Hiscox1164 describes a detached pendulum escapement with one impulse pallet I. A bell-crank unlocks the escape wheel when it meets a balanced click C near the middle of the pendulum swing. The pendulum is otherwise detached from the wheel. The drawing below identifies those parts rather than substituting a generic anchor or gravity escapement.
Detached Pendulum · Beat and Impulse-Window Calculator
Compare target beat, local gravity, swing amplitude and one central impulse window. The drawing separates the bell-crank lock, balanced click and single impulse pallet.
Equation Used
- One beat means one swing, half a full period.
- Pendulum length is an ideal small-angle effective length.
- The time-window estimate assumes sinusoidal motion.
- One working contact passage is counted per full cycle.
- The source-specific components are I pallet, bell-crank and C click.
- Lever travel and tooth contact geometry are illustrative.
When the half-window equals amplitude it covers the full working half-cycle. A brief detached impulse requires a narrower window.
A separate lock and a single impulse pallet
The pendulum frame carries the impulse pallet and balanced click. The independently pivoted bell-crank holds the escape wheel until the click operates it near the middle of the stroke. The released wheel then acts on the single impulse pallet.
The selected demonstration shows one working release in a full pendulum cycle. During the return passage the balanced click yields while the bell-crank continues to hold the wheel. That separation makes the roles of release, impulse and free swing visible.
The source gives no dimensioned contact profiles or train ratio. The enlarged three-tooth wheel, one-tooth-per-cycle sequence, lever travel and clearances are explanatory selections. The animation does not calculate tooth impact, recoil or the dynamics of the balanced click.
Size an ideal pendulum and compare contact windows
Enter a target beat time, meaning the time for one swing from one extreme to the other. Two such beats make one full period. Local gravity sets the small-angle effective pendulum length for that target.
The amplitude and working half-window let you compare how much time a sinusoidally moving pendulum spends in the chosen impulse zone. This is one working passage per full period; the return crossing is excluded from the contact-time output.
Effective length applies to an ideal point-mass pendulum. A real rod, bob and frame require an equivalent length based on inertia and centre of mass. The illustration fits the available space and is not a scale drawing of the calculated length.
Beat time and a sinusoidal window estimate
For target beat B and local gravity g, the small-angle pendulum length is L=gB²/π². The full period is T=2B and target swings per day are86400/B.
For sinusoidal angle θ=A sin(2πt/T), the time spent in one passage from−α to+α is Δt=T asin(α/A)/π. Working contact share is100Δt/T percent. The displayed angular contact arc is2α.
The contact-time equation is an estimate based on sinusoidal motion. It is not simply the contact-angle fraction of the total swing: the pendulum moves fastest near the middle. The selected input ranges keep α≤A. At α=A, the window covers the whole working half-cycle, so that setting no longer represents a brief detached impulse.
Finite-amplitude period correction, suspension elasticity, drive torque, air resistance and escapement error are outside this small-angle sizing model.
A1 s beat with a narrow central window
At g=9.80665 m/s² and B=1 s, the small-angle effective length is about0.99362 m and the full period2 s. There are86400 target swings per day.
With amplitude±4° and impulse half-window0.5°, the selected contact arc is1°. One working passage lasts2 asin(0.5/4)/π≈0.07979 s, about3.989% of the full period.
Doubling the target beat quadruples the small-angle length and doubles the contact duration at the same angular ratio. Widening the impulse window increases contact time; increasing amplitude at a fixed window reduces it.
Detached operation is not an accuracy specification
Reducing contact with the train can reduce one source of disturbance, but the drawing alone cannot establish daily accuracy, quality factor or shock tolerance. It also does not identify this particular arrangement as a Riefler or Shortt-Synchronome mechanism.
Contact angle, contact time and energy delivered are different quantities. The calculator estimates the first two for a selected motion model; it does not compute impulse energy or a correct driving force.
Detached-pendulum questions
Is a1 s beat a1 s full period?
No. One beat is one swing; the full oscillation takes2 s.
Why is contact time not just the angular percentage?
The pendulum speed varies through its swing. The time equation follows the sinusoidal motion estimate.
Does the return click deliver another impulse?
In this selected single-impulse demonstration it yields without releasing another tooth.
Are the bell-crank and pallet dimensions suitable for manufacture?
No. Their contact profiles and clearances are explanatory, and the source provides no dimensioned design.
Primary mechanism reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, device1164, printed page286: detached pendulum, single impulse pallet I, bell-crank release and balanced click C. The enlarged geometry and phase timing are an explanatory reconstruction.
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