#### Reverse-Engineering the Stanford Clock Tower

During my visit in the summer of 2019, I tried to figure out exactly how the clock worked...from the other side of the glass panes. Here's what I came up with. I think I figured out nearly everything, but there might be some mistakes. This is a long read, but I think (don't quote me on this), it's the only article on the internet that details how every part of Stanford's clock tower works!

You can think of the whole thing as three different parts, with one central time-keeping part and two chiming parts that depend on the time-keeping part. I will explain the nitty-gritty of all these parts. By the end of this, you should know (to a certain degree) what every gear and lever does!

# The Time-Keeping Section

These are the three main "modules" to the clock: time-keeping, quarter-chime, and hour-chime. This time-keeping section (the one that turns the clock hands and drives the other two modules) is the easiest to understand, but the most important and the center of the physical assembly. Like the other two modules, it is driven by a falling weight's torque on a large drum (green box). This drum is connected via many high-ratio gear pairs, ending in the escapement (red box), which regulates the rate at which the weight falls, and subsequently, the "ticking" of the clock.

How does this escapement work? This caliper-looking device and spiky gear (red box) act like a sort of turn-style. Every swing of the pendulum will allow the spiky gear to "slip" one notch, and this "slip" makes the ticking sound, as well as acting like the time-keeping restriction. Because the pendulum has a period of one second, this spiky gear can only slip once per second (and as an added bonus, the gear also adds energy to the pendulum!). So, this whole drum-gear-escapement assembly creates a (very slow) constant angular velocity setup. This slow-but-steady rotation is used in all parts of the clock. For the clock hands, the rotation is passed through a hinged rod (right image) and into the top of the tower, where additional gears drive the hands.

The main timekeeping mechanism. Green box is the weight-driven drum. Red box is the escapement.

The skew-axis coupling that transfers the rotation to the top of the tower, where the hands are moved.

# The Quarter Chime Section

This is the second module of the clock, and it is responsible for sounding the chime every fifteen minutes.

This module (and the hourly chimes) are essentially a giant music box, driven by a second falling weight, geared drum, and high-ratio gear pairs. This time, however, instead of ending in an escapement device, it ends in...paddles? This is a stroke of physics genius! A constant torque will apply a constant angular acceleration, meaning that the song would speed up as it's being played! However, because drag is proportional to velocity-squared, these paddles allow for one single angular velocity (think skydiving. The paddles have a "terminal velocity")

So, at each quarter-hour, a lock is released (I'll get to this), and the drum-gear-paddle assembly is suddenly free to spin. On the large drum, you will see a bunch of metal "protrusions." (green box) As it turns, these protrusions push down on the three metal levers (foreground), which are connected by long rods to bells at the top of the tower. By spacing these protrusions in a specific manner, the characteristic quarter chimes can be played.

How the bells are played. Green box shows the protrusions on the main barrel.

But how does the whole mechanism start? The entire drum-gear-paddle assembly is braked in a very interesting example of negative feedback. But first, how do we exert the braking force needed to counteract a huge weight falling? Answer: we don't. Remember: the high-ratio gears will mean more turns of the paddle per turn of the drum, but also less torque (because conservation of energy). So, by braking/regulating the paddle assembly axis, a very minimal force is needed. Actually barely any is needed! Careful observation of the paddle assembly reveals a ratcheting device (see below). This device allows torque in only one direction, the direction that the paddles normally turn. However, once the axis is braked, the angular momentum of the paddles is dissipated by the ratcheting device (because from the perspective of the paddles, this axis is now going the opposite direction!) This dissipation is what gives the tower a "buzzing" sound immediately after the quarterly and hourly chimes.

Close-up of ratchet.

But what IS this braking device? At the surface, it's super simple. There's a "t" bar on the paddle axis, and if the horizontal bar is in the right position, the "t" bar will hit it and catch. But what determines the position of the horizontal bar? Well, this horizontal bar rides on a special wheel, mounted directly on the large drum! This wheel has a few divots on it (see video), which divides the drum into sections. Each section corresponds to a quarter-hour jingle, and one single rotation of the large drum corresponds to an hour's worth of chimes. At the end of quarter-hour chime, the bar will fall into the divot, which puts the end of the bar into a collision course with the "t" bar on the paddle axis. This is the braking device, and it uses a very clever form of negative feedback.

This is the braking device viewed from the side. The red box is the divoted wheel. The green box shows the "t" bar

This is the braking device viewed from the front. The t-bar collision with the horizontal braking bar is very apparent here.

