A crown ratchet has teeth on an axial-facing rim rather than around a flat wheel’s outside edge. An oscillating arm carries a pawl that advances the wheel, then returns across the tooth ramps. The calculator gives nominal angular indexing and two tooth-profile comparisons; it does not calculate a load rating.
Crown-Ratchet Rag-Wheel Interactive Calculator
Compare nominal angular indexing and tooth-profile angles. See the face-toothed wheel, oscillating arm and pawl lift, with a separate developed tooth profile.
Equation Used
- Equal tooth pitch and ideal one-tooth indexing.
- Click count is a selected total, not arm stroke amplitude.
- Output is assumed held during return.
- Developed tooth geometry uses a normalized reference radius.
- No force, strength, spring dynamics or holding-capacity calculation.
One-tooth demonstration assumes output retention during return. Undercut geometry is shown without applying the top-contact pawl model.
Face teeth and pawl motion
Brown’s movement 237 shows a reciprocating arm operating a pawl above the rim of a crown ratchet. The rebuilt illustration uses the same face-ratchet principle with an axial sliding pawl guided by the arm. This makes the lift over the ramps visible.
The ideal demonstration advances one tooth during the drive stroke and assumes the wheel is held during the arm’s return. A real mechanism needs appropriate retention and pawl loading. Those forces and the retaining arrangement are outside this calculator.
Compare an indexing increment
Use tooth count to compare nominal angular resolution. The number of selected clicks multiplies the single-tooth increment. The illustration demonstrates individual one-tooth strokes; the selected click count is a total index calculation, not the arm’s stroke amplitude.
Index and profile geometry
For N equally spaced teeth, the nominal increment is 360/N degrees per click. A total of c clicks gives 360c/N degrees. This total may exceed one revolution and is not reduced modulo 360.
Ramp slope is tan(α), the rise per unit tangential run in the developed profile. Stop deviation is |90°−β|. Neither result establishes the contact force or resistance to reverse rotation.
The developed triangular tooth has pitch p, height h and peak run x. Its geometry satisfies h=p/[cot(α)+cot(β)] and x=h cot(α). The drawing uses a representative radius, so the dimensions are normalized rather than manufacturing specifications.
Examples
Twelve teeth give 30 degrees per click. Three selected clicks therefore give a nominal 90-degree total index. With a 25-degree ramp, the rise/run ratio is approximately 0.466. An 85-degree stop face differs from a perpendicular face by 5 degrees.
A stop angle above 90 degrees produces an undercut profile in this convention. That geometry is still drawn, but the simple top-contact pawl demonstration is not applied. The arm moves with the pawl lifted clear and the wheel stationary; the arithmetic indexing values remain nominal.
Model boundaries
More teeth reduce the nominal angle per click. The four inputs do not establish tooth strength, pawl strength, shaft load, material, contact stress, spring force, friction, backlash or holding capacity.
The animation prescribes an ideal drive-and-return cycle. It does not solve impacts, spring compression force or the possibility that an inclined stop face lifts a loaded pawl. A vertical-looking stop face alone does not certify a holding mechanism.
Crown-ratchet questions
Why are the teeth raised from the rim?
The pawl acts against an axial-facing tooth profile. This distinguishes the illustrated crown ratchet from a radial flat-wheel ratchet.
Does the click-count slider change the arm stroke?
No. It changes the nominal total index calculation. The demonstration continues to show one tooth per drive stroke.
Why does an undercut profile stop the indexing animation?
The simple sliding pawl contact model does not cover engagement under that overhang. The geometry remains visible without pretending to validate its operation.
Is stop deviation a strength result?
No. It is only the angular difference from a 90-degree face.
Reference
Henry T. Brown, 507 Mechanical Movements, movement 237, for the crown wheel, oscillating arm and axial pawl arrangement. The drawing here uses a sliding-pawl educational variant; the indexing and developed-profile equations are elementary geometric calculations.
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