The double three-legged gravity escapement uses two locking wheels on a common arbor, with one shared set of three lifting pins between them. The pins reset two weighted arms; the arms fall against the pendulum to supply impulse. The train supplies the extra lift, while alternate locking contacts let the common arbor advance 60° at each beat.
Double Three-Legged Gravity Escapement · Energy and Timing
Enter one arm’s mass, its extra COM rise supplied by the train and the beat interval. Compare available gravitational energy and a selected 60° transfer duration.
Equation Used
- Two three-legged locking wheels share one arbor.
- A common set of three pins raises the gravity arms.
- Each alternating release advances 60°.
- Equal arms supply one extra gravitational drop per beat.
- Entered rise is the extra vertical displacement of the full arm COM.
- The drawing enlarges motion and uses selected contact profiles.
The model does not size the fly, predict contact stresses or establish clock accuracy. Available gravitational energy is an ideal upper estimate before losses.
Two locking planes and one shared lifting-pin set
Brown 311 shows the two locking wheels separated enough for the gravity-arm pallets to lie between them. Each wheel has three legs and meets the stop on its corresponding arm. The animation uses blue and red to distinguish these two axial planes.
The three pins near the arbor raise the arms. As the pendulum travels outward, it carries one arm farther outward and releases a locking leg. The wheel train advances until the other wheel locks. On the pendulum’s return, the falling arm bears against it.
The pendulum gives back part of the energy it received when it lifted an arm itself. The useful net addition comes from the extra lift supplied by the wheel’s pins. The calculator therefore uses that extra rise of the arm’s centre of mass, not its complete excursion.
Measure the extra lift and estimate available energy
Enter the mass of one complete gravity arm and the extra vertical rise of that arm’s centre of mass caused by the train. If the arm is not a point mass, use its total mass and the rise of its actual centre of mass.
One of the two arms supplies impulse at each beat. For equal arms and equal extra rise, the ideal energy per beat is mgh. Counting both arms on every beat would double-count the energy.
The last control selects the time assigned to a60° wheel step. It changes the slowed animation’s transfer duration and the mean step-speed calculation. It is not a computed fly stopping time or a prediction of aerodynamic drag.
Extra potential energy and wheel timing
With mass m in kilograms, extra centre-of-mass rise h in metres and g=9.80665 m/s², the available potential energy per beat is E=mgh joules. Mean ideal power is P=E/B watts, where B is the time between alternate releases.
The full pendulum period is2B. With60° per beat, mean common-shaft speed is10/B rpm. For a selected step-time share q percent, step duration is tₛ=Bq/100 and mean angular speed during that step is60/tₛ degrees/s.
Daily extra energy is E×86400/B. The energy outputs exclude losses in pivots and contact, so they are available-energy estimates rather than a measurement of energy actually delivered to the pendulum.
The arms and contact travels are enlarged to make the sequence readable. The entered COM rise remains a measured physical quantity; it is not inferred from the illustrative drawing.
50 g lifted an extra3 mm every1.5 s
E=0.050×9.80665×0.003≈0.001471 J, or1.471 mJ per beat. At a1.5 s beat the ideal mean power is about0.981 mW. The full pendulum period is3 s and mean escape-arbor speed6.667 rpm.
If the wheel step occupies10% of the beat, its selected duration is0.15 s. A60° movement in that time has a mean angular speed of400°/s. That is the average during movement, not the peak speed and not the shaft’s mean speed over its stops.
The mass/rise/beat example corresponds approximately to values reported by the Trinity College clockkeeper. It is not a universal specification for all gravity escapements.
What the fly and gravity arms do
The fly helps control the rapid wheel transfer between locking events. The drawing shows it during those transfers, but does not solve its air resistance, inertia or gearing. A prescribed step duration cannot establish a suitable fan size.
The gravity arms reduce direct dependence of the pendulum impulse on the train’s drive torque. This does not make a real clock independent of friction, temperature, air pressure, wear or setup. No daily accuracy or universal repair tolerance follows from this calculation.
Gravity-escapement questions
Are there three lifting pins on each wheel?
In the arrangement shown, one common set of three pins lies between the two locking wheels.
Why not use the arm’s total drop?
Part of that excursion was supplied by the pendulum. The calculator counts the extra height supplied by the train, which is the net additional gravitational energy available.
Why is only one arm counted per beat?
The two arms alternate. Each full pendulum cycle contains two beats and two impulses.
Does the fly control set an actual stopping time?
No. It supplies a chosen transfer duration for comparison; braking dynamics are not solved.
Mechanism and operating references
Henry T. Brown, 507 Mechanical Movements, movement311: two spaced locking wheels, separate pallet stops and one lifting-pin set between the wheels.
Hugh Hunt, Trinity College clock, escapement explanation and animation: separate locking planes, three lifting pins, gravity-arm energy and the approximately50 g/3 mm/1.5 s example.
Bryan Mumford, The Gravity Escapement: direct observation of the Santa Barbara Courthouse clock, including the distinction between pendulum-supplied arm motion and the extra lift supplied by the pins. This drawing is a new explanatory reconstruction.
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