## Thursday, August 25, 2022

### Last experiments with prototype #4

For a last round of experiments on prototype 4, I looked at the effect of the weight and drum size. I had been fixing the seconds wheel to its arbor with a set screw. I think this still resulted in extra friction, either from constraining the meshing with the other gears, or (more likely) because of friction between the seconds arbor and the minute tube. For the next experiments, I removed the set screw. The second arbor (and hand) no longer turn, of course, but the friction is significantly less.

How does the weight affect the running of the clock? I tried different weights, and in each case measured the swing of the pendulum against a ruler. Some minor trigonometry turns this into the swing in degrees, each side of the center. Here's a graph of how things change, showing the angle against the weight in grammes. The values are approximate:

Two things are noticeable here. First, in this low friction configuration, you can reduce the weight to a really low value. It would still just about run with only 160g, though at this level any slight upset (such as a strong draft of air) could stop it. Second, it's really apparent that a small relative increase in the weight matters a lot more for small weights than for larger ones: the relationship is not linear.

I measured the the weight to drop at about 17.6 cm/hour. The drum is 50mm in diameter, so you expect this to be more like 15.7 cm/hour. I haven't adjust the pendulum length, and I estimate the clock is running about 10% fast, so from it's point of view, it is 17.6cm per 66 minutes, which is 16.0 cm/hr, closer to what it should be. At this rate, the clock would run for 10 hours on a 1.6m (5 foot) drop.

Next, I swapped out the weight drum for one with half the diameter. Now we would expect 7.85 cm/hr. The measured value was 9.4 cm/hr, or after correcting for the clock running fast 8.5 cm/hr. It's a bigger discrepancy than before; I'm not sure why. This would give a run time of a little under 19 hours. The minimum weight in this case was around 400g. Even with my larger 1100g weight, the running was a little flaky, and this proved to be that minute wheel was sliding backwards on it arbor and sometimes interfering with the escape wheel. As I've iterated on the design, I've been using slacker tolerances on the spacers, and I think I've taken it too far.

Finally I did a crude version of doubling by looping the weight cord through the top of the weight and clipping the end of it to the frame. It runs, though a little weakly at 1100g, giving 4.8 cm/hr. After the 10% correction, this would run for 37 hours on a 1.6m drop, which is starting to look good.

The smallest weight I tried was around 700g, and it ran better with this than I expected.

I wanted to try using a reduction gear from the weight to the minute wheel, but the frame design doesn't allow enough space for anything other than 1:1.

What next?

This is as far as I intend to take prototype 4. I have a number of ideas for the next version:

1. Change to cycloidal gears. There is some argument that they have lower friction (ref 1, ref 2), though I think I have seen this disputed. In any case, redesign the gears so that there is more clearance.
2. Change the geometry by flipping G1 to put the escape part at the front and the pinion (gear) at the back. Then G2 can be flipped as well. This may help reduce the change of G3 running into the G2 hub.
3. Make a fixed position for the pendulum. It still needs to be movable, to set the beat, but the experiments I did on its horizontal position show that it doesn't matter.
4. Stronger clicks in the ratchet. One broke off.
5. Redesign the escape wheel teeth. This goes with the previous one. They need to be designed to that the slice better. Currently both of them have odd profiles due to the slicer switching the number of perimeters at the narrow points.
6. Make the two intermediate wheels, G3 and G5, smaller, by changing the gear ratios around. The point of this is so that the pillars between the front and back of the clock can be moved to make more space for different ratios in the winding gear. Alternatively make pillars which are curved to allow extra space.
7. Consider changing the period of the pendulum, and the number of teeth on the escapement gear and the seconds wheel so that they are not commensurate (i.e. don't have prime factors in common). This reduces the risk of a specific pair of gear teeth being a problem.
8. Change the seconds, minutes and hours arrangement that end up at the hands. In prototype 4, the seconds arbor is a 3mm rod, the minutes uses a brass 4mm tube, and the hours uses a printed tube as part of the gear. I'm considering an arrangement where there is a 3mm arbor (or smaller) rigidly fixed into the frame, and each of the seconds, minutes and hours gears has a printed tube, nested on the arbor. It will take more space but might overcome the extra friction I think I saw when the seconds wheel was rigidly fixed to the arbor. Other options might work here.
9. Make the spacers have stricter tolerances. You want some endshake on each gear, but they have become too slack as I've made the tolerances gradually looser.