A modified three-legged gravity escapement with stopping teeth is a pendulum escapement that uses two coaxial three-legged escape wheels and a separate set of stopping pins to deliver a fixed gravity-arm impulse to the pendulum once per beat. Turret clockmakers rely on it because mainspring or weight-train torque variation never reaches the pendulum — only the constant weight of the lifting arm does. That isolation is what made the Westminster clock at the Palace of Westminster keep public time to within a second a week.
Modified Three-legged with Stopping Teeth Interactive Calculator
Vary wheel radius, lifting-leg tolerance, and stopping-pin drift to see impulse symmetry error and trip risk in the escapement.
Equation Used
The calculator follows the article's tolerance rule: a 0.05 mm lifting-leg radius tolerance on a 75 mm wheel corresponds to about 1% impulse symmetry error. Stopping-pin drift is compared with that leg tolerance; when drift is several times larger, the pin can lock or release at the wrong instant and the pendulum can trip.
- Uses the article rule of thumb that 0.05 mm leg tolerance on a 75 mm wheel corresponds to about 1% impulse symmetry error.
- Stopping-pin drift is compared directly with lifting-leg tolerance as a trip-risk indicator.
- Positive train isolation assumes the gravity arm, not train torque, delivers the pendulum impulse.
How the Modified Three-legged with Stopping Teeth Works
The mechanism works by separating two jobs that older recoil and deadbeat escapements try to do at once. The escape wheels never push the pendulum directly. Instead, each swing of the pendulum lifts a small gravity arm — a pivoted lever weighted by a brass slug — and on the return swing that arm falls a fixed angular distance onto an impulse pallet on the pendulum rod. The fall delivers the impulse. Because gravity does not vary with train torque, the energy delivered every beat is identical to within the precision of the arm geometry, which is what readers usually mean when they ask why this escapement is so accurate.
The stopping teeth are the part that gives the modified version its name. On Lord Grimthorpe's original double three-legged design the escape wheels themselves carried both the lifting lobes and the locking faces, which meant a single chipped tooth could halt the clock. The modified arrangement places three stopping pins on a separate disc, offset axially from the lifting legs, so the locking action and the lifting action no longer share the same surface. If you machine the lifting legs to within ±0.05 mm of nominal radius but let the stopping pin radius drift by 0.2 mm, you will see the pendulum trip — the leg lifts the gravity arm before the stopping pin has cleared, and the train stalls or runs away depending on direction. The fly fan on the back of the train absorbs the kinetic energy left in the wheels at the moment of locking. Without it the stopping pins hammer themselves flat inside a year.
Common failure modes are predictable. Worn pivot holes in the gravity arms let the arms drop further than designed, which over-impulses the pendulum and the clock gains. A bent stopping pin shifts the locking instant by a few milliseconds and the beat goes audibly uneven — clockmakers call this being out of beat. Oil migration from the lifting legs onto the impulse pallet contaminates the pallet face and the pendulum starts losing amplitude within weeks.
Key Components
- Three-legged escape wheels (pair): Two coaxial wheels, each with three lifting legs spaced at 120°, mounted with a 60° angular offset so one wheel acts on each pendulum swing. Leg radius tolerance should hold ±0.05 mm on a 75 mm wheel to keep impulse symmetry within 1%.
- Stopping teeth (pin disc): Three hardened steel pins on a separate disc, offset axially from the lifting legs by 8-12 mm, that arrest the train at the end of each lift. Separating them from the lifting legs is the modification — it prevents a single damaged surface from killing both functions.
- Gravity arms (left and right): Two pivoted brass arms weighted to deliver a fixed impulse, typically 1.5 to 4 g·cm of effective torque depending on pendulum mass. The pivots must run in jewelled or hardened steel bushes — plain brass pivots wear oval inside two years and the impulse drops.
- Impulse pallet: A polished steel block on the pendulum rod that catches the falling gravity arm. Surface finish matters — Ra above 0.4 µm doubles friction loss and the pendulum amplitude drops by 0.5° within a month.
- Fly fan: Two-bladed air brake on the high-speed end of the train, sized to dissipate the kinetic energy released between unlocking and locking. Without the fan, stopping pins peen over and locking becomes unreliable inside 6-12 months.
- Locking detents: Spring-loaded detent pawls that hold the stopping disc against the pin during the locked phase. Detent spring force should sit between 5-15 grams — too light and the train trips on vibration, too heavy and the unlocking impulse robs energy from the pendulum.
Industries That Rely on the Modified Three-legged with Stopping Teeth
This escapement lives almost exclusively in tower clocks, regulators, and high-precision public timekeepers where temperature, weather, and dirt make a constant-impulse drive worth its complexity. You see it anywhere a mechanical pendulum has to keep public time without electrical assistance, and you see it in observatory regulators built before quartz took over.
