An old-fashioned clock escapement

Only the input is driven; every other part of this model moves by physics (MuJoCo), and its ratios are measured. Run it live, change its parameters, or switch the friction off to see the output stop.

Modelled as

Gravity on. Brown's figure is a side view of a crown-wheel, its rim hatched and its sawtooth teeth standing up, with the verge seen end-on above it. Two pallets on the verge, at about a right angle to each other, reach down to the teeth on the near and far sides of the wheel. Here, as in No. 234, a crown-wheel of 15 sawtooth teeth turns on an upright axle under a constant torque (the clock's weight). An odd number of teeth means a tooth stands at one end of a diameter when a space is at the other. The verge lies across the wheel 3.7 above the rim. Its two pallets, 3 long, lean 47° either side of straight down (94° apart) over the teeth at the two ends of the diameter. The old clocks hung a short pendulum on the verge itself, and so does this one: a rod and a bob, 10 from the verge to the bob's centre, outside the wheel. A tooth pushes one pallet aside and the verge swings. The other pallet swings down in front of a tooth on the far side, which stops the wheel, drives the verge back (the recoil) and escapes in turn. The only input is the torque on the wheel. The pendulum starts hanging at rest.

Measured

The wheel goes 0.2092 rad per beat (half a tooth; 0.2094 expected) over 25 beats. The pendulum's swing settles at about 12.5° either side. The period is 0.579 s against 0.629 s for the pendulum swinging freely. The verge is well known for this: its pallets push the pendulum back on every beat, so it runs quick, and its rate depends on the drive. A lighter weight gives a smaller swing and a period nearer the free one. The deepest contact is 0.06 mm.

Notes

Brown gives no sizes. The wheel, verge and pallets are No. 234's, with the pallets leaning a little further, to suit the figure's near right angle. The pendulum's length and bob are choices. The camera looks along the verge from slightly to one side and above, so that both pallets and the pendulum can be seen.

Film (MP4) · Still (PNG) · Spec (YAML) · Model (MJCF)