An old-fashioned watch 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

A plan of the watch (gravity off). Brown's figure shows an escape-wheel with ratchet teeth, and an arbor across its top carrying two pallets. On the same arbor is a toothed sector that gears with a pinion on the balance's staff, so the balance swings several times as far as the pallets do. Here the pallets are a recoil anchor laid out as in No. 288: a 30-tooth wheel that turns counter-clockwise, with the pallets embracing 7 1/2 teeth. Above the anchor's axis, a sector of 7 teeth gears with an 8-leaf pinion on the balance's staff, so the balance turns 4 times as far as the anchor, the other way. The teeth are a clock-maker's: radial flanks inside the pitch circles and epicycloidal tips, with a little backlash. The balance has a hairspring. The only input is a constant torque on the escape-wheel (the mainspring). The anchor and balance start at rest, and the teeth pressing on the pallets set them going.

Measured

The wheel goes 0.1047 rad per beat of the balance (half a tooth; 0.1047 expected) over 12 beats. The balance turns 4.02 times as far as the anchor (4 expected). Its swing builds to a steady 19.7° either side. As in any recoil escapement, the pallets push the wheel back a little after each catch, by up to 0.011 rad. The period is 0.602 s, against 0.629 s for the balance on its spring carrying the anchor through the gearing. It runs a little quick because the recoil faces push it back toward the middle. The deepest contact after the first second is 0.09 mm.

Notes

Brown gives no sizes. In the figure the pallets' arbor lies across the wheel, with the sector and pinion at right angles to it. Here everything is laid out in one plane, with the pallets of No. 288. The gear ratio, the tooth counts and the hairspring's stiffness are choices: the stiffness is set so that the balance keeps the anchor's beat close to No. 288's pendulum. The measured ratio varies a little with the mainspring's torque, because of the backlash.

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