A single-pin pendulum escapement is a clock escapement in which a single impulse pin — mounted on either the escape wheel or a separate impulse roller — delivers one push per swing to a pendulum through a pair of pallets. The pendulum unlocks the pin once per cycle, the pin slides across the impulse face, and the wheel advances one tooth before the next pallet catches it. Horologists use it because it needs very little drive torque and tolerates dirty pivots, which is why it shows up in skeleton clocks, novelty pendulettes, and low-cost regulators where a Graham deadbeat would be overkill.
Single-pin Pendulum Escapement Interactive Calculator
Vary pendulum beat time, gravity, impulse angle, and drop angle to see pendulum length, escape-wheel speed, and escapement geometry response.
Equation Used
The calculator uses the pendulum small-angle relation. The beat time b is one half-swing, so the full pendulum cycle is T = 2b. In a single-pin escapement the escape wheel advances one revolution per full pendulum cycle, so wheel speed is 60/T rpm. The impulse and drop sliders do not change pendulum length; they score the pallet geometry against the article guidance of about 1.5-2.5 deg impulse and about 1 deg drop.
- Small-angle pendulum approximation is used.
- Single impulse pin means the escape wheel makes one revolution per full pendulum cycle.
- Beat time is one half-swing; full cycle time is twice the beat time.
- Geometry score is advisory, centered on impulse = 2 deg and drop = 1 deg.
How the Single-pin Pendulum Escapement Works
The single-pin escapement strips the impulse function down to one steel pin and two pallet faces. On every half-swing the pendulum lifts a pallet clear of the pin, the wheel rotates until the pin lands on the impulse face of the opposite pallet, slides across that face — handing energy to the pendulum — and then the wheel locks on the next tooth. One pin, one impulse, per full pendulum cycle. Compare that to a Graham deadbeat which impulses on every half-cycle through 30 teeth, and you see immediately why the single-pin design needs an escape wheel that turns much faster for the same beat rate, but with vastly less torque demand at the pinion.
The geometry that matters is the impulse angle and the drop angle. Impulse angle is typically 1.5° to 2.5° of pendulum swing — too little and the pendulum starves on a dirty pivot, too much and amplitude climbs until the pallets bang into the pin instead of catching it cleanly. Drop is the small angular gap the wheel travels after the pin leaves one pallet before the next pallet locks. You want drop around 1° — anything below 0.5° and you risk the pin not clearing on a cold morning when oils thicken; anything above 1.5° wastes energy and you hear it as a loud, uneven tick.
If the pin is bent, off-centre, or worn flat on its leading edge, the impulse force shifts in time relative to the pendulum's centre crossing — and the clock gains or loses asymmetrically depending on which way you knock it. That's the most common failure mode you will diagnose in the field, ahead of pivot wear or hairspring drift, because the pin is a tiny component carrying every joule of drive energy through a single contact line.
Key Components
- Impulse Pin: A hardened steel pin, typically 0.6 mm to 1.2 mm diameter, mounted radially on the escape wheel or on a separate impulse roller. It is the single contact point that transfers drive energy to the pendulum each cycle. The pin must be polished and perfectly cylindrical — a flat spot of even 0.05 mm changes impulse timing measurably.
- Pallets (Locking and Impulse Faces): Two hardened pallet faces, usually agate, ruby, or hardened steel, mounted on the pendulum crutch or on a separate pallet lever. One face locks the pin between impulses; the other delivers impulse. Pallet face angle is ground to roughly 12° to 15° relative to the pin path.
- Escape Wheel: A light brass or steel wheel carrying the single impulse pin. Because there is only one impulse per revolution, the wheel rotates once per pendulum cycle — for a 1-second pendulum that is 1 revolution every 2 seconds. Wheel inertia must be low so the pin lands gently on the locking face.
- Pendulum and Crutch: Standard pendulum with a crutch that engages the pallet lever. For a seconds pendulum the rod length is 994 mm at g = 9.81 m/s². The crutch pin must have less than 0.05 mm sideshake or you lose the impulse cleanly to lost motion.
