{ "schemaVersion": "vehiclelab.macpherson-evidence.v1", "evidenceVersion": "1.0.0", "status": "PASS", "solver": { "id": "vehiclelab.macpherson.rack-tie-rod", "version": "1.0.0" }, "scope": "Rigid ideal spherical/telescoping MacPherson, fixed rack/tie rods; no compliance, handling, forces or Full-Car integration.", "reference": "Independent carrier frame construction, steering-circle/tie-sphere intersection and scalar arm bisection. No production solver, Jacobian, orientation or continuation imports in the reference.", "geometryCount": 3, "axlePointCount": 79, "cornerPointCount": 158, "inputs": { "jounceM": [-0.05, -0.025, 0, 0.025, 0.05], "rackM": [-0.02, -0.01, 0, 0.01, 0.02], "derivativeStepsM": [0.001, 0.0001, 0.00001], "boundaryPairsM": [ [-0.14, -0.03], [-0.14, 0.03], [0.14, -0.03], [0.14, 0.03] ] }, "acceptance": { "positionM": 5e-10, "frame": 5e-9, "angleRad": 5e-9, "closureM": 1e-11, "jacobianMPerRad": 5e-10, "pointDerivativeMPerM": 0.000003, "angularDerivativeRadPerM": 0.00002, "carrierBasisDerivativePerM": 0.00002, "armDerivativeRadPerM": 0.00002, "lengthDerivativeMPerM": 0.000003, "headingDerivativeRadPerM": 0.00002, "implicitResidual": 1e-12 }, "maximumErrors": { "positionM": 1.545370081901254e-11, "frame": 7.109823840778517e-11, "angleRad": 7.548667246837226e-11, "closureM": 9.026654423927027e-12, "jacobianMPerRad": 1.0004370248895e-10, "pointDerivativeMPerM": 3.966110218023289e-9, "angularDerivativeRadPerM": 1.5092652461135003e-8, "carrierBasisDerivativePerM": 2.2554324630164047e-8, "armDerivativeRadPerM": 1.261585946821242e-9, "lengthDerivativeMPerM": 3.4179843330650606e-10, "headingDerivativeRadPerM": 2.8843651023180428e-8, "implicitResidual": 4.440892098500626e-16 }, "definitions": [ { "schemaVersion": "vehiclelab.macpherson-study.v1", "mechanism": "macpherson-strut-rack-tie-rod", "upperJoint": "ideal-spherical-telescoping", "metadata": { "name": "Closed-form planar MacPherson", "source": "custom" }, "rack": { "referenceM": [-0.12, 0, -0.16], "axis": [0, 1, 0], "leftOffsetM": 0.45, "rightOffsetM": -0.45, "minimumM": -0.03, "maximumM": 0.03 }, "left": { "hardpoints": { "lowerFront": [0.18, 0.4, -0.16], "lowerRear": [-0.18, 0.4, -0.16], "lowerBall": [0, 0.75, -0.16], "topMount": [0, 0.75, 0.54], "strutLower": [0, 0.75, 0.04], "axisReference": [0, 0.75, 0.29], "wheelCentre": [0, 0.75, -0.16], "spindleReference": [0, 0.85, -0.16], "outerTieRod": [-0.12, 0.75, 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"damperLowerOffsetM": 0.04 } }, { "schemaVersion": "vehiclelab.macpherson-study.v1", "mechanism": "macpherson-strut-rack-tie-rod", "upperJoint": "ideal-spherical-telescoping", "metadata": { "name": "Spatial skew-hinge MacPherson", "source": "custom" }, "rack": { "referenceM": [-0.12, 0, -0.12], "axis": [0, 1, 0], "leftOffsetM": 0.46, "rightOffsetM": -0.46, "minimumM": -0.03, "maximumM": 0.03 }, "left": { "hardpoints": { "lowerFront": [0.2, 0.39, -0.13], "lowerRear": [-0.17, 0.42, -0.155], "lowerBall": [0.008, 0.747, -0.167], "topMount": [0.055, 0.59, 0.51], "strutLower": [0.018, 0.729, 0.04], "axisReference": [0.0365, 0.6595, 0.275], "wheelCentre": [0, 0.8, 0], "spindleReference": [0.002, 0.902, 0.006], "outerTieRod": [-0.125, 0.735, -0.11] }, "tieRodLengthM": 0.2752271788904576, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 }, "right": { "hardpoints": { "lowerFront": [0.2, -0.39, -0.13], "lowerRear": [-0.17, -0.42, -0.155], "lowerBall": [0.008, -0.747, -0.167], "topMount": [0.055, -0.59, 0.51], "strutLower": [0.018, -0.729, 0.04], "axisReference": [0.0365, -0.6595, 0.275], "wheelCentre": [0, -0.8, 0], "spindleReference": [0.002, -0.902, 0.006], "outerTieRod": [-0.125, -0.735, -0.11] }, "tieRodLengthM": 0.2752271788904576, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 } } ], "failedCases": [ { "kind": "lower-arm-toggle", "definition": { "schemaVersion": "vehiclelab.macpherson-study.v1", "mechanism": "macpherson-strut-rack-tie-rod", "upperJoint": "ideal-spherical-telescoping", "metadata": { "name": "Closed-form planar MacPherson", "source": "custom" }, "rack": { "referenceM": [-0.12, 0, -0.16], "axis": [0, 1, 0], "leftOffsetM": 0.45, "rightOffsetM": -0.45, "minimumM": -0.03, "maximumM": 0.03 }, "left": { "hardpoints": { "lowerFront": [0.18, 0.75, -0.51], "lowerRear": [-0.18, 0.75, -0.51], "lowerBall": [0, 0.75, -0.16], "topMount": [0, 0.75, 0.54], "strutLower": [0, 0.75, 0.04], "axisReference": [0, 0.75, 0.29], "wheelCentre": [0, 0.75, -0.16], "spindleReference": [0, 0.85, -0.16], "outerTieRod": [-0.12, 0.75, -0.16] }, "tieRodLengthM": 0.3, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 }, "right": { "hardpoints": { "lowerFront": [0.18, -0.75, -0.51], "lowerRear": [-0.18, -0.75, -0.51], "lowerBall": [0, -0.75, -0.16], "topMount": [0, -0.75, 0.54], "strutLower": [0, -0.75, 0.04], "axisReference": [0, -0.75, 0.29], "wheelCentre": [0, -0.75, -0.16], "spindleReference": [0, -0.85, -0.16], "outerTieRod": [-0.12, -0.75, -0.16] }, "tieRodLengthM": 0.3, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 } }, "jounceM": 0, "rackM": 0, "code": "singular", "message": "left design configuration has constraint-rank loss.", "independentReason": "" }, { "kind": "tie-tangency", "definition": { "schemaVersion": "vehiclelab.macpherson-study.v1", "mechanism": "macpherson-strut-rack-tie-rod", "upperJoint": "ideal-spherical-telescoping", "metadata": { "name": "Closed-form planar MacPherson", "source": "custom" }, "rack": { "referenceM": [-0.35, 0, -0.16], "axis": [0, 1, 0], "leftOffsetM": 0.75, "rightOffsetM": -0.75, "minimumM": -0.03, "maximumM": 0.03 }, "left": { "hardpoints": { "lowerFront": [0.18, 0.4, -0.16], "lowerRear": [-0.18, 0.4, -0.16], "lowerBall": [0, 0.75, -0.16], "topMount": [0, 0.75, 0.54], "strutLower": [0, 0.75, 0.04], "axisReference": [0, 0.75, 0.29], "wheelCentre": [0, 0.75, -0.16], "spindleReference": [0, 0.85, -0.16], "outerTieRod": [-0.12, 0.75, -0.16] }, "tieRodLengthM": 0.22999999999999998, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 }, "right": { "hardpoints": { "lowerFront": [0.18, -0.4, -0.16], "lowerRear": [-0.18, -0.4, -0.16], "lowerBall": [0, -0.75, -0.16], "topMount": [0, -0.75, 0.54], "strutLower": [0, -0.75, 0.04], "axisReference": [0, -0.75, 0.29], "wheelCentre": [0, -0.75, -0.16], "spindleReference": [0, -0.85, -0.16], "outerTieRod": [-0.12, -0.75, -0.16] }, "tieRodLengthM": 0.22999999999999998, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 } }, "jounceM": 0, "rackM": 0, "code": "singular", "message": "left design configuration has constraint-rank loss.", "independentReason": "" }, { "kind": "alignment", "definition": { "schemaVersion": "vehiclelab.macpherson-study.v1", "mechanism": "macpherson-strut-rack-tie-rod", "upperJoint": "ideal-spherical-telescoping", "metadata": { "name": "Closed-form