Ok, so we explained how the chime ends, but how does it start?? Let's pretend that we have JUST finished hearing a quarter-hour chime. What does it look like now? Well, the horizontal bar is sitting firmly in its divot, and this lowered position of the bar is keeping the "t" bar from moving. So, the only way for the paddles to start spinning again is to push this bar out of the divot! But how?

Right after the chimes stop, the braking bar (white) is preventing the "t" bar (red)

from moving.

This is where another engineering stroke of genius comes in. Key observation: we can push the bar out of the divot beforehand, but as long as the "t" bar remains blocked, nothing will move. So, we do a bait and switch. There's a second bar (green outline) below the main braking bar (outlined in white), and RIGHT NOW, IMMEDIATELY AFTER A QUARTER-HOUR CHIME, it is completely out of the way. However, it won't stay that way. As time passes, this bar slowly rises (thanks to a specially-shaped gear mounted on the timekeeping module's hour axis). This secondary bar will eventually make contact with the main braking bar, and in the process of rising, it will push the main braking bar out of the divot. Here's the clever bit: while doing so, the secondary bar replaces the main braking bar's role as the "t" bar blocker

This second bar (outlined in green) is slowly pushing the braking bar out of the divot, but in doing so, it also replaces the braking bar's role of blocking the "t" bar (red). So, nothing moves...yet.

Fast forward to seconds before the next quarter chime. Now, the main braking bar is completely out of its divot. The only thing holding the "t" bar from rotating is the secondary bar, which is held up with the specially-shaped gear. Now, this gear looks like four cliffs (see picture below). Throughout fifteen minutes, it slowly pushes the bar up, but at the end of the quarter hour, there's a vertical drop. On the quarter-hour, the secondary bar encounters this vertical drop on the gear, and now, there's nothing preventing the end from falling! (A weight attached to this bar helps the process). As the secondary bar falls, now there is nothing holding "t" bar in place, and the paddles start to spin! (sadly, I didn't catch this start-up action on video). Actually, there's nothing holding the main braking bar in place either, but the "t" bar is too fast, and before the braking bar can fall back into the divot, the paddles have already started rotating, and with it, the main drum rotates. Now, there is no divot to fall back into, until the chime is complete. At the end, the braking bar falls into a new divot, braking the "t" bar. Now we are back to where we started, and the secondary bar makes another slow journey up to replace the primary braking bar, to drop again after fifteen minutes.

This shows the four-cliffed gear (outlined in red), connected to the hour-axle of the clock. As this side of the lever (outlined in white) is pushed down, the other side (the side near the "t" bar) is pushed up, bringing the upper braking bar with it.

# The Hour Chime Section

This last section of the bell tower hardware is the most intricate. Before, we just needed to figure out how to start a giant music box, and the wheel divots did the whole start-stop thing. However, for the hour chimes, the number of bell chimes depends on the time of day. So, how is this implemented?

Well, let's start with two things that aren't very different from the quarter-chimes: the starting mechanism and the chiming mechanism. In both the quarter and hour chime sections, a large weight is connected to a drum-gear-paddle assembly, which spins at a constant velocity after being released. Protrusions on the large drum cause the hour-bell lever to move up and down, ringing the bell. Also, as seen in the image below, the same two-bar assembly is present. Right after an hour chime, the top breaking bar (outlined in green) is holding the "t" bar of a second drum-gear-paddle assembly (outlined in white) in place. During the hour, the lower secondary bar (outlined in red) will move up, replacing the top breaking bar's role in holding the "t" bar in place. The only difference is that this "lower" secondary bar is actually curved! (see picture). Furthermore, because the "lower" rod and the upper braking rod are technically located side-by-side, there's a flat portion of the "lower" rod that the upper rod rests on (highlighted in yellow). The gear that pushes on this secondary lever is very similar to the quarter-chime gear, but instead of having four cliff-like protrusions, it has one large one. At the end of the hour, the bar falls off the "cliff" on the gear, causing the end of the bar to fall as well, which leaves the "t" bar free to start spinning.

This shows the two-lever system of the hour chime section. Note that these two levers are slightly more complicated (especially the bent lower lever!) The gear that moves the lower lever is near the top of the image (where the red outline ends). However, unlike the four-cliffed gear, this gear is hard to take a picture of.