- Public tower clocks: The Great Clock at the Palace of Westminster (Big Ben), built by Edward John Dent to Lord Grimthorpe's specification in 1859, runs a double three-legged gravity escapement and is the canonical implementation.
- University and college clocks: Trinity College Cambridge clock and the King's Cross station clock both use Grimthorpe-pattern escapements with separate stopping teeth.
- Observatory regulators: Dent and Frodsham astronomical regulators of the late 19th century occasionally used a single three-legged gravity escapement with stopping pins for sidereal timekeeping installations.
- Civic and cathedral installations: Manchester Town Hall clock and the cathedral clock at St Paul's both run gravity escapements derived directly from the Grimthorpe pattern.
- Railway terminus clocks: Several Great Western Railway terminus clocks built by Smith of Derby in the 1880s used the modified three-legged design for resistance to wind-loading on long minute hands.
- Restoration and heritage horology: Smith of Derby and Cumbria Clock Company still rebuild original Grimthorpe-pattern escapements for listed-building turret clock restorations across the UK.
The Formula Behind the Modified Three-legged with Stopping Teeth
The number that matters most for this escapement is the energy delivered to the pendulum per beat, because that energy must exceed the air-drag and pivot losses of the pendulum or amplitude collapses. At the low end of the typical range — small turret clocks with a 1-second pendulum and a 30 kg bob — you need about 0.3 mJ per beat. At the nominal Westminster scale with a 300 kg bob and a 2-second pendulum you need closer to 4 mJ. Push the gravity arm fall angle past about 4° and the impulse becomes too violent, the pendulum overshoots, and the rate becomes amplitude-dependent — exactly the fault Grimthorpe was trying to engineer out.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Eimp | Energy delivered to the pendulum per impulse | J (joules) | ft·lbf |
| marm | Effective mass of the gravity arm acting at its centre of gravity | kg | lb |
| g | Local gravitational acceleration | 9.81 m/s² | 32.2 ft/s² |
| Larm | Distance from gravity arm pivot to its centre of gravity | m | in |
| θfall | Angular fall of the gravity arm between fully lifted and resting on the impulse pallet | radians (or °) | radians (or °) |
Worked Example: Modified Three-legged with Stopping Teeth in a Victorian municipal town hall clock
A municipal restoration team in Leeds is recommissioning an 1885 Potts of Leeds turret clock with a 1.5-second pendulum, a 120 kg cast-iron bob, and a modified three-legged gravity escapement with separate stopping teeth. The gravity arms each carry a brass slug giving an effective mass of 0.18 kg at a pivot-to-CG distance of 110 mm. The original drawings call for a 3° fall angle. You need to verify the impulse energy is sufficient to maintain the measured pendulum loss of roughly 1.6 mJ per beat.
Given
- marm = 0.18 kg
- g = 9.81 m/s²
- Larm = 0.110 m
- θfall = 3 °
Solution
Step 1 — convert the nominal fall angle from degrees to radians and compute (1 − cos θ):
1 − cos(3°) = 1 − 0.99863 = 0.00137
Step 2 — calculate the impulse energy at the nominal 3° fall:
Both arms fire on alternate beats, so per-beat impulse is 0.27 mJ — well below the 1.6 mJ pendulum loss. That means the original 3° figure on the drawing is wrong, or the arm mass has been reduced by a previous restorer fitting lighter slugs. A 0.27 mJ impulse on a 120 kg bob would let the pendulum die down to a sub-degree amplitude inside an hour.
Step 3 — at the low end of practical fall angle, 2°, the impulse drops further:
At the high end of safe operation, around 4.5°:
Even at 4.5°, with the present 0.18 kg arms you cannot reach 1.6 mJ per beat. The realistic fix is to increase the gravity arm effective mass to roughly 1.1 kg at Larm = 110 mm and θfall = 3°, which gives E ≈ 1.63 mJ — matching the measured loss with the design fall angle preserved. That is consistent with the original Potts pattern books, which list a 1.0-1.2 kg arm slug for a 120 kg bob.
Result
Nominal impulse with the present 0. 18 kg arms at 3° fall is 0.27 mJ per beat — roughly six times too low for the measured 1.6 mJ pendulum loss, which is why the clock would not maintain amplitude after the previous restoration. The low-end 2° figure of 0.12 mJ shows how steeply the energy collapses at small fall angles, while the high-end 4.5° figure of 0.60 mJ proves you cannot solve the problem by increasing the fall — you must increase the arm mass back to the original ~1.1 kg. If a rebuilt clock measures impulse below prediction, look first for: (1) gravity arm slugs replaced with lighter brass during a non-specialist service, (2) worn arm pivot holes letting the arm bottom on the impulse pallet before completing its full angular fall, or (3) a bent or peened stopping pin shifting the lift-start position so θfall is effectively reduced by 0.5-1°.
