A two escape-wheel pallet escapement is a precision regulator escapement that splits the locking and impulse functions across two coaxial or side-by-side escape wheels acting on a single pallet assembly. Top examples — like the Sigmund Riefler and Strasser style regulators — held rates within ±0.01 seconds per day in temperature-controlled rooms. The split geometry reduces pendulum interference, isolates impulse from locking friction, and was the standard for German observatory regulators from roughly 1890 to 1950 in time-service work at observatories like Hamburg-Bergedorf.
Two Escape-wheel Pallet Escapement Side Interactive Calculator
Vary wheel tooth count, phase window, and pallet swing to see the target impulse lead, tooth-pitch fraction, and escapement motion.
Equation Used
This calculator converts the escape-wheel tooth count into angular tooth pitch, then places the impulse timing at the centre of the specified phase-lead window. The phase-to-tooth value shows how much of one tooth pitch the target lead represents, while total pallet swing doubles the entered one-sided pallet arc.
- Locking and impulse wheels are matched and phased on a common or closely coupled arbor.
- Phase minimum and maximum represent the acceptable lead window after locking release.
- Pallet arc is entered as one side of the centre line, so total swing is twice that value.
- Tooth count is the effective escape-wheel tooth count used for angular pitch.
The Two Escape-wheel Pallet Escapement (side) in Action
The mechanism puts two escape wheels on the same arbor — or on closely coupled arbors — running side by side. One wheel handles locking, the other delivers impulse to the pallets. When the pendulum swings through its centre line, the locking wheel releases first, then the impulse wheel transfers a small dose of energy to the pallet flag for a few degrees of arc, then the locking wheel catches the next tooth. Because impulse and locking happen on different teeth on different wheels, you get cleaner separation of forces. The pendulum sees a near-constant supplementary arc — the small extra swing beyond what gravity alone would produce — which is what keeps the rate stable.
The geometry matters more than almost any other escapement. Tooth pitch on both wheels must be matched within roughly 0.01 mm of theoretical, and the angular phase between locking and impulse wheels must be set so that the impulse arrives only after locking has cleanly released — typically a 2° to 4° lead. If the phase is off, you get either re-locking (the pallet hits the locking face mid-impulse and the pendulum loses energy in a jerk) or trip (locking releases but impulse never arrives, and the wheel runs free for a fraction of a second). Both faults show up as erratic seconds-beat audio and a wandering rate trace.
The most common failure mode in the field is pivot-end shake on the impulse wheel arbor. End-shake above 0.03 mm lets the impulse wheel skew relative to the locking wheel, and you'll hear an uneven tick — a distinct double-beat about every fifth oscillation. Worn pallet jewels, contaminated oil on the locking faces, and a bent pendulum suspension spring round out the top four causes of rate drift in a side pallet escapement of this type.
Key Components
- Locking escape wheel: Holds the train static between impulses. Tooth count typically 30, with locking face hardened and polished to under Ra 0.05 µm. Locking depth is set by the back banking and runs 0.15 to 0.25 mm into the locking jewel.
- Impulse escape wheel: Delivers a brief, controlled push to the pallet flag during the centre portion of the pendulum swing. Tooth profile is shaped for a 3° impulse angle and the wheel is phased 2° to 4° behind the locking wheel.
- Pallet assembly (side-mounted): Carries two jewelled flags — one engaging the locking wheel, one engaging the impulse wheel. Mounted on the side rather than overhead so the pendulum suspension stays straight. Pallet arbor end-shake must stay under 0.02 mm.
- Crutch and suspension spring: Couples the pallet motion to the pendulum. Suspension spring is typically 0.10 mm Elinvar or similar low-thermal-coefficient stock, clamped square within 0.5° to avoid lateral pendulum drift.
- Pendulum: 1-second beat for most regulators, with an Invar or Elinvar rod to keep thermal expansion under 1.2 µm/m/°C. Bob mass commonly 6 to 8 kg in observatory builds for high inertia and small Q-factor sensitivity to disturbance.
Where the Two Escape-wheel Pallet Escapement (side) Is Used
The two escape-wheel pallet escapement lives almost entirely in precision timekeeping — it was never economic for domestic clocks, and it has no place in a wristwatch. The split geometry pays off only when you need the supplementary arc and the impulse-locking isolation it gives. That means observatory regulators, time-service master clocks, scientific instrument timing, and a handful of high-end horological reference standards. You'll find them named on the dials of Strasser & Rohde, Sigmund Riefler, and a few independent makers who built to that pattern.
