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

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

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