- Banking Pins: Two fixed stops that limit pallet lever travel beyond the impulse arc. They prevent the pin from over-riding the pallet on heavy amplitude. Banking pin position is set so the pallet just clears the impulse pin with about 0.2 mm safety margin.
Industries That Rely on the Single-pin Pendulum Escapement
The single-pin escapement earns its keep in clocks where simplicity, low torque demand, and tolerance to imperfect oils matter more than chronometer-grade rate stability. You see it in 19th-century French novelty work, in budget regulators, and in modern skeleton movements where the maker wants the impulse action visible to the viewer. It is rarely chosen for serious astronomical regulators because the single impulse per cycle means amplitude is more sensitive to drive train friction variation than a deadbeat of equivalent build quality.
- Horology — French clockmaking: Achille Brocot's pin-pallet escapement, patented in the 1840s, used in countless French mantel and pendulette clocks throughout the 19th century
- Horology — Skeleton clocks: Hettich Pendulum Clock skeleton movements built in Schwenningen, where the visible single-pin action is part of the display value
- Education and kit-building: Wooden pendulum clock kits like the Abong wooden gear clock and various Etsy maker-designed acrylic clock kits, where laser-cut tolerances suit a forgiving single-pin geometry
- Restoration trade: Replacement movements for 1880s–1920s American shelf clocks originally built by Seth Thomas or Ansonia, where the original pin-pallet movement is rebuilt rather than swapped to a Graham deadbeat
- Public art and installation clockwork: Large slow-rate display clocks in shopping arcades and museum lobbies — the Long Now Foundation's 10,000-Year Clock prototype escapement studies considered single-pin variants for their low torque characteristics
- Precision pendulum demonstrators: Physics-department pendulum apparatus where the instructor wants the impulse moment visible — a single pin under a strobe is far more legible than a 30-tooth deadbeat
The Formula Behind the Single-pin Pendulum Escapement
The torque a single-pin escapement demands at the escape wheel arbor depends on pendulum amplitude, impulse angle, pin radius, and drive-train friction. At the low end of the typical operating range — a small skeleton clock with a 0.5-second pendulum and 2° amplitude — required wheel torque sits at fractions of a gram-millimetre. At the nominal mid-range — a 1-second pendulum at 3° amplitude — torque demand climbs to a few gram-millimetres. Push to the high end — a 1.5-second long-pendulum regulator at 4° amplitude with a heavier bob — and torque demand can reach tens of gram-millimetres, at which point the single-pin geometry starts losing its advantage over a deadbeat. The sweet spot is firmly at the low-amplitude, light-bob end where this escapement was conceived.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Mw | Required torque at the escape wheel arbor per impulse | N·mm | oz·in |
| Eimp | Energy delivered to the pendulum per impulse, equal to the energy lost to air drag and pivot friction over one cycle | µJ | in·oz·force × radian |
| θimp | Impulse angle — the angular arc through which the pallet face contacts the pin | rad | rad |
| η | Mechanical efficiency of the pin-on-pallet contact, typically 0.55 to 0.75 depending on lubrication and pallet face polish | dimensionless | dimensionless |
Worked Example: Single-pin Pendulum Escapement in a small-batch kitchen-mantel skeleton clock build
A boutique clock workshop in Asheville, North Carolina is prototyping a 50-piece run of skeleton mantel clocks with a single-pin pendulum escapement. The pendulum is 248 mm rod length giving a 0.5-second beat, the bob is 80 g brass, and total cycle energy loss to pivot friction and air drag is measured at 12 µJ per full cycle. The workshop wants to size the mainspring barrel torque at the escape wheel arbor and see how it changes if amplitude drifts low (warm room, fresh oil) or high (cold morning, thickening oil shifts impulse timing).
