A Three-toothed Escapement is a pendulum escapement that uses an escape wheel with only 3 teeth — one tooth releases per pendulum swing, giving 6 beats per full rotation. It solves the problem of making the escape wheel visually dramatic and mechanically slow in skeleton and feature clocks, where a normal 30-tooth wheel would spin invisibly fast. The pallets catch and release each oversized tooth in turn, transferring impulse to the pendulum. The result is a slow, theatrical escape wheel rotation — typically one full turn every 12 seconds on a 1-second pendulum — that lets the viewer actually see the escapement work.
Three-toothed Escapement Interactive Calculator
Vary tooth count, pendulum half-period, and swing arc to see escape-wheel beat timing and the animated pallet action.
Equation Used
This timing model follows the worked example: a wheel with N teeth takes two pallet beats per tooth, so beats per revolution are 2N. Multiplying by the pendulum half-period gives the visible escape-wheel rotation time.
- Uses the worked-example convention that one full escape-wheel revolution takes two pallet beats per tooth.
- Pendulum half-period is the time for one half-swing, or one beat.
- Swing arc is the peak pendulum angle on either side of center and is used in the visualizer.
How the Three-toothed Escapement Actually Works
The Three-toothed Escapement, also called the Tri-Toothed Pendulum Escapement in show-clock and skeleton-movement work, runs on a simple principle. The escape wheel carries 3 large teeth spaced 120° apart. Two pallets — entry and exit — sit on the pendulum's crutch arm, and as the pendulum swings, each pallet alternately catches a tooth, holds it briefly, then releases it so the next tooth drops onto the opposite pallet. One pendulum half-swing equals one tooth release. With a 1-second pendulum (half-period 1 second), the wheel advances one tooth per second, or 120° per second, completing a full turn every 6 seconds at 6 beats per revolution.
Why build it this way? The reason is visual and didactic. A 30-tooth deadbeat wheel running on the same pendulum turns once a minute — too fast and too small a movement per beat to register on the eye. Drop the tooth count to 3 and every beat advances the wheel a clearly visible 60° of pallet engagement. You see the escapement work. The trade-off is impulse geometry: with only 3 teeth, the pallet impulse face has to swing through a much wider arc per beat, typically 8° to 12° of pendulum arc per impulse, against the 1.5° to 3° you'd see in a Graham deadbeat. That wide impulse means the pendulum is being driven hard during a big chunk of its swing — circular error and supplementary arc become real concerns.
Get the tolerances wrong and the failure modes are immediate. If the drop angle (the gap between tooth release and the next tooth landing) falls below 1°, the wheel locks. If pallet face angles deviate by more than about 0.5° from the designed impulse angle, the clock either trips (no recoil, racing) or stalls (excessive recoil eating the drive torque). Pivot friction matters more than in a 30-tooth design because the impulse delivered per beat is 10× the energy of a fine-tooth escapement — any pivot drag manifests as visible rate variation, often 30 to 60 seconds per day.
Key Components
- Three-toothed escape wheel: The signature part — a wheel with exactly 3 teeth at 120° spacing. Tooth tip radius typically 18 to 30 mm in a skeleton clock, with tooth face length around 6 to 10 mm to give the pallet a proper impulse surface. Concentricity must be held to within 0.05 mm or the rate varies tooth-to-tooth.
- Entry and exit pallets: Hardened steel or jewelled pallets mounted on the crutch arm. The angular separation between pallet faces sets the lock angle and must match the wheel geometry to within 0.25°. The impulse face is angled 8° to 12° to drive the pendulum during release.
- Pendulum and crutch: A 1-second pendulum (994 mm rod length at standard gravity) is the usual pairing. The crutch couples pallet motion to the pendulum with as little side-shake as possible — more than 0.3 mm of crutch slop and the impulse becomes erratic.
- Drive train and mainspring or weight: Because each impulse delivers a large energy slug, the drive torque must be steady. Weight-driven setups behave better than spring-driven for this escapement; a 2 kg weight on a 30 mm barrel is typical for a 30-day skeleton clock.
- Banking pins or stops: Limit pendulum overswing. With wide impulse arcs, the pendulum can run away if the drive torque rises (e.g. a freshly wound spring), so banking is a safety net, not a normal contact surface.
Where the Three-toothed Escapement Is Used
You won't find the Three-toothed Escapement in a wristwatch or a precision regulator — it lives in clocks where the escapement itself is the show. Skeleton clocks, museum demonstration pieces, mantel features, and educational kits all use the tri-toothed pendulum escapement specifically because the slow, deliberate rotation of the escape wheel reads as the heartbeat of the clock. The accuracy you sacrifice — typically ±20 seconds per day against the ±2 seconds of a Graham — is the price of the visual drama.