How about the braking mechanism? Ok, this part is complicated. There's no "divot" for the top main braking bar to fall into and collide with the "t"-bar, because such a divot would need to be adjusted each hour! Instead, there's a very cleverly-designed gear system. This looks like a quarter of a gear (ok, ok it's more like an eighth but who's counting?), with exactly twelve teeth.

This gear, however, is not attached to the drum-gear-paddle assembly. It is on its own pivot, and two things are touching it. One: a normal gear, mounted on one of the axles in the drum-gear-paddle assembly. As this axle turns during chiming operation, this quarter-gear is turned by this normal gear, at a rate of one tooth per chime. Do you see where we're going here? This quarter-gear is the counting mechanism! So, the second thing touching the quarter gear makes sense: it's the top braking bar! Right after the start of chiming, the secondary lever has fallen below the level of the "t" bar, while the main braking bar is above the level of the "t" bar. What is holding this top braking bar from falling and slamming into the "t" bar? It's the quarter gear! Through a long vertical protrusion, this top braking bar rides on top of the quarter gear as the gear turns, staying out of the way of the "t" bar. However, because the quarter-gear is only part of a circle, what goes up must come down. IMMEDIATELY after the right number of tolls, the quarter-gear would have turned such that the vertical protrusion of the top braking bar rests right over the edge of the gear's end. Moments later, the protrusion falls over the edge, bringing the top braking bar right down into the path of the "t" bar. Falling off the edge of this quarter-gear is the braking-action, which is somewhat similar to falling into the divot of the quarter-chime mechanism.

This video shows the start-up of the hour chime system. The quarter-gear, normal gear that turns the quarter-gear, and vertical protrusion are annotated.

This video shows the stopping of the hour chime system. The red annotation shows the vertical protrusion dropping off the edge of the quarter-gear, and the green annotation shows the "t"-bar collision

Well, ok. So the number of chimes is dependent on the rotational position of the quarter gear. But how is this determined?? For this, we need to look at a gear that is smack-dab in the front of the clock assembly, and it looks like a mollusk's spiral shell, except that there are exactly twelve discrete circle sectors on it, of varying radii. Now, this "shell gear" is mounted to a 12-hour axle, meaning that the shell turns once every twelve hours. But how does this correspond to the rotational position of the quarter-gear? Well, for this, there's a long horizontal rod. The quarter-gear is quite an odd shape. It's like a pizza slice, with an anchor at the end of the wedge (blue dot). However, there's another "bulge", where a horizontal rod is connected (via a pivot, red line). This assembly actually has a center of gravity (roughly at the green dot, with the help of some small weights) that is slightly off-center. More on this later. What's important now, is that the horizontal rod is connected directly to an "L"-shaped piece that "rides" on the shell-gear! So, the rotational position that the quarter-gear is in depends on the rotational position of the shell-gear, which depends on the hour.

This diagram shows (in an exaggerated way) how the horizontal bar is connected to the quarter-wheel. Yes, I made this in MS paint.

This picture shows the quarter-wheel's horizontal rod (outlined in red). Scroll down for a front view of the shell-gear.

Now, you might ask, how does this quarter-gear rotate during chiming when it's bound to the shell-gear by the horizontal rod? Answer: it's not bound! Actually, the only restriction that this shell-gear provides through the "L"-piece is how much the quarter-gear can spring back after being released.

Wait...what release? Also, how does it spring back??? Well, let's rewind back to IMMEDIATELY after the braking mechanism activates. Now, the vertical protrusion has fallen off the lip of the quarter wheel. Now, remember my previous discussion about the center of gravity. Even in the current state, the green dot is still to the RIGHT of the center (with respect to my crude diagram above). The process of ringing the bell and turning the gear to the LEFT has actually RAISED the center of gravity of the quarter-gear, and now, it wants to come back down, by turning to the RIGHT. Why doesn't it do it? The vertical protrusion!! To stop the mechanism, the protrusion slipped off the edge, and now, it's blocking the quarter-gear from turning back. (The orange in the diagram)

So, the vertical protrusion is actually "cocking" the quarter gear! The piece of metal is preventing the quarter-gear from turning back. At this fully-cocked position, the "L" piece at the end of the horizontal rod is actually not touching the shell-gear! This "cocked" position is what's shown below (unfortunately, I wasn't able to take a picture of the rider (outlined in yellow) on the shell-gear. I was too busy with the action on the other side!!). Why is the cocking necessary? Because the shell gear is made out of discrete circle sections that get larger and larger from one to twelve o'clock. So, without the complete disengagement of the "L"-shaped "runner", the clock would jam on the "steps" of the gear.

