A mechanical escapement meters gear motion through repeated oscillator cycles. Explore an ideal timer that advances one escape-wheel tooth per complete cycle, and calculate the duration of the selected output travel.
Ideal Escapement and Gear-Ratio Calculator
Set escape-wheel tooth count, full oscillator cycles per second, escape-wheel revolutions per output revolution and desired output turns. The result is exact only for the declared ideal counting model.
Equation Used
- Exactly one tooth advances per complete oscillator cycle.
- The declared train ratio is constant and slip-free.
- Start-up, stopping, torque, friction, backlash, spring behavior, accuracy and wear are excluded.
One complete oscillator cycle advances one tooth in this model. Tooth count, gear ratio and desired output turns determine the required cycle count; the entered cycle rate determines ideal duration.
Oscillator, pallet and escape wheel
NIST describes a mechanical escapement as converting the periodic output of an oscillator into countable pulses. A primary timer patent describes one escape-wheel tooth advancing during one complete escapement cycle.
This page adopts that specific one-tooth-per-full-cycle convention. It avoids the ambiguous word beat, which may mean a half-cycle in some contexts.
Ideal timer duration
Use the calculator to relate oscillator cycles and gear ratio to ideal output speed and duration. It does not select, calibrate, troubleshoot or certify a timer, escapement, spring, contact, appliance or safety function.
Cycle and ratio identities
N is escape-wheel teeth, f is full oscillator cycles per second, G is escape-wheel revolutions per output revolution and R is desired output turns.
Ideal counting example
With 15 escape-wheel teeth, 4 full cycles per second, a 600:1 escape/output revolution ratio and one output turn, the calculation gives 9,000 cycles, 37.50 minutes, 16 rpm at the escape wheel and 0.02667 rpm at the output.
Limits of the ideal timer calculation
Real performance depends on the exact timer, oscillator, escapement, gear train, spring, lubrication, loads and environment.
Mechanical timer questions
Is a cycle the same as a tick?
Not necessarily. This calculator deliberately uses complete oscillator cycles and assumes one tooth per complete cycle.
Does the duration predict real accuracy?
No. It is an ideal count based on an entered constant cycle rate and ratio.
Does it size a mainspring or electrical contact?
No.
Primary and authoritative references
- NIST, A Stopwatch and Timer Calibration Guide: balance wheel, escapement, spring energy and impulses.
- NIST, How Do We Know What Time It Is?: periodic oscillators, mechanical escapements, pulses and counting ticks.
- US2431395A, Timer escapement: one escape-wheel tooth per full escapement cycle.
- CN215680541U, Mechanical timer: gear train, escape wheel, pallet and periodic tooth advance.
Building or designing a mechanism like this?
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