- Observatory time service: Strasser & Rohde regulators installed at Hamburg-Bergedorf Observatory in the 1910s for transit-circle timing reference
- National timekeeping: Riefler regulators used at the Physikalisch-Technische Reichsanstalt in Berlin as primary time standards before quartz
- University horology departments: Reference regulators in the Glashütte horological school workshops for student calibration training
- Private collector restoration: Restoration of pre-1930 Strasser Nr. 3 regulators by independent conservators across Germany and the UK
- Maritime navigation training: Shore-station reference clocks used at naval observatories for chronometer rate-checking before satellite time
- Geodetic and seismic stations: Pre-1950 timing references at geodetic observatories where seconds-pulse output drove chart recorders for transit timing
The Formula Behind the Two Escape-wheel Pallet Escapement (side)
The number that matters most in setting up this escapement is the supplementary arc — the small extra swing the pendulum picks up beyond its natural free-swing amplitude because of the impulse. Too little supplementary arc and the clock stops on the slightest disturbance. Too much and circular error dominates and the rate becomes amplitude-sensitive. The sweet spot for most observatory builds sits around 1.5° of supplementary arc on top of a 2° to 3° free amplitude. At the low end of the typical range — say 0.8° supplementary — the clock runs but is fragile to pressure and temperature shifts. At the high end, 2.5° or more, you start seeing measurable rate drift with barometric pressure changes. The formula below estimates supplementary arc from the impulse energy delivered per beat and the pendulum's stored energy.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| θs | Supplementary arc added by the impulse wheel per beat | rad | rad |
| Eimp | Energy delivered to the pallet per impulse | J | ft·lbf |
| m | Pendulum bob mass | kg | lb |
| g | Local gravitational acceleration | m/s² | ft/s² |
| L | Pendulum effective length to centre of oscillation | m | ft |
| θ0 | Free pendulum amplitude (half-arc) | rad | rad |
Worked Example: Two Escape-wheel Pallet Escapement (side) in a Strasser & Rohde regulator restoration
A horological restoration atelier in Hamburg is recommissioning a 1912 Strasser & Rohde Nr. 3 observatory regulator with the two escape-wheel side pallet escapement. The pendulum bob is 7.0 kg, effective length 0.994 m for a 1-second beat at local g = 9.813 m/s², and the free amplitude measured by optical timing comes out to 2.5° (0.0436 rad). The impulse energy delivered per beat, calculated from the train torque at the escape wheel and the impulse arc, is 1.5 mJ. The shop wants to know whether the supplementary arc sits in the design window before they sign off the rate certificate.
Given
- m = 7.0 kg
- L = 0.994 m
- g = 9.813 m/s²
- θ0 = 0.0436 rad
- Eimp = 0.0015 J
Solution
Step 1 — at nominal impulse energy 1.5 mJ, compute the denominator (the pendulum's working energy term):
Step 2 — divide impulse energy by that term to get supplementary arc at nominal:
That's small in absolute terms but the right order — a Strasser regulator running properly delivers a per-beat supplementary kick in the 0.02° to 0.05° range. Multiply across many beats per amplitude decay cycle and you get the visible 1° to 2° steady-state supplementary arc.
Step 3 — at the low end of the typical impulse range (0.9 mJ, what you'd see with a partly fouled locking jewel or oil contamination):
The pendulum will still run but the steady-state amplitude will collapse below 1.8° within a few minutes of a small disturbance, and the rate will drift fast with any change in air pressure. Step 4 — at the high end (2.2 mJ, what you'd see if a fresh mainspring or unregulated remontoire is over-driving the escapement):
Now the pendulum is running too hot. Circular error dominates, and you'll see seconds-per-day rate change measurably with barometric pressure swings of just 5 mbar.
Result
Nominal supplementary arc per beat is 5. 04 × 10⁻⁴ rad, or about 0.029° — squarely inside the design window for a Strasser Nr. 3. In practice you'd watch the steady-state amplitude settle at 2.5° free arc plus the integrated supplementary contribution, with a clean even tick on the seconds beat. The low-end (0.9 mJ) case at 0.017° per beat leaves the clock fragile to disturbance, while the high-end (2.2 mJ) case at 0.042° pushes you into amplitude-sensitive rate territory. If your measured supplementary arc lands well below the predicted value, look first at impulse jewel chipping (a fractured working face drops energy transfer 30% or more), second at incorrect impulse-wheel phasing — anything beyond 5° lead causes partial trip — and third at a suspension spring clamp that's not square, which bleeds energy laterally into the pendulum mounting block instead of into useful arc.