Here, we see the front view of the shell-gear (green outline). We also see the horizontal bar, "L"-shaped, and "runner", outlined in red. The part that contacts the shell-gear when the quarter-gear is released is outlined in yellow.

Review: at the end of chiming, the quarter-gear is "cocked", meaning that it has turned and pushed the horizontal rod to the farthest-back point possible, such that the shell-gear "runner" is not making contact anymore. However, the quarter-gear WANTS to turn the other way (opposing the direction that chiming turns it), which is a convenient way of resetting the chiming counter. So, what releases this cocked quarter gear? Let's fast forward to minutes before the next hour. Now, the second, lower bar has taken the place of the top bar, and it is still rising. Remember the upper braking bar's vertical protrusion? Now, the braking bar is so high up that the vertical protrusion is just about to clear the lip of the quarter-gear! In a few moments, as this protrusion lifts above the lip (thanks to the lower secondary bar), there is nothing holding this quarter-gear from un-cocking itself, moving in the direction OPPOSITE to normal chiming rotation. But wait! Wouldn't the quarter-gear want to rotate all the way back, to lower its center of gravity as much as possible? No! This is where the shell gear comes in! As the quarter-gear rotates, it pulls on the horizontal rod, and thus, the "L"- shaped piece. Remember: up to this point, the cocked quarter-gear has caused this "L"-shaped piece to not make contact with the shell gear. However, the un-cocking rotating action will cause this "L"-shaped piece to approach, and then hit the shell gear on one of its 12-radii circle sectors with the "runner" (outlined in yellow in the image above), limiting further quarter-gear rotation in the un-cocking direction. So, the natural gravity-induced torque on the gear is responsible for resetting the quarter-gear, and the connection to the shell-gear is responsible for setting the right rotational position of the quarter-gear. Now, remember that the "L"-shaped piece merely rests on the shell-gear, so although this contact prevents further un-cocking action from the quarter gear, the cocking action that happens during a bell-chime is not restricted.

This shows the shell-gear (edge outlined in white) and "L"-shaped rod (red) fully engaged through the "runner" (contact point outlined in yellow). You can also see the horizontal rod going back to the quarter-gear (outlined in green). At this point, the quarter-gear is completely released, and the hour-chimes will be happening in just a few minutes.

So, now, as the second bar comes crashing down at the end of the hour and the "t" bar-axle-paddle assembly starts to turn again, the quarter-gear is slowly rotated again. As the upper braking bar rides on the quarter-gear, it serves two purposes: one is to fall off the edge and stop the chiming at the required number of chimes, as determined by the shell-gear assembly. Two: as a ratcheting mechanism. The vertical protrusion will ride up each of the gear bumps, and as such, locking the gear on each toll. Of course, this vertical protrusion also locks the gear in its final cocked position after its braking rod falls off the quarter-gear lip, and then unlocks it after the braking rod lifts high enough, a few minutes before the next hourly chime.

# The "Silencer"

This thing isn't another whole section, but it's an intimate connection between the time-keeping and quarter-chime sections. This is the only component that I was never able to see in action, so this is purely based on deductive logic. At night, I assume that the bell tower needs to be hushed so that you aren't woken up every fifteen minutes to the quarter-chimes. I think this is done through a small gear assembly at the back of the machine. Looking at the gear reduction, the large gear (shown below) should rotate only once per day. There is a steep incline on one part of it, and this connects to another horizontal rod. This time, instead of pushing and pulling, this rod is transferring rotation. Where does it go?

The gear at the center of the picture is the "silencer" gear. You can see that there is a fat portion (roughly one-third) and a skinny portion.

It turns out that this horizontal rod passes through the apparatus and emerges through the other side, in the form of a hook--mounted near the secondary bar! As the silencer gear reaches the fat portion, the horizontal rod will turn such that it catches this secondary bar. By pulling the bar down and holding it there, it keeps the other end permanently up. So, even though the primary braking bar may be out of the divot, the horizontal rod and hook effectively disengage the secondary bar from the four-cliffed gear, meaning that throughout the night, this rod won't fall. Because this rod won't fall, the "t" bar will be held in place until the next morning, when the skinny portion of the silencer gear is reached and the hook disengages.

Here you can see where this horizontal rod ends up. The brass "hook" will latch onto the nut (outlined in red), holding down the secondary bar until the morning.

Did I mess up? Was my mechanical reasoning sub-par? Let me know below!

(Harsh criticism is always welcome)

Thanks for submitting!