Arnold’s chronometer or free escapement, sometimes used in watches
Arnold’s chronometer or free escapement, sometimes used in watches. A spring, A, is fixed or screwed against the plate of the watch at b. To the under side of this spring is attached a small stop, d, against which rest successively the teeth of the escape-wheel, B; and on the top of spring is fixed a stud, i, holding a lighter and more flexible spring which passes under a hook, k, at the extremity of A, so that it is free on being depressed, but in rising would lift A. On the axis of the balance is a small stud, a, which touches the thin spring at each oscillation of balance-wheel. When the movement is in the direction shown by the arrow, the stud depresses the spring in passing, but on returning raises it and the spring, A, and stop, d, and thus allows one tooth of escape-wheel to pass, letting them fall immediately to arrest the next. At the same time that this tooth escapes another strikes against the side of the notch, g, and restores to balance-wheel the force lost during a vibration. It will be understood that only at one point is the free movement of balance opposed during an oscillation.
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, so gravity is off. The balance turns on its axis a, held by its balance spring (a joint spring) for a 1.0026 s vibration pair. Its rim is behind the plate. In front it carries a small roller with the impulse pallet (the side of the notch g) and, in front of that, the discharging stud a. The 12-toothed escape-wheel B is urged clockwise by a constant torque (the mainspring). A tooth rests on the stop d under the detent spring A, a light blade from its foot b, sprung down onto its banking. On A, at the stud i, the lighter passing spring runs out under the stud's path and lies up against the hook k at A's end; it is a hinge on A whose upper stop is the hook. Swinging clockwise (Brown's arrow), the stud bends the passing spring down and A does not move. Swinging back, the stud lifts the passing spring, which bears on k and lifts A and d. One tooth escapes, the next at once strikes the pallet and pushes the balance on, and A falls back to arrest the following tooth. The only input is the torque on the wheel.
- Measured
- The balance is let go 2.2 rad from its rest and runs on by itself. The wheel goes exactly one tooth each vibration pair (0.2618 rad a beat over 16 beats). The swing grows to 139.5° and holds (135.8° in the first third of the window). The period is 1.0060 s against the free balance's 1.0026 s (0.3% slow): the balance is touched only while the stud passes the spring and the tooth gives the impulse. The wheel bounces back at most 0.012 rad when the stop catches it. The deepest contact is 0.33 mm.
- Notes
- Brown gives no sizes. The tooth count, the springs' stiffnesses and the balance's starting twist are choices. The detent and passing springs are modelled as stiff blades on sprung hinges, not as bending blades. The balance spring is a joint spring and is not drawn. A chronometer is not self-starting, so the balance is set going by hand: it starts turned 2.2 rad from its spring's free position.
Film (MP4) · Still (PNG) · Spec (YAML) · Model (MJCF)
