A stud escapement is a clock escapement in which studs on the escape wheel alternately rest on a front pallet and a rear pallet. Henry T. Brown's movement 292 states that the pallet curves are arcs described from the pallet arbor F, making the arrangement a repose or dead-beat escapement. The calculator below reports only ideal torque-radius and angular-work arithmetic; it does not predict oscillator impulse, rate, wear or safe dimensions.
Stud Escapement Interactive Calculator
Enter a constant wheel torque, stud-circle diameter, total equally spaced stud count and an angular drop. The animation shows alternating front and rear repose pallets. The results describe ideal torque, work and stud spacing, independently of the illustrated lock-and-release timing.
Equation Used
- T is constant over the entered angular drop and acts about the wheel axis.
- D is the diameter through the stud centers, so r = D/2.
- N is the total number of equally spaced studs; adjacent-stud pitch is therefore 360/N.
- The drop/pitch result is a geometric ratio, not efficiency, timing quality or an allowable limit.
- Friction, contact angle, pallet lift, recoil, oscillator coupling, train inertia, rate, wear, strength and safe design dimensions are omitted.
The total stud count gives an adjacent-stud pitch of 360/N. Torque times the entered angle gives ideal work at the wheel; it does not calculate the impulse delivered to an oscillator.
How Brown's Stud Escapement Locks
Henry T. Brown describes movement 292 as a stud escapement used in large clocks. One pallet works in front of the wheel and the other works behind it. The studs are arranged to rest alternately on those front and rear pallets.
Brown also states that each pallet curve is an arc described from the pallet arbor F. A stud resting on that concentric locking face therefore does not drive the pallet merely by trying to turn the wheel; this is the source's reason for calling the arrangement a repose or dead-beat escapement.
Reading the animation
- Solid orange studs and the solid pallet represent the front plane.
- Outlined dashed studs and the dashed pallet represent the rear plane.
- Both locking faces and their rigid arms rock together about F.
- The wheel angle is held through each lock and advances by one adjacent-stud pitch through each release, bringing the alternating plane to the common projected contact point.
What This Model Is Useful For
The page is useful for identifying Brown's front/rear topology and for checking four transparent quantities from user-entered values: ideal tangential force at the stud circle, ideal wheel work over an angular drop, adjacent-stud pitch and drop as a fraction of that pitch.
It does not size a clock escapement. A real design requires the actual pallet and stud geometry, contact normals, lift, clearances, oscillator coupling, train inertia, friction, material and manufacturing data.
Ideal Torque, Work and Stud-Pitch Relations
With entered wheel torque T and stud-circle diameter D, the radius is r = D/2 and the corresponding ideal tangential force is:
For an entered wheel rotation delta theta expressed in radians, ideal wheel work is:
For N total equally spaced studs, the angle from one stud to the next is:
The displayed percentage is 100 times entered drop divided by that successive-stud pitch. It is only a geometric comparison.
Worked Example: Ideal Entered Quantities
For T = 50 mN m and D = 150 mm, T = 0.050 N m and r = 0.075 m, so the ideal tangential force is 0.050/0.075 = 0.667 N.
For an entered drop of 1.5 degrees, delta theta = 0.02618 rad and ideal wheel work is 0.050 × 0.02618 = 0.001309 J, or 1.309 mJ. With 24 total equally spaced studs, successive-stud pitch is 360/24 = 15 degrees and the entered drop is 10.0% of that pitch.
Those results do not determine how much impulse reaches an oscillator or whether the pallet geometry will lock and release correctly.
What the model includes
- Historical arrangement: alternating front/rear pallets, alternating stud rests, locking arcs centered on F and repose/dead-beat classification.
- Calculated exactly from entered values: T/r, T delta theta, 360/N and drop/pitch.
- Not calculated: pallet contact force, impulse delivered to an oscillator, lift, recoil, rate, friction loss, wear, clearance, strength or service interval.
The animation illustrates the alternating lock-and-release sequence. It does not supply a dimensioned design or manufacturing clearances.
Frequently Asked Questions
How is the successive-stud pitch calculated?
N is defined here as the total count of equally spaced studs around one full revolution, so the angle between adjacent studs is 360 degrees divided by N.
Is ideal wheel work the impulse delivered to the pendulum?
No. T delta theta is work released by the ideal constant-torque wheel over the entered angle. Pallet geometry, contact, friction and oscillator coupling determine how much energy reaches an oscillator.
What makes this a repose or dead-beat escapement?
Brown states that the pallet curves are arcs described from F, the pallet arbor. The concentric locking faces provide the repose or dead-beat condition described in the source.
Do the front and rear pallets lie in the same plane?
No. Brown explicitly places one pallet in front of the wheel and the other behind it, with studs resting alternately on them.
Can this calculator provide manufacturing dimensions?
No. It omits the detailed contact geometry, clearances, lift, recoil, loads, materials and tolerances required for a working design.
References
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