Belt & Pulley Speed/Length Calculator mechanism

Model scope

The formulas are acceptable for an ideal, no-slip, open-belt drive when all length units are consistent and C > (D1+D2)/2. Review is required because the specification does not define the direction of "speed ratio" and does not state that the belt-length result is approximate.

• The term "speed ratio" is ambiguous: it could mean N1/N2 = D2/D1 or N2/N1 = D1/D2. The specification must define the direction explicitly.
• The belt-length equation is the standard approximate open-belt-length formula, not an exact geometric belt-length calculation; the output should be labeled approximate.
• N1D1=N2D2 assumes no belt slip and that D1 and D2 are effective pitch diameters, not necessarily outside diameters.

Units and conventions

• D1, D2, and C must use the same length unit; the resulting L has that same unit.
• N1 and N2 must use the same rotational-speed unit, such as rpm.
• The test vectors interpret speed ratio as input speed divided by output speed: N1/N2 = D2/D1.
• The diameter-speed relation assumes ideal no-slip transmission using effective pitch diameters.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "D1": 100,
    "D2": 200,
    "C": 1000,
    "N1": 1200,
    "length_unit": "mm",
    "speed_unit": "rpm"
  },
  "expected_outputs": {
    "N2": 600,
    "belt_length_L": 2473.738898,
    "speed_ratio": 2
  },
  "working": "N2 = N1D1/D2 = 1200 × 100 / 200 = 600 rpm. Speed ratio = N1/N2 = 1200/600 = 2. Belt length L = 2C + π(D1+D2)/2 + (D2−D1)²/(4C) = 2×1000 + π(100+200)/2 + (200−100)²/(4×1000) = 2000 + 150π + 10000/4000 = 2000 + 471.238898 + 2.5 = 2473.738898 mm."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The calculator can encounter an undefined belt-length expression when C=0, can return a plausible but physically invalid length when C is below the open-belt geometric limit unless that limit is explicitly checked, and can disagree on the sign of N2 because the speed-direction convention is unspecified.

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