teeth back and forth, the drive train then tries to move the escape-wheel forward, but the verge only allows one tooth to pass per vibration (a vibration is one half oscillation). The "Swiss Escapement" has largely replaced this mechanism.  This is essentially the same thing.
 The Cylinder Escapement. In the 60's the Swiss freaked out because the Japanese started producing cheap, disposable watch movements. The result of this was a huge loss of Swiss watch companies as they struggled to compete. One of the ideas they came up with was to produce a large number of cheap watches, but they couldn't just drop prices, they also had to retool and drop quality, substantially. The cylinder escapement was not a new invention in the 60's, but it started to get a lot of use around then. On a personal note, these are terrible things. They were designed to be disposable, and subsequently were marketed to kids quite often. This is where a number of the Ingersoll watches came from (like the old Mickey Mouse watches). The original ones that are worth more than most startups in Mountain View are cylinder watches, and finding one that runs is the equivalent of founding a Facebook for watch collectors.  This is how it works when looking at it interacting with it's escape wheel.
 The Swiss Lever Escapement. B is the pallet, D is the oscillator (Balance Wheel). Escapements essentially work all the same. They're mostly just renditions of one idea. The swiss lever escapement was up until the mid 2000's practically the only escapement produced in wristwatches. The pallet stones have since been upgraded to be synthetic ruby, along with the majority of the other bearing surfaces in watches, since the introduction of this book, however.
 This is what I'd call a Daniels Escapement, or Co-Axial Escapement. If you've looked at an Omega watch since the mid 2000's (as referenced above), you've probably heard about the Co-Axial Escapement. This is what it looks like. It's much more complicated than any of the other escapements, and has whole books written about it, and yet is the simplest mechanism once you figure out how it ticks. It quite literally only touches the oscillator once an oscillation. All the previous escapements are required to touch the oscillator twice (once going up, once coming back down). This is literally the difference between a tick and a tock. This only ticks, it has no tock. The less interaction the pallet has with the oscillator means that there is less energy lost in it's oscillation, and helps with both accuracy and longevity (they wear out less, and can run longer per wind).
 This is a rotary Wankel engine, like the Mazda RX. Not a watch part, but still a "modern device"
The book I used in school was "Theorie de l'horologie" , which is a fairly modern book. I supplemented this with "The Bulova Watch Repair Training Manual"  and "Practical Benchwork for Horologists" . I would argue that the most useful book for practice was "Practical Benchwork", which was originally released in 1938, it's latest edition being from 1988.
Still, I'd read about how these machinese were developed and then made obsolete by other technology.
I imagine this is blocked from being appearing higher up on the page by the parent not having more votes than the parent's siblings.
(Do votes for a child have an effect on the parent's sort order? A workaround would be to vote the parent up when voting for the child, but you shouldn't have to do that...)
Wonderfully elegant solution. Oh, and great post, uxp.
As far as texts go, I would just search Google or Amazon for "Machine design". I don't have any particular recommendations because at the time I viewed text books with the same level of excitement as most other students, which is to say none at all. The two books that I did keep after college are the following:
1) Product Design and Development: http://www.amazon.com/Product-Design-Development-Karl-Ulrich...
2) Machine Design: An Integrated Approach: http://www.amazon.com/Machine-Design-Edition-Robert-Norton/d...
I love the 507 movements book (I've had the paper copy for years) but an important thing to remember is that many of these mechanisms have been replaced by modern electronics, motors and software. Mechanisms are cool to watch, but they often have to be aligned when initially set up, they wear in complex ways, may have to be taken apart to be lubricated and can be very difficult to fabricate. In many cases a mechatronic solution (combo of electronic motion control and a simpler mechanism) is better than a purely mechanical one.
A car differential that lets wheels rotate at different speeds as the car turns is interesting. A performance car differential supplanted with solenoid-driven clutch packs under software control gives you the ability to immediately give each wheel the maximum amount of power that it can transfer to the ground
There are many similar books, such as "A Victorian Handbook of Mechanical Movements" , and "1800 Mechanical Movements, Devices and Appliances" .
The little pins hit the V in the center gear and cause it to shift to the other gear. Neat!
Building stuff, pressing the "On' button, and seeing it all work is just the best feeling in the world.
A couple of them describe stuff that used it but most were just technical details. It would be nice if there was a link to something that used it so you could see why it was ever made (or maybe some of these are just for fun).
I couldn't get through them all but will come back because it's fun to watch. More fun than it should be really.
example of one that has me guessing why it exists:
Normally you can take the output tray off and turn it over to see the mechanism.
Another thing that would be interesting is to know when some of these came about (some are older than people might think ).
I find that the amount of large scale steel industrial works, done before our current era are incredible.
The fact that these movements, visualized in the mind - then described in 2D, drawn by hand, are fascinating.
Edit: ah, only the color diagrams are animated. The top of the page links to a blurb about that.