jes notes .

# 2024-06-18

< 2024-06-17 2024-06-22 >

## Anniversary clock

I've done some more thinking on an "anniversary clock"-style balance wheel.

Traditionally I think they use a flat spring in torsion as the "hairspring", but instead of having to mess about with spring steel, what if we instead had the balance wheel suspended from 2 strings that are separated by a small distance? As the strings twist around each other, they'll raise the balance wheel up, and as they untwist they'll drop it down again.

A bit like the spinning button toy: https://en.wikipedia.org/wiki/Whirligig

And we'd put some equivalent of "banking pins" to stop the lever part from moving too far, and then it just operates a normal escapement. But just like you can test a pendulum without having an associated escapement, I think I can test this without an associated escapement.

I'll 3d print these parts:

A ball-race bearing goes between them. I think this is necessary, because otherwise the force from hitting the banking will displace the string horizontally, which is not what we want. The friction from the bearing won't be a very big deal, because it doesn't move very far. The motion of the balance wheel is not mediated by the bearing, only the motion of the lever.

The housing is meant to be held in a vice, and then you manually wind up the string and let it settle vertically, then let the balance wheel go and measure the time taken for the lever to flip from one side to the other, and back, etc. - if the time is quite consistent then it is viable for a clock.

And then I don't know if it is enough to suspend the balance wheel directly from the lever (supported by the bearing) or whether it needs to be suspended from above, and just have the strings pass through the lever. Maybe suspending from above is better because then there's much less weight on the bearing.

Other questions:

• does the cord material matter?
• is it preferable for the holes to be further apart or closer together?
• what if the hole spacing at the balance wheel does not match the spacing at the lever?
• how can you tune the period?

Intuitively I would say the cord material does matter. You want it to behave the same regardless of temperature, humidity, etc., and you don't want it to sag over time. And you don't want string-to-string friction as it winds up. Maybe a metal wire is best? At that point are we just approximating a flat spring-steel suspension? Maybe, but that's probably OK.

I think if the hole spacing at the balance wheel does not match the spacing at the lever, then the string will twist around itself preferentially at the end where the spacing is smallest. After that is used up it will have to move down the string. So I think the effect is to reduce the period in the long arcs. If we find that it is slow in the long arcs, then separating the holes at one end might be able to help!

And intuitively I think that as the holes get closer together the "lifting" effect is reduced. I think if it lifts faster then it will tick faster, so if you want it to tick slowly you want the holes close together.

So you can tune the period by:

• changing hole spacing
• changing balance wheel moment of inertia
• changing length of string (?)

Now I need a balance wheel for this thing. I think just a plastic disc with various options for hole spacing, and provision to put M6 bolts around the perimeter.

Here it is with some braided cable:

And clip of it ticking: https://youtu.be/1C1sWnZN0pg

Here's a plot of the tick rate, tick time is in seconds:

It is reasonably consistent until it loses too much energy and then slows down rapidly. It's out of beat because the 2 wires have different amounts of tension on them.

I've learnt:

• it does work (in that it toggles the lever back and forth, as expected)
• if anything it is slightly fast in the long arcs, which we can't correct with asymmetric hole spacing
• this wire is much too stiff
• it's hard to equalise the tension on the 2 wires

I think there may be a discontinuity in the period based on how many times the string touches itself? Maybe this whole idea is fatally flawed.

I think next step is try it again but with string or thread or something. I can't see anything convenient. I'll try some thinner electrical wire instead (from the red and black spools I have).

The thin electrical wire is no good, it takes a set too easily, which means it only does about 2 ticks before stopping, and doesn't even manage to uncoil the wire all the way.

I found some thin cotton thread and tried that. Also no good. It spins for a long time, and spins a long way, and has a very low ticking frequency, which is good, except that it doesn't actually operate the lever because there is no stiffness in the string at all. The thread uncoils all the way and starts coiling up the other way, and the lever doesn't even move. I tried suspending the thread from above the lever using a screwdriver, and the lever still didn't move.

This raises another point about the stiffness of the spring: if it doesn't take much energy to coil up the spring, then you also don't get much energy from the escapement rotating the spring by 20 degrees or so.

This suggests a difference between adjusting the hole spacing on the lever vs on the balance wheel. If you increase hole spacing on the lever then I think you get more energy input from the lever, because it has to move the large part.

I'm going to try again with cotton thread but through some further-apart holes in the balance wheel.

Cotton thread through the furthest-apart holes didn't seem to help, but making the thread a lot shorter did help! I've ran out of time today to do a proper test of the tick frequency, but I've left it set up in the vice.

I would propose a redesign with:

• string suspended above the lever, to reduce load on the bearing
• holes much further apart at the lever

You can make the "holes" further apart at the lever without making the bearing any bigger, because the string doesn't really have to pass through the bearing. You just need to make the bit that the string goes through, underneath the bearing, wider. The lever will probably have to be in 2 parts though, because both the bit above and the bit below the bearing need to be too wide to pass through it.

Anyway, good progress. If it actually does have reasonably good isochronism, then the year-going clock will be a cakewalk, because it is easy to make this mechanism tick very slowly indeed.

< 2024-06-17 2024-06-22 >