Choosing the Modified Three-legged with Stopping Teeth: Pros and Cons
Gravity escapements are not the right answer for every pendulum clock — they are heavy, expensive to make, and need a fly fan and a stiff train. Compare them against the two escapements you would actually choose between for a serious pendulum installation.
| Property | Modified three-legged with stopping teeth | Graham deadbeat | Original Grimthorpe double three-legged |
|---|---|---|---|
| Timekeeping accuracy (long-term) | ±0.5 s/week typical, ±0.1 s/week achievable | ±5-10 s/week typical | ±0.5 s/week typical |
| Sensitivity to train torque variation | Effectively zero — gravity arm isolates pendulum | Direct — torque changes amplitude and rate | Effectively zero |
| Tolerance to dirt and weather (turret use) | High — separated stopping teeth resist single-point failure | Low — pallet contamination changes rate quickly | Medium — combined lift/lock surface is a wear point |
| Manufacturing complexity | High — two wheels plus separate pin disc plus arms | Low — single escape wheel and two pallets | High — two wheels with combined surfaces |
| Service interval before measurable rate drift | 8-12 years | 2-3 years | 5-8 years |
| Suitable pendulum mass range | 30-300+ kg | 1-30 kg | 30-300+ kg |
| Cost to rebuild from scratch (UK 2024) | £12,000-£25,000 | £3,000-£6,000 | £14,000-£28,000 |
Frequently Asked Questions About Modified Three-legged with Stopping Teeth
Almost always the gravity arms are over-impulsing the pendulum. If a previous restorer machined the impulse pallet thicker than original, the gravity arm falls a slightly larger angle than designed and dumps more energy per beat. The pendulum amplitude rises, and on a circular-error pendulum a higher amplitude makes the clock gain.
Check pallet thickness against the original drawing — a 0.3 mm increase on a 110 mm arm length is enough to add 5 seconds a day. Re-cutting the pallet is the correct fix, not shifting the bob.
The single design difference — putting stopping pins on a separate disc instead of integrating them into the escape wheel teeth — roughly doubles the service interval before the locking surfaces need refacing. On the original Grimthorpe pattern, every unlocking event hammers the same tooth surface that also handles lifting, so wear concentrates at one point. Separating those functions spreads wear across two parts that can be individually replaced.
For a clock expected to run 100+ years between major overhauls — which is the design life of any serious civic installation — the modified pattern pays for itself the first time you avoid an escape-wheel rebuild.
This is the classic symptom of a tripping escapement. One of the stopping pins is too short, or the detent spring force is too low, and an external disturbance — wind on the hands, a heavy bell strike — lets the train trip past one stopping position and lock on the next. You lose roughly half a beat of time, which on a 1.5-second pendulum is exactly the order of error you are seeing.
Diagnostic check: watch the escape wheel by torchlight during a gust or during the strike. If you see the wheel jump two pin positions instead of one, the detent spring needs reinforcement to about 12-15 grams of holding force.
The fly fan has to absorb the kinetic energy left in the train at the moment the stopping pin engages. Rule of thumb: size the fan so the train decelerates from full speed to locked in roughly 200-400 ms. Too fast and the pin takes a hammer blow that peens it within a year. Too slow and the lifting phase eats into the locked-rest period that the pendulum needs.
For a typical Westminster-scale train, that means a two-bladed fan of 150-200 mm span on the highest-speed arbor. You tune by trimming blade area — start oversized and reduce until the audible click of the stopping pin becomes a soft tick rather than a sharp tap.
The escapement does deliver constant energy to within fractions of a percent. What varies seasonally is pendulum air drag — humid summer air at 25 °C has roughly 8% lower density than dry winter air at 0 °C, which changes the energy a swinging bob loses per cycle. Constant impulse in, varying loss out, equals varying amplitude.
This is why the most accurate gravity-escapement clocks — the Shortt free pendulum and the Riefler — eventually went into vacuum tanks. For a turret clock, accept the seasonal amplitude variation and use a pendulum design with low circular error so that rate stays nearly amplitude-independent.
Mechanically yes, but it is rarely the right call on an original. The retrofit requires a new arbor extension to carry the pin disc plus matched detents, and on a listed-building original you destroy the historical authenticity of the movement. The conservation standard is to maintain the original architecture and accept the shorter service interval.
The retrofit makes sense only on a 20th-century reproduction or on a movement that has already been heavily modified. In that case offset the pin disc by 8-12 mm axially and machine the pins from hardened EN24T steel to resist peening from the fly fan release energy.
References & Further Reading
- Wikipedia contributors. Gravity escapement. Wikipedia
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