I'm a trained watchmaker. I use, fix and sometimes build many of these as components of watch movements.

[1] 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.

[2] 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)

[3] 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.

[4] 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)

[5] 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. [6] This is essentially the same thing.

[7] 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. [8] This is how it works when looking at it interacting with it's escape wheel.

[9] 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.

[10] 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).

[11] This is a rotary Wankel engine, like the Mazda RX. Not a watch part, but still a "modern device"

[1] http://507movements.com/mm_212.html

[2] http://507movements.com/mm_097.html

[3] http://507movements.com/mm_064.html

[4] http://507movements.com/mm_046.html

[5] http://507movements.com/mm_234.html

[6] http://507movements.com/mm_302.html

[7] http://507movements.com/mm_294.html

[8] http://507movements.com/mm_295.html

[9] http://507movements.com/mm_296.html

[10] http://507movements.com/mm_313.html

[11] http://507movements.com/mm_425.html