This page now isolates a neutral pawl-and-toothed-quadrant topology and exact declared arc arithmetic. Unsupported weapon-use, capacity, material, tolerance, speed, life and field-service claims are removed.
Declared Quadrant Arc and Index Ledger
Enter a declared arc radius, circular arc pitch and sweep. The worksheet reports pure geometry and uses an explicit starting-position convention; it does not predict holding capacity or equipment performance.
Equation Used
- p is declared circular arc length measured at radius R.
- R and p use the same length unit and the declared sweep is converted to radians.
- The starting location is counted as position 1; each full interval within the sweep adds one position.
- Any fractional remainder at the end of the sweep is reported in the interval count but is not counted as another full position.
- The connected animation is qualitative and does not dimension pawl or tooth geometry.
- Loads, tooth form, backlash, spring force, friction, wear, materials, tolerances, speed, life, ratings, selection and safe operation are excluded.
Retains exact declared arc-pitch arithmetic with an explicit position-count convention and removes unsupported weapon-use, capacity, materials, tolerance, performance and field-service claims.
A pawl can engage a toothed quadrant
Patent US2016436 describes a lever dog engaging a quadrant tooth and a handle-linked release arrangement. WO2001010688A1 likewise documents a toothed quadrant, locking pawl, bias spring and operating rod.
The animation shows only that connected topology. It does not model tooth contact or holding force.
Use only as a declared arc-index ledger
The worksheet converts declared circular arc pitch at a declared radius into an angle per interval and counts full intervals within a declared sweep.
It cannot design, rate, select, operate or troubleshoot a catch mechanism.
Arc length divided by radius gives angle
N follows the stated convention: index 0 plus every complete pitch interval not exceeding the sweep.
A transparent declared-geometry example
For R=200 mm, p=5 mm and A=30 degrees, one interval is about 1.432 degrees, the arc is about 104.720 mm, n is about 20.944 intervals and N is 21 stated positions including index 0.
Arc arithmetic is not catch design
The equations say nothing about tooth profile, pawl engagement, backlash, spring force, friction, strength, wear or load direction. Those require device drawings and verified engineering data.
The former weapon operation, aiming, reaction-load, materials, hardness, tolerance, speed, life, failure, selection and troubleshooting claims are removed.
Declared quadrant-index questions
Is p a straight chord?
No; this worksheet defines p as circular arc length at radius R.
Why add one to the full interval count?
To include the declared starting position at index 0.
Does a fractional final interval create another position?
No under this stated convention.
Does the calculator prove the pawl can hold a load?
No.
Arc and pawl-quadrant references
- NIST SP 330, The International System of Units: plane angle in radians as circular arc length divided by radius and degree-radian conversion.
- US Patent 2,016,436, Lever Catch: lever dog, toothed quadrant and handle-linked release topology.
- WIPO Patent WO2001010688A1: toothed quadrant, locking pawl, bias spring and operating rod topology.
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