An escapement meters gear-train motion and supplies impulse to an oscillator. This animation shows a Graham-pattern dead-beat clock escapement, with two pallets alternately locking and releasing the escape wheel.
Dead-beat lock, release and impulse
This model follows Hiscox figure 1171. The pendulum rocks an anchor carrying two pallets. One pallet releases a tooth, the escape wheel advances approximately half a tooth pitch during that beat, and the opposite pallet catches the next tooth.
The locking faces are concentric with the anchor axis. Continued pendulum motion while locked therefore does not force the escape wheel backward, which is the defining dead-beat feature.
Scope of this form
Dead-beat escapements are associated with pendulum clocks and regulators. Watches, chronometers, turret clocks and mechanical timers can use different escapement families and should not be inferred from this one diagram.
Ideal pendulum and wheel timing
For pendulum length L and gravity g, the small-angle period is T=2pi sqrt(L/g). There are two beats per period, so beat interval is T/2 and beat rate is 120/T beats per minute.
An ordinary two-pallet anchor advances about half a tooth pitch per beat, or one tooth pitch per full pendulum period. For N teeth, ideal escape-wheel speed is 60/(N T) rpm.
Dead-beat Clock Escapement Interactive Calculator
Watch a Graham-pattern dead-beat escapement alternate lock, release and impulse. Calculate ideal pendulum timing and escape-wheel speed.
Equation Used
T=2pi sqrt(L/g); beat interval=T/2; beats/min=120/T; wheel rpm=60/(N T).
Ideal small-angle pendulum timing. The escape wheel advances one tooth pitch per full pendulum period in this two-pallet model.
- Graham-pattern dead-beat anchor form.
- Small pendulum angle and ideal point-mass timing.
- Half-tooth-pitch advance per beat.
- No friction, circular error, impulse disturbance or temperature compensation.
This is a Graham-pattern dead-beat teaching model, not every escapement form. The ideal small-angle pendulum equation omits circular error, impulse disturbance, air drag, suspension elasticity and temperature effects. Tooth and pallet proportions are schematic.
One-metre pendulum example
At L=1.0 m and g=9.80665 m/s2, ideal period is about 2.006 s, beat interval about 1.003 s and beat rate about 59.82 beats/min. A 30-tooth escape wheel then turns about 0.997 rpm.
Scope and limitations
The equation is an ideal small-angle timing relation. The animation enlarges teeth and pallets and slows playback for observation. It does not calculate pallet layout, drop, lock, impulse energy, recoil, friction, wear, rate error or strength.
Questions
Does every escapement look like this?
No. This is a Graham-pattern dead-beat clock escapement.
Why does the wheel stop between releases?
A pallet locks a tooth until the pendulum moves the anchor far enough to release it.
Why is wheel speed 60/(NT)?
Two beats make one full pendulum period and advance one tooth pitch, so N periods produce one wheel revolution.
Primary reference
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