Source: https://guthlabs.ai/docs/instruments/free-body-diagram-reaction-solver-2d-rigid-body/mechanism/

instrument mechanism / verified-clean

# Free Body Diagram / Reaction Solver (2D Rigid Body) mechanism

The inspectable method record for Free Body Diagram / Reaction Solver (2D Rigid Body), kept separate from implementation and qualification.

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

## Model scope

The equilibrium method is standard and appropriate for rigid-body static analysis, but the current specification is not sufficiently precise to implement or verify universally. NEEDS_REVIEW is required because support geometry/orientation, coordinate and sign conventions, unit handling, and behavior for indeterminate or unstable systems are unspecified. The honest label correctly limits the instrument to rigid-body static equilibrium, but it should also disclose that results require a stable, statically determinate support configuration unless a separate solver is provided.

- ΣFx=0, ΣFy=0, and ΣM=0 are the correct equilibrium equations for a 2D rigid body in static equilibrium.

- The specification does not define force-component decomposition, moment sign convention, position-reference convention, or the support constraint equations required to apply the three equilibrium equations.

- The solver must reject or explicitly report statically indeterminate, unstable, and incompatible support configurations rather than silently returning a result.

## Units and conventions

- Each test vector states a consistent force, distance, and moment unit system; force and reaction components use the stated force unit, and moments use force-distance units.

- The coordinate system is x positive to the right and y positive upward.

- Angles are measured counterclockwise from the positive x-axis.

- Positive moments are counterclockwise.

- Forces are applied at the stated coordinates relative to the global origin, with M_z=xF_y-yF_x.

- Pin supports provide Rx and Ry but no reaction moment; roller supports on a horizontal surface provide Ry only; fixed supports provide Rx, Ry, and M.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "units": "kN, m, kN·m",
    "coordinate_convention": "x right, y up; positive moment counterclockwise",
    "supports": {
      "A": {
        "type": "pin",
        "position_m": [
          0,
          0
        ]
      },
      "B": {
        "type": "roller_horizontal",
        "position_m": [
          4,
          0
        ]
      }
    },
    "forces": [
      {
        "magnitude_kN": 10,
        "angle_deg": 270,
        "position_m": [
          1,
          0
        ]
      },
      {
        "magnitude_kN": 6,
        "angle_deg": 270,
        "position_m": [
          3,
          0
        ]
      }
    ],
    "applied_couples": []
  },
  "expected_outputs": {
    "A_Rx_kN": 0,
    "A_Ry_kN": 9,
    "B_Ry_kN": 7,
    "A_M_kN_m": 0,
    "B_M_kN_m": 0
  },
  "working": "Resolve forces: F1x=10 cos(270°)=0, F1y=10 sin(270°)=-10 kN; F2x=6 cos(270°)=0, F2y=6 sin(270°)=-6 kN. ΣFx=Ax+0+0=0, so Ax=0 kN. Take moments about A: 4By+(1)(-10)+(3)(-6)=0; 4By-10-18=0; 4By=28; By=7 kN. ΣFy=Ay+By-10-6=0; Ay+7-16=0; Ay=9 kN. Pin and roller supports have no moment reactions."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The solver must reject coincident supports when the reaction calculation divides by the zero support spacing; otherwise it can produce an undefined or nonphysical reaction. Angle-sign ambiguity can also reverse the vertical reactions if the convention is not explicit.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/free-body-diagram-reaction-solver-2d-rigid-body/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/free-body-diagram-reaction-solver-2d-rigid-body/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/free-body-diagram-reaction-solver-2d-rigid-body/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-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`