Source: https://guthlabs.ai/docs/instruments/friction-wedge-inclined-plane-solver/
instrument / verified-clean
# Friction Wedge / Inclined Plane Solver
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration
**Tranche**: tranche-4
**Evidence ID**: t4-166
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The core equations can be accepted after the missing conventions are made explicit. The product should not claim to determine a unique force or slip direction from the current specification alone, because force-angle reference, sign mapping, coefficient selection, and unit conventions are unspecified.
### Formula and scope findings
- The generalized formula is standard only when the signs are correlated and the force-angle convention is defined: for impending motion up the incline, F=W(sinθ+μcosθ)/(cosφ−μsinφ); for impending motion down the incline, the corresponding signed-force relation is F=W(sinθ−μcosθ)/(cosφ+μsinφ) under a positive-upslope force convention.
- The specification does not define whether φ is measured from the incline surface, the horizontal, or the vertical; the stated formula assumes φ is measured from the incline surface.
- The specification does not define the sign convention for applied force or explicitly map each ±/∓ combination to impending upward versus downward slip.
- The angle-of-repose formula θ=atan(μ) is valid for dry Coulomb friction with no other applied force and impending slip, using the static coefficient μs; it is not generally an angle based on μk.
- The specification conflates μs and μk without stating whether the solver computes impending motion with μs or post-slip motion with μk.
### Unit assumptions
- W is a force, such as N or kN, not a mass; if mass is supplied, it must first be converted using W=mg.
- θ and φ must use one declared angular unit internally; the test vectors below use degrees converted to radians for trigonometric evaluation.
- θ is measured from the horizontal incline reference, and φ is measured from the incline surface.
- μ is dimensionless; use μs for impending motion and angle of repose, and μk only for motion after sliding has begun.
- The output force has the same force unit as W.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The generalized formula has a true singularity when cos(phi)-mu*sin(phi)=0, producing an undefined force that must be rejected rather than numerically evaluated. The unspecified sign convention for applied-force angle also changes the computed force from 61.4087 N to 87.1377 N for the same plausible angle input.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"W_N": 1000,
"theta_deg": 30,
"mu": 0.5,
"phi_deg": 0,
"branch": "impending motion up incline",
"coefficient_type": "mu_s"
},
"expected_outputs": {
"required_force_N": 933.013,
"angle_of_repose_deg": 26.565051
},
"working": "θ=30°: sinθ=0.5, cosθ=0.8660254. φ=0°: cosφ=1, sinφ=0. Up-incline branch: F=W(sinθ+μcosθ)/(cosφ−μsinφ)=1000(0.5+0.5×0.8660254)/(1−0.5×0)=1000(0.9330127)=933.0127 N≈933.013 N. Angle of repose=atan(0.5)=26.565051°."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche4/tranche4-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`