"Can you explain the purpose of pallets and how the pallets are "connected" to the escape wheel and balance wheel?"
I guess the easiest way to answer your question would be to provide a link to Wikipedia, "Lever Escapement." The only problem with that is that these seven paragraphs of explanation are written by someone who has either never seen a watch or who copied the whole article from a 600-page book called "Theoretical watchmaking."
To save your time, I've read the said article just a minute ago, and quite frankly it was so dry that they've lost me in the third paragraph.
Therefore my explanation will be somehow different.
No technical background needed, just plenty of imagination!
Let's say you and your kid decided to have some outdoor fun and build a swing. Since the only suitable tree in your backyard is a very tall one, you had no choice but to suspend the rope from a branch which is 10m above ground.
(Are you using your imagination? Can you picture that really long rope? I don't want you to think of a small playground sand pit swing, but a BIG one!)
Six hours later, working on a hot summer day, your swing is finally ready for a ride.
The kid is on, and you've given him that strong initial push.
(Now imagine the swing swinging swishhh......swishhh.... and the kid having fun!)
Then your wife comes out and yells: slow it down!! So you let the swing slow down, to rock gently, while you maintain the action by pushing the kid with just a gentle touch. Like all good fathers do on a hot summer day.
Once again, we are talking about a very long swing with a very low amplitude.
So here is the first postulate: in order to keep the swing swinging, you must continually provide a bit of force, or an impulse as watchmakers would say.
No impulse, no joy- the swings stop.
Now let's move to the second postulate.
After a few minutes, the kid is going to get bored. Since you've just spent six hours building the darn thing, you want him to play a bit longer. (This is also known as quality time). So you've come up with a game: Every time the swing comes your way, the kid will give you a high five and yell a number.
The mental picture: Here comes the swing - your hands touch and he yells ONE - then you gently push him away. Here he comes again - touch,TWO, push; touch,THREE, push... and so on.
Every time you two do the high five, the kid is impulsing your hand. A fraction of a second later, you are impulsing the swing back. And because the kid is counting swings, he is acting as a tick-tock generator - a time piece!
Your swing is an oscillator which is impulsed from the outside, and at the same time it
provides an impulse which is 'fed back' into the system.
This concept is really extremely simple yet magnificently efficient and accurate. The swing is a pendulum and the kid is a pendulum bob (weight on the bottom). Since you are receiving and giving an impulse, YOU are acting like clock pallets.
The reason why students of horology don't understand this concept is because two things happen almost instantaneously, and only one is obvious. However if you try to explain the geometry of impulsing without understanding the basic concept behind it, you too will be lost in 7 paragraphs of Wiki explanation.
You have probably noticed that I am not talking about watch pallets, but clock pallets instead. For a simple reason: while watch and clock oscillators work on different principles, the impulsing part is almost identical (and easier to demonstrate in simple terms on clock pendulum).
Essentially, pallets provide a connection between gear work and oscillators and their purpose is to transfer the force from the mainspring (via gears) to the oscillator AND to receive feedback impulse which does the 'tick tock' counting.
While we are at clocks, let me just expand a bit on pendulums (your big swing ticking at low amplitude). The search for accuracy in mechanical timekeeping went on for at least 2000 years. It came to an end in 1656. when a clever dutchman by the name of Huygens attached a pendulum to a clock movement. Within a couple of weeks of experimenting, he managed to improve the daily error in clocks from 15 minutes per day to 15 seconds per day! This was such an amazing and revolutionary discovery! Of course, he could not keep it secret and a few months later the good news spread to London which was at the time the horological capital of the world. The rest was just history...
So what is so special about clock pendulums?
If you remember, last week we have talked about watch oscillators and concluded that the period of oscillation depends on two things: inertia and stiffening of the hair spring.
Here is that formula once again:
Obviously, it is difficult to get a steady rate of oscillation when you have to jiggle two variables - we are dealing with complex and challenging engineering requirements.
Unlike with hair spring-return system, the beauty of the pendulum is this: pendulums are gravity driven!
Here is the formula which describes its period of oscillation:
Now note that T is not exactly defined in the formula; this simplified formula works only for a pendulum with a very small amplitude. This is why I wanted you to picture that LONG swing, not a short one.
(Just in case you want to see the formula which does take into account amplitude or theta-angle of swing here is that nasty and ugly beast. Note the 3 dots after last + sign: the equation extends for ever!!!
So let's go step back and have a closer look at T in the simplified formula: it is directly related to two things: L = length of the pendulum and g = gravity. Since gravity is a constant, there is really just one thing we need to worry about! What a beauty!
Indeed, you know so well that timekeeping adjustment in clocks is done by adjusting the length of the pendulum bob. Lower the bob, slower the clock.
And the weight of the pendulum is irrelevant - whether you have a 10 kg kid on a swing or a 30kg one, the preriod of oscillation is always the same. You can actually sit on the swing yourself and let the kid push you - and number of ticks and tocks will not change a bit!
Because of constant gravity, clock built in London will keep equally correct time in Sydney, Hong Kong or New York.
But let's say we have built two identical clocks and we send one to the Moon while the other stays in Sydney. We set time on both clocks at noon Sydney time. My question is this: twenty-four hours later, would both clocks display the same time?
While this sounds like a tricky question, the answer is really simple. According to our formula -
the period of oscillation is gravity dependent. And since gravity on the Moon is only 1/6 of gravity on Earth, the moon clock will go significantly slower. Actually we would have to reduce the length of the pendulum from 1m to 16.6cm if we want both clocks to show identical time!
That is probably the reason why Apollo astronauts took Omegas to the moon, not their grandfather clocks :-)
To conclude, understanding the function of watch pallets starts with the understanding of impulsing action. Transfer of forces is pure geometry, and I have to say a fairly complex one. For many years, watchmakers have struggled to perfect the geometry of pallet stones, shape of the escape wheel, polishing, lubricants.
The smallest misalignment will inevitably result in loss of power transferred to the balance wheel and in loss of amplitude. The timing when transfer of power occurs is absolutely critical, and it is determined not just by the shape of the escape wheel and pallets, but by their relative positions. Once again, it goes without saying that external disturbances like shock or lack of regular servicing will result in poor time keeping.
Here is a photo of (broken) pallets and a (rusted) escape wheel from my junk box:
Final curiosity: the weight of the Rolex escape wheel is 0.006 gram. In other words, the total of 167 wheels would have the combined weight of 1 gram. With the price of US$28 per wheel, 1 gram of escape wheels is worth US$ 4,676.00!
Do you know of any other machine-made and mass-produced piece of metal worth 4.6 million US dollars per kilogram? That's why the Swiss don't bother about making hammers and screwdrivers. If they did, you'd have to be Warren Buffet to take up carpentry as a hobby :-)