Given
- Eimp = 12 µJ
- θimp (nominal, 3° amplitude) = 0.0524 rad
- η = 0.65 dimensionless
- Pendulum period = 1.0 s (full cycle, 0.5 s half-period)
Solution
Step 1 — at nominal 3° pendulum amplitude, convert impulse angle to radians and compute required wheel torque:
That is the sweet-spot torque this escapement was designed for. In gram-force-millimetres that is roughly 36 g·mm at the escape arbor — a feathery load that a fusee chain or even a modest spring barrel handles with ease.
Step 2 — at the low end of the typical range, amplitude drops to 2° (warm room, low pivot drag):
Counterintuitive but real — at lower amplitude the impulse arc shrinks and the wheel must push harder per impulse to deliver the same energy. If the workshop's pendulum settles at 2° in a quiet room they will need 50% more drive torque than nominal, which is why single-pin clocks often feel finicky to regulate.
Step 3 — at the high end, amplitude climbs to 4° (cold morning, sluggish oil increases cycle losses to ~16 µJ):
The geometry advantage at higher amplitude almost exactly cancels the increased loss — torque demand stays near nominal. But push past 5° amplitude and the pin starts slamming the pallet edge instead of landing on the impulse face cleanly, and you'll hear it as a hard, uneven tick before the rate goes off entirely.
Result
Nominal escape-wheel torque demand is 0. 36 N·mm — roughly 36 gram-millimetres, which a 30 mm spring barrel with a 0.15 mm thick mainspring delivers comfortably across an 8-day run. At 2° amplitude torque demand jumps to 0.53 N·mm; at 4° amplitude it stays near 0.35 N·mm; the practical operating window is 2.5° to 4° and the clock feels smoothest at the upper half of that band. If your prototype shows a measured torque demand 30%+ above predicted, the most likely causes are: (1) the impulse pin has developed a flat from undersized fillet at the wheel hub, shifting effective contact radius inward by 0.1 mm or more; (2) pallet face polish is below mirror finish, dropping η from 0.65 to under 0.5; or (3) the crutch pin has more than 0.05 mm sideshake and is eating impulse energy as lost motion before the pendulum even sees it.
When to Use a Single-pin Pendulum Escapement and When Not To
The single-pin escapement competes mainly against the Graham deadbeat and the recoil (anchor) escapement in pendulum work. It wins on simplicity and low torque demand, loses on rate stability and amplitude tolerance. Pick the right one against the application — not the prettiest one in the textbook.
| Property | Single-pin Pendulum Escapement | Graham Deadbeat | Recoil (Anchor) Escapement |
|---|---|---|---|
| Typical rate stability | ±10 to ±30 sec/day | ±1 to ±5 sec/day | ±20 to ±60 sec/day |
| Required drive torque (relative) | Lowest — about 0.3 to 0.5 N·mm typical | Medium — 1 to 3 N·mm typical | Medium-high — 1.5 to 4 N·mm typical |
| Pendulum amplitude needed | 2° to 4° | 1.5° to 3° | 4° to 6° |
| Manufacturing complexity | Low — 1 pin, 2 pallet faces | High — 30 precise teeth + matched pallets | Medium — 30 teeth, anchor |
| Tolerance to dirty oil | High — works dirty for years | Low — needs 5-year service interval | Medium |
| Cost (movement scale) | Lowest | Highest | Medium |
| Best application fit | Skeleton, novelty, low-cost regulators | Astronomical regulators, precision longcase | Domestic longcase, kitchen clocks |
Frequently Asked Questions About Single-pin Pendulum Escapement
Textbook circular-error theory says a longer-amplitude pendulum should run slow, not fast. If yours runs fast with higher amplitude, the cause is almost always escapement error — the impulse is being delivered before the pendulum reaches its centre crossing. On a single-pin design this happens when the locking face is worn or the pin has shifted radially outward by even 0.05 mm, causing the unlock-to-impulse delay to shrink. The pendulum gets its push earlier in the swing, which adds energy in phase advance and the rate climbs.
