Source: https://guthlabs.ai/docs/instruments/belt-pulley-speed-length-calculator/mechanism/

instrument mechanism / verified-clean

# Belt & Pulley Speed/Length Calculator mechanism

The inspectable method record for Belt & Pulley Speed/Length Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/belt-pulley-speed-length-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/belt-pulley-speed-length-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/belt-pulley-speed-length-calculator/qualification/>)

## 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`