planar MacPherson", "source": "custom" }, "rack": { "referenceM": [-0.12, 0, -0.16], "axis": [0, 1, 0], "leftOffsetM": 0.45, "rightOffsetM": -0.45, "minimumM": -0.03, "maximumM": 0.03 }, "left": { "hardpoints": { "lowerFront": [0.18, 0.4, -0.16], "lowerRear": [-0.18, 0.4, -0.16], "lowerBall": [0, 0.75, -0.16], "topMount": [0.01, 0.75, 0.54], "strutLower": [0, 0.75, 0.04], "axisReference": [0, 0.75, 0.29], "wheelCentre": [0, 0.75, -0.16], "spindleReference": [0, 0.85, -0.16], "outerTieRod": [-0.12, 0.75, -0.16] }, "tieRodLengthM": 0.3, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 }, "right": { "hardpoints": { "lowerFront": [0.18, -0.4, -0.16], "lowerRear": [-0.18, -0.4, -0.16], "lowerBall": [0, -0.75, -0.16], "topMount": [0, -0.75, 0.54], "strutLower": [0, -0.75, 0.04], "axisReference": [0, -0.75, 0.29], "wheelCentre": [0, -0.75, -0.16], "spindleReference": [0, -0.85, -0.16], "outerTieRod": [-0.12, -0.75, -0.16] }, "tieRodLengthM": 0.3, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 } }, "jounceM": 0, "rackM": 0, "code": "invalid-definition", "message": "left: design upper mount must lie on the positive telescoping strut axis.", "independentReason": "" }, { "kind": "undefined-strut-axis", "definition": { "schemaVersion": "vehiclelab.macpherson-study.v1", "mechanism": "macpherson-strut-rack-tie-rod", "upperJoint": "ideal-spherical-telescoping", "metadata": { "name": "Closed-form planar MacPherson", "source": "custom" }, "rack": { "referenceM": [-0.12, 0, -0.16], "axis": [0, 1, 0], "leftOffsetM": 0.45, "rightOffsetM": -0.45, "minimumM": -0.03, "maximumM": 0.03 }, "left": { "hardpoints": { "lowerFront": [0.18, 0.4, -0.16], "lowerRear": [-0.18, 0.4, -0.16], "lowerBall": [0, 0.75, -0.16], "topMount": [0, 0.75, 0.54], "strutLower": [0, 0.75, 0.04], "axisReference": [0, 0.75, 0.04], "wheelCentre": [0, 0.75, -0.16], "spindleReference": [0, 0.85, -0.16], "outerTieRod": [-0.12, 0.75, -0.16] }, "tieRodLengthM": 0.3, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 }, "right": { "hardpoints": { "lowerFront": [0.18, -0.4, -0.16], "lowerRear": [-0.18, -0.4, -0.16], "lowerBall": [0, -0.75, -0.16], "topMount": [0, -0.75, 0.54], "strutLower": [0, -0.75, 0.04], "axisReference": [0, -0.75, 0.29], "wheelCentre": [0, -0.75, -0.16], "spindleReference": [0, -0.85, -0.16], "outerTieRod": [-0.12, -0.75, -0.16] }, "tieRodLengthM": 0.3, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 } }, "jounceM": 0, "rackM": 0, "code": "invalid-definition", "message": "left: strut axis reference is undefined.", "independentReason": "" }, { "kind": "unreachable-rack", "definition": { "schemaVersion": "vehiclelab.macpherson-study.v1", "mechanism": "macpherson-strut-rack-tie-rod", "upperJoint": "ideal-spherical-telescoping", "metadata": { "name": "Closed-form planar MacPherson", "source": "custom" }, "rack": { "referenceM": [-0.12, 0, -0.16], "axis": [0, 1, 0], "leftOffsetM": 0.74, "rightOffsetM": -0.74, "minimumM": -0.1, "maximumM": 0.1 }, "left": { "hardpoints": { "lowerFront": [0.18, 0.4, -0.16], "lowerRear": [-0.18, 0.4, -0.16], "lowerBall": [0, 0.75, -0.16], "topMount": [0, 0.75, 0.54], "strutLower": [0, 0.75, 0.04], "axisReference": [0, 0.75, 0.29], "wheelCentre": [0, 0.75, -0.16], "spindleReference": [0, 0.85, -0.16], "outerTieRod": [-0.12, 0.75, -0.16] }, "tieRodLengthM": 0.010000000000000009, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 }, "right": { "hardpoints": { "lowerFront": [0.18, -0.4, -0.16], "lowerRear": [-0.18, -0.4, -0.16], "lowerBall": [0, -0.75, -0.16], "topMount": [0, -0.75, 0.54], "strutLower": [0, -0.75, 0.04], "axisReference": [0, -0.75, 0.29], "wheelCentre": [0, -0.75, -0.16], "spindleReference": [0, -0.85, -0.16], "outerTieRod": [-0.12, -0.75, -0.16] }, "tieRodLengthM": 0.010000000000000009, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 } }, "jounceM": 0, "rackM": 0.1, "code": "singular", "message": "left: singular constraint Jacobian; sensitivities are unavailable.", "independentReason": "At zero wheel height the planar ball has y=.75 or .05. In either assembly, distance from ball to requested inner joint exceeds the .12 m carrier steering-arm radius plus .01 m tie length (triangle inequality)." }, { "kind": "unreachable-travel", "definition": { "schemaVersion": "vehiclelab.macpherson-study.v1", "mechanism": "macpherson-strut-rack-tie-rod", "upperJoint": "ideal-spherical-telescoping", "metadata": { "name": "Closed-form planar MacPherson", "source": "custom" }, "rack": { "referenceM": [-0.12, 0, -0.16], "axis": [0, 1, 0], "leftOffsetM": 0.45, "rightOffsetM": -0.45, "minimumM": -0.03, "maximumM": 0.03 }, "left": { "hardpoints": { "lowerFront": [0.18, 0.725, -0.16], "lowerRear": [-0.18, 0.725, -0.16], "lowerBall": [0, 0.75, -0.16], "topMount": [0, 0.75, 0.54], "strutLower": [0, 0.75, 0.04], "axisReference": [0, 0.75, 0.29], "wheelCentre": [0, 0.75, -0.16], "spindleReference": [0, 0.85, -0.16], "outerTieRod": [-0.12, 0.75, -0.16] }, "tieRodLengthM": 0.3, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 }, "right": { "hardpoints": { "lowerFront": [0.18, -0.725, -0.16], "lowerRear": [-0.18, -0.725, -0.16], "lowerBall": [0, -0.75, -0.16], "topMount": [0, -0.75, 0.54], "strutLower": [0, -0.75, 0.04], "axisReference": [0, -0.75, 0.29], "wheelCentre": [0, -0.75, -0.16], "spindleReference": [0, -0.85, -0.16], "outerTieRod": [-0.12, -0.75, -0.16] }, "tieRodLengthM": 0.3, "springUpperOffsetM": 0.04, "springLowerOffsetM": 0.12, "damperUpperOffsetM": 0.025, "damperLowerOffsetM": 0.04 } }, "jounceM": 0.05, "rackM": 0, "code": "out-of-branch", "message": "left: request left the selected design assembly branch.", "independentReason": "Wheel centre equals ball joint; its hinge-circle vertical amplitude is .025 m. Requested .05 m height is impossible independently of Newton convergence." } ], "rows": [ { "geometry": "Closed-form planar MacPherson", "jounceM": -0.05, "rackM": -0.02, "state": { "solver": { "id": "vehiclelab.macpherson.rack-tie-rod", "version": "1.0.0" }, "jounceM": -0.05, "rackM": -0.02, "left": { "side": "left", "lowerArmAngleRad": 0.14334756890533998, "carrierBasis": [ [0.9851621757243731, 0.17162404466982517, -0.0008214701384090343], [-0.17162601062198724, 0.9851508908283256, -0.004715376775680799], [4.257846981663538e-12, 0.0047863964863901175, 0.9999885451387303] ], "hardpoints": { "lowerFront": [0.18, 0.4, -0.16], "lowerRear": [-0.18, 0.4, -0.16], "lowerBall": [0, 0.7464101615137768, -0.2099999999999912], "topMount": [0, 0.75, 0.54], "strutLower": [8.515693963327076e-13, 0.7473674408110549, -0.010002290972245143], "axisReference": [1.916031141748592e-12, 0.7485640399326524, 0.23999484531243737], "wheelCentre": [0, 0.7464101615137768, -0.2099999999999912], "spindleReference": 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