Diagnostic check: time the clock at two amplitudes 30 minutes apart by adjusting drive weight or spring tension. If rate moves more than 5 sec/day per degree of amplitude change, the impulse timing is your problem, not the pendulum.
Steady-state torque demand and starting torque demand are different problems. A single-pin escapement at rest sits with the pin against the locking face and zero pendulum momentum. To self-start you need the wheel torque to overcome pallet static friction AND give the pendulum enough first impulse to clear about 1.5° of arc minimum, or the next half-cycle does not unlock cleanly.
Rule of thumb: size starting torque at 2.5× to 3× steady-state demand. If your spring barrel delivers 0.4 N·mm steady-state but only 0.5 N·mm peak, that is why it will not self-start. Either increase mainspring strength or give the pendulum a manual first push of 3° as part of the start procedure.
They are close cousins but not interchangeable. Brocot's pin-pallet design has the pins on the pallet lever and a conventional toothed escape wheel — there are typically 15 to 30 teeth. The single-pin design I'm describing here puts one pin on the escape wheel itself and uses solid pallet faces.
For a 19th-century French restoration, match what was there originally. If the original movement is Brocot-style with semicircular pin-pallets visible through the dial, replace like-for-like — collectors will spot a substitution. If you are building new and want the visible single-pin animation as a design feature, the wheel-mounted single-pin variant is the right call. Brocot wins on rate stability; single-pin wins on visual drama.
An efficiency drop of that scale almost always points to surface-finish failure on the pallet impulse face. The pin slides across the impulse face for roughly 1 to 2 mm of contact length per cycle, and any roughness above Ra 0.2 µm starts dragging meaningfully. A pallet face that looks polished to the eye can easily be Ra 0.4 to 0.8 µm, especially if it was lapped on a worn diamond plate.
Diagnostic: pull the pallet, inspect the impulse face under 40× magnification with raking light. You are looking for a band of micro-scratches running parallel to the pin path. If you see them, re-lap on a fresh 6000-grit then 14000-grit diamond film, finish on chrome oxide. Efficiency typically returns to 0.6+ after this.
Uneven tick on a single-pin is almost always 'out of beat' — the pendulum's centre crossing is not aligned with the midpoint of the impulse arc. Because there is only one impulse per cycle, asymmetry that a deadbeat would mask through 30-tooth averaging shows up loud and clear here.
Fix: with the clock running, listen for tick-tock-tick-tock. If the gap between tick and tock is uneven, bend the crutch slightly in the direction of the longer interval until the intervals match. On a well-built movement this adjustment is under 0.5 mm of crutch displacement. If you cannot get it in beat with the crutch alone, the pallet lever pivot is off-centre to the wheel pivot and you have a layout error to fix at the plate.
Mechanically yes, but you will need to redesign the gear train ratios. The recoil anchor typically uses a 30-tooth escape wheel and gives 60 impulses per minute of pendulum swing on a 0.5-second pendulum. A single-pin escapement at the same beat rate needs the wheel turning at one revolution per cycle — so the pinion ratio feeding the escape wheel from the centre wheel changes substantially.
Practical rule: expect to replace the escape wheel pinion and the third wheel to suit. The mainspring barrel torque demand drops by roughly half, so the existing mainspring will run far longer between winds — typically a 30-hour movement becomes a 60+ hour movement. Owners often consider this an upgrade, but purists will not.
A clean 0.1 to 0.2 second hesitation on the locking face is normal — that is the dead interval where the pendulum is swinging through its arc with the wheel locked, and it is exactly what gives this design its modest rate-stability advantage over a recoil escapement. Hesitation is only a problem if it varies cycle-to-cycle, or if you can see the wheel actually backing up (recoil) before going forward.
If you see recoil on a design that should be deadbeat, the locking face angle is wrong — typically too steep, pushing the wheel backward as the pendulum continues its swing. Re-grind the locking face to about 12° from the radial line through the wheel centre, and the recoil disappears.
References & Further Reading
- Wikipedia contributors. Escapement. Wikipedia
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