- Skeleton clock manufacturing: Sinclair Harding and Dent skeleton mantel clocks have used 3-tooth and small-tooth-count escape wheels in feature movements where the buyer wants to watch the action.
- Educational kits and horology training: Bench-top demonstration escapements at horology schools like WOSTEP and BHI use 3-tooth wheels because students can see each impulse cycle clearly without a stroboscope.
- Museum and science centre exhibits: Working escapement demonstrators at the Royal Observatory Greenwich and the Deutsches Uhrenmuseum use enlarged tri-toothed pendulum escapement models to show visitors how a clock counts time.
- Custom and one-off art clocks: Independent clockmakers like Miki Eleta and Buchanan of Chelmsford have built feature movements where a 3-tooth or low-count escape wheel becomes the focal point of a sculptural clock.
- Theatrical and film prop horology: Period-piece prop clocks built for stage and screen use oversized 3-tooth escape wheels because the camera needs to read the tick visually — a 30-tooth wheel just blurs.
- Tower clock demonstration models: Smith of Derby and similar firms build scale demonstration models with 3-tooth escapements for client showrooms to explain how their tower clocks work.
The Formula Behind the Three-toothed Escapement
The headline number for any Three-toothed Escapement build is the time per revolution of the escape wheel — that's what governs the visual cadence and what the customer actually pays for. At the low end of the practical range (a half-second pendulum, T = 0.5 s), the wheel turns once every 3 seconds, which reads as a busy ticking blur on a small mantel clock. At the nominal 1-second pendulum the wheel turns once every 6 seconds — the sweet spot, slow enough to follow with the eye but quick enough to feel alive. Push to a 2-second pendulum (used in some large skeleton longcase builds) and the wheel takes 12 seconds per turn, which crosses into hypnotic-but-slow territory and can make customers think the clock has stopped.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Trev | Time for one full revolution of the escape wheel | seconds | seconds |
| Nteeth | Number of teeth on the escape wheel (3 for this mechanism) | count | count |
| Thalf | Pendulum half-period (time per beat) | seconds | seconds |
| fbeat | Beat rate (beats per second) | Hz | Hz |
Worked Example: Three-toothed Escapement in a custom skeleton mantel clock build
A custom clockmaking studio in Portland Oregon is finalising a one-off skeleton mantel clock for a private collector. The brief calls for a Three-toothed Escapement that visibly rotates without looking sluggish. The pendulum is a 670 mm rod giving a half-period of 0.82 seconds, the escape wheel has 3 teeth, and the escape wheel diameter is 60 mm. The studio needs the time per revolution to set customer expectations and to verify the impulse geometry is workable.
Given
- Nteeth = 3 teeth
- Thalf = 0.82 s
- Dwheel = 60 mm
Solution
Step 1 — at the nominal 0.82 s half-period specified in the brief, calculate one full revolution time:
Step 2 — beat rate at nominal:
Step 3 — at the low end of the practical pendulum range for this build (a 250 mm rod, Thalf ≈ 0.50 s):
At 3 seconds per revolution the wheel reads as a fast tick — the eye sees rotation but the deliberation is gone. You'd lose most of the theatrical effect that drove the design choice in the first place.
Step 4 — at the high end of the practical range (a 1 m rod giving a true 1-second pendulum, Thalf = 1.00 s):
6 seconds per revolution is the classic skeleton-clock cadence — slow enough to feel ceremonial, fast enough that the wheel is clearly alive. Most buyers prefer this end of the range.
Result
At the brief's nominal 0. 82 s half-period, the escape wheel completes one full revolution every 4.92 seconds and beats at 1.22 Hz. That cadence reads as brisk but still deliberate — you can follow each tooth release with your eye without effort. The 3-second low-end revolution feels rushed, while the 6-second high-end at a true 1-second pendulum hits the visual sweet spot most skeleton-clock buyers expect. If the studio measures actual revolution time more than 5% off the predicted 4.92 s, the usual culprits are: (1) escape wheel concentricity error above 0.05 mm causing tooth-by-tooth rate variation that averages out wrong, (2) crutch-to-pendulum side-shake exceeding 0.3 mm so impulse delivery is inconsistent, or (3) a pendulum rod that has not been properly temperature-compensated, drifting the half-period as the workshop warms.