Two Escape-wheel Pallet Escapement (side) vs Alternatives
The two escape-wheel pallet escapement is a specialist's choice. It earns its place against the Graham deadbeat and the Riefler gravity-impulse only when you genuinely need the impulse-locking isolation and you have the workshop discipline to set the wheel phasing correctly. Here's how it compares against the two escapements that share the precision-regulator territory.
| Property | Two escape-wheel pallet escapement | Graham deadbeat escapement | Riefler gravity-impulse escapement |
|---|---|---|---|
| Achievable rate accuracy (per day) | ±0.01 to —0.05 s | ±0.1 to ±1.0 s | ±0.005 to ±0.02 s |
| Setup complexity (skill hours to phase correctly) | 8-16 hours specialist | 2-4 hours competent | 20-40 hours master only |
| Sensitivity to oil condition on locking faces | Moderate — split function helps | High — single wheel friction dominates | Low — gravity arms re-energise mechanically |
| Production cost relative to deadbeat | 3-4× deadbeat | 1× baseline | 5-7× deadbeat |
| Service interval for jewel and pivot inspection | 3-5 years | 5-10 years | 2-3 years |
| Application fit | Observatory and reference regulators | General precision and turret clocks | National time-service standards |
| Tolerance to disturbance (foot traffic, pressure) | Good with proper supplementary arc | Moderate | Excellent |
Frequently Asked Questions About Two Escape-wheel Pallet Escapement (side)
That's almost certainly bedding-in of the new pallet jewels and locking surfaces. Fresh jewels on a freshly cleaned locking wheel run with slightly higher friction for the first 10⁵ to 10⁶ beats — about 1 to 2 weeks of running — until the contact patches polish in. The impulse energy delivered drops as friction settles, supplementary arc creeps up slightly, and circular error nudges the rate slower until equilibrium.
Don't chase it with the regulating nut in the first 10 days. Let it run, log the rate daily, and only adjust once the daily delta drops below 0.3 s. If it never settles, suspect a high spot on one impulse face — pull the wheel and check under 20× magnification.
Pick on the basis of your power source and your workshop capability. The Riefler isolates the pendulum from the train almost completely via the gravity arms, so it's the better choice if you want absolute insensitivity to mainspring or weight-train torque variation. But the Riefler is brutal to set up correctly — gravity arm geometry, locking depths, and arm lift timing all interact, and a 0.05 mm error anywhere shows up as rate instability.
The two escape-wheel pallet design is more forgiving in setup and gives you 80 to 90% of the Riefler's rate stability if your power source is already well regulated (a remontoire or constant-force device upstream). For a workshop without master-grade gravity-escapement experience, the side pallet escapement is the more sensible target.
A periodic double-tick at long intervals usually points to escape-wheel runout — one of the two wheels has a slightly bent arbor or a tooth that's 0.02 to 0.04 mm out of true. As the wheel rotates, that one tooth lands on the pallet at a slightly different angular position, briefly offsetting the locking-impulse phase, and you hear it as a doubled or weakened tick once per wheel revolution.
Confirm by counting beats between the audible glitches — if it matches your escape wheel tooth count divided by 2 (one wheel revolution per N beats), you've found it. The fix is to depivot, true the arbor between centres, and check tooth pitch with a depth indicator.
Slightly less, but only if you've got the supplementary arc inside the 0.025° to 0.035° per-beat window. Pressure affects rate primarily through air buoyancy on the bob (about 0.011 s/day per mbar uncorrected) and through air drag on the swinging pendulum, which interacts with the supplementary arc.
Because the split impulse-locking design lets you tune supplementary arc more precisely than a deadbeat, you can dial circular error sensitivity down further. But neither escapement is barometrically compensated by itself — for sub-0.01 s/day rates you still need an aneroid compensator or a sealed enclosure, just as the original Strasser and Riefler installations used.
The most common culprit, after pivot oil drag, is the suspension spring clamp. If the clamp blocks aren't dressed flat and parallel, the spring flexes off-axis and dissipates energy as lateral motion in the suspension bracket rather than as pendulum arc. Check the clamp faces with a marking compound — you want full contact across the spring width, not a line contact at one edge.
Second suspect is crutch slop. End-play in the crutch pin against the pendulum rod above 0.05 mm wastes a noticeable fraction of impulse energy as small free-flight events. A rule of thumb: tighten crutch fit to 0.02 mm and you'll typically recover 5 to 10% of measured impulse energy.
Mechanically possible but rarely worthwhile. The supplementary arc and impulse-locking isolation that justify the design only matter when your other error sources are already pushed below ±0.1 s/day. A turret clock with hand-set going barrel, a long crutch with thermal flex, and a non-Invar pendulum will never see the benefit — you'll spend weeks setting up an escapement whose precision the rest of the clock can't deliver.
Spend the same effort on a temperature-compensated pendulum, a remontoire, and a sealed pendulum case, and you'll get more rate improvement for less work. The two escape-wheel design belongs in a regulator built from the start around precision goals.
References & Further Reading
- Wikipedia contributors. Escapement. Wikipedia
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