Spur Gear Geometry Calculator mechanism

Model scope

The honest label is directionally appropriate but should explicitly state that the calculator uses standard full-depth, unshifted external spur-gear proportions and does not calculate undercut, backlash, profile shift, root fillets, strength, or AGMA rating. An AGMA or applicable standards table is needed if proportions other than the stated 20-degree full-depth approximation are supported.

• The imperial dedendum is incorrect or incomplete: it must be 1.25/P, not 1.25m.
• Formulas for the stated outside diameter and root diameter outputs are missing. For standard full-depth proportions, outside diameter = d + 2a and root diameter = d - 2b, where a is addendum and b is dedendum.
• The center-distance formula must be expressed for both unit systems: (N1+N2)m/2 for metric or (N1+N2)/(2P) for imperial.
• The formulas assume two external gears with the same module or diametral pitch; this constraint is not stated.
• Pressure angle is listed as an input but is not used by the formulas. It should be identified as a standards/proportion-selection input or removed from the required inputs.

Units and conventions

• Metric module m is in millimetres per tooth; all metric diameters and center distances are in millimetres.
• Imperial diametral pitch P is teeth per inch; all imperial diameters and center distances are in inches.
• The calculations use standard 20-degree full-depth involute proportions: addendum = m or 1/P, dedendum = 1.25m or 1.25/P.
• N1 and N2 are dimensionless positive tooth counts.
• Both gears are external gears and use the same module or diametral pitch.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "system": "metric",
    "module_m": 2,
    "N1": 20,
    "N2": 40,
    "pressure_angle_deg": 20
  },
  "expected_outputs": {
    "pitch_diameter_1_mm": 40,
    "pitch_diameter_2_mm": 80,
    "addendum_mm": 2,
    "dedendum_mm": 2.5,
    "outside_diameter_1_mm": 44,
    "outside_diameter_2_mm": 84,
    "root_diameter_1_mm": 35,
    "root_diameter_2_mm": 75,
    "center_distance_mm": 60
  },
  "working": "d1 = mN1 = 2 x 20 = 40 mm; d2 = mN2 = 2 x 40 = 80 mm; addendum = m = 2 mm; dedendum = 1.25m = 1.25 x 2 = 2.5 mm; outside diameter 1 = d1 + 2a = 40 + 2(2) = 44 mm; outside diameter 2 = 80 + 2(2) = 84 mm; root diameter 1 = d1 - 2b = 40 - 2(2.5) = 35 mm; root diameter 2 = 80 - 2(2.5) = 75 mm; center distance = (N1 + N2)m/2 = (20 + 40) x 2 / 2 = 60 mm."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification exposes two hazardous acceptance failures: module m=0 gives a degenerate zero-size gear that should be rejected, and imperial diametral pitch P=0 causes division by zero and undefined outputs. Pressure-angle sign is also not defined, although it does not affect the supplied arithmetic formulas.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json