Choosing the Three-toothed Escapement: Pros and Cons
Picking the Three-toothed Escapement against alternatives is a decision about visual presence versus accuracy. Compare it on the dimensions that actually matter — beat rate, accuracy, energy per impulse, and where it fits — against the Graham deadbeat (the precision standard) and the recoil anchor (the historical workhorse). The tri-toothed pendulum escapement is the clear visual winner but the clear accuracy loser.
| Property | Three-toothed Escapement | Graham Deadbeat | Recoil Anchor |
|---|---|---|---|
| Typical accuracy (s/day) | ±15 to ±30 | ±1 to ±5 | ±10 to ±60 |
| Beats per escape wheel revolution | 6 | 60 (30-tooth wheel) | 60 (30-tooth wheel) |
| Energy per impulse (relative) | 10× | 1× (reference) | 1.2× |
| Visual cadence | Highly visible, theatrical | Imperceptible without strobe | Visible but blurred |
| Build cost (skeleton-clock context) | High — bespoke geometry | Moderate — standard parts | Low — historical patterns |
| Best application fit | Skeleton, demo, art clocks | Precision regulators | Domestic longcase clocks |
| Pivot friction sensitivity | Very high | Moderate | Low |
Frequently Asked Questions About Three-toothed Escapement
Tooth-to-tooth rate variation in a 3-tooth wheel almost always comes down to two things: tooth profile inconsistency between the three teeth, or wheel concentricity error. Because each tooth carries a third of the wheel's angular duty, any geometric difference between teeth shows up directly in the rate every time that tooth engages.
Check the tooth impulse face angles with an optical comparator — they should match within 0.25°. Then check wheel runout on the arbor; anything above 0.05 mm TIR means the effective tooth radius changes as the wheel turns, and the impulse delivered to the pendulum varies with it. A 30-tooth wheel averages this kind of error away across many beats; a 3-tooth wheel cannot.
Yes — they are the same mechanism. Tri-Toothed Pendulum Escapement is the term used more often in modern skeleton-clock and demonstration-movement literature, while Three-toothed Escapement is the older horological description. Both refer to a pendulum escapement with exactly 3 teeth on the escape wheel, giving 6 beats per revolution.
The decision is purely about visual cadence versus impulse energy. A 3-tooth wheel gives the slowest, most theatrical rotation — one turn every 6 seconds on a 1-second pendulum — but each impulse is huge, so pivot friction and drive torque variation hit the rate hard. A 5-tooth wheel softens the impulse by 40% and turns once every 10 seconds, which still reads as a clear rotation. A 7-tooth wheel is closer to a normal escapement in feel and runs much steadier but the visual drama is mostly gone.
Rule of thumb: if the customer wants to point at the escape wheel and watch it move, go 3-tooth. If they want a skeleton clock that keeps better time and just looks interesting, 5 or 7 is the better choice.
On a Three-toothed Escapement, large positive rate errors that don't respond to pendulum length adjustment usually trace back to excessive impulse arc combined with circular error. The pendulum is being driven through a wider supplementary arc than the design assumed, and circular error makes a wide-arc pendulum run fast.
Measure the actual pendulum amplitude. If you're seeing more than about 4° peak-to-peak, the drive torque is too high — reduce the driving weight or check that the train hasn't seized partially and is dumping energy in bursts. The other common cause is pallet impulse face angle steeper than designed, which kicks the pendulum harder than it should. Both issues fix themselves with proper amplitude control.
Tripping at full power is a classic three-tooth problem. With a freshly wound mainspring or a freshly raised weight, peak drive torque spikes high. The pendulum amplitude swells, and if the safety drop angle is undersized — below about 1.5° in this escapement — the next tooth lands while the pallet hasn't fully cleared, and the wheel skips one or even two teeth in a single beat.
The fix is usually to recut the pallet angles to give a 2° to 2.5° drop angle, accepting a small efficiency loss for reliability. Alternatively, fit a remontoire or stackfreed-style torque limiter ahead of the escapement so peak torque can't spike.
You can, but the train ratios have to be reworked completely. A 30-tooth escape wheel running on a 1-second pendulum needs the train to deliver 30 beats per minute of escape wheel input — its motion work and going train are sized for that. Drop to 3 teeth and the same pendulum drives the escape wheel 10× faster relative to the rest of the train, so the centre wheel and motion work will read minutes 10× too fast unless you re-gear.
In practice, retrofits are only worth doing if you're willing to redesign the going train from the escape wheel back to the centre arbor. Most builders find it easier to start with a movement designed around the 3-tooth ratio from the outset.
References & Further Reading
- Wikipedia contributors. Escapement. Wikipedia
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