ARCHITECTURE
THE DERIVATION ENGINE: WHY PHYSICS DERIVES GEOMETRY AND AI HANDLES AMBIGUITY
ABSTRACT / SUMMARY
Why generative AI should never output raw CAD files: how Rigel decouples natural language constraint extraction from deterministic Shigley fatigue derivation, PicoGK B-Rep modeling, and CalculiX FEA.
01. The Core Inversion: AI as Interpreter, Math as Author
Current 'generative CAD' tools attempt to train neural networks to predict geometric mesh coordinates directly from prompts. This architecture is fundamentally flawed: neural networks interpolate probabilities, whereas mechanical structures operate under non-negotiable physical laws. In the Quantrix architecture, we institute an inviolable boundary: AI handles ambiguity. Math handles precision. These roles never swap. The LLM (a local quantized LLaMA 3.2 3B) is restricted strictly to parsing informal human inputs into a structured JSON load and boundary constraint specification.
[ Natural Language Input ]
│
▼
[ LLaMA 3.2 3B Extractor ] ──> [ Structured Load Spec (F, Material, FOS) ]
│
═════════════════════════════╪═════════════════════════════ (INVIOLABLE BOUNDARY)
▼
[ Shigley Fatigue Math (Eq 6-2) ]
│
▼
[ PicoGK B-Rep Geometry Kernel ]
│
▼
[ Gmsh Tet10 ──> CalculiX Static FEA ]
│
▼
[ 4 Output Artifacts + SHA-256 Audit Chain ]02. The Deterministic Derivation Pipeline
Once the JSON constraint specification is validated, deterministic engineering math derives the actual dimensions. For fatigue and dynamic shear loading, we apply Shigley's Mechanical Engineering Design fatigue equations (Eq 6-2: S_e = k_a * k_b * k_c * k_d * k_e * S_e'). The derived dimensional parameters are passed directly to Leap 71's PicoGK open-source computational geometry kernel, synthesizing a watertight B-Rep solid. Gmsh generates a second-order tetrahedral mesh (Tet10), which is solved by CalculiX for Von Mises stress, displacement, and true factor of safety (FOS).
{
"rigel_run_id": "rigel-cantilever-7882b",
"input_hash": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855",
"load_case": {
"force_n": 2500.0,
"vector": [0.0, -1.0, 0.0],
"material": "Al-6061-T6",
"target_fos": 2.0
},
"analytical_derivation": {
"shigley_endurance_limit_mpa": 96.4,
"derived_web_thickness_mm": 6.82,
"derived_flange_width_mm": 38.5
},
"fea_verification": {
"solver": "CalculiX-ccx-2.20",
"mesh_elements": 48210,
"max_von_mises_mpa": 184.2,
"effective_fos": 2.12,
"status": "CONVERGED_WITHIN_TOLERANCE"
}
}03. Ground-Truth Validation at PSG Workshop
Simulation is an unvalidated hypothesis until tested against physical matter. In collaboration with the mechanical engineering workshop at PSG College of Engineering, Coimbatore, we 3D-print and CNC-mill derived brackets and subject them to destructive hydraulic press load-to-failure testing. Our target is strict: the physical failure point must fall within 15% of the CalculiX FEA prediction. In our benchmark 6061-T6 bracket series, initial yield occurred at 5,820 N against a predicted 5,200 N target, an 11.9% variance, safely within our engineering threshold.
04. Cryptographic Audit and the Public FAILURES.md
Every execution of Rigel outputs exactly 4 immutable artifacts: bracket.step (standard exchange geometry), bracket.dxf (2D fabrication drawing), report.pdf (formal engineering calculation package), and audit.json (cryptographic SHA-256 chain). Furthermore, every single test failure, mesh divergence, or load cell discrepancy is committed to our public FAILURES.md repository. In high-integrity engineering, hiding mistakes is negligence; documenting them is the only path to deterministic reliability.
CITATIONS & PRIMARY SOURCES
- Shigley's Mechanical Engineering Design (11th Edition), Budynas & Nisbett, McGraw-Hill (2020)
- PicoGK: Open-Source Computational Geometry Kernel for Algorithmic Engineering, Lin Kayser, Leap 71 (2024)
- CalculiX: A Free Software Three-Dimensional Structural Finite Element Program, Guido Dhondt, MTU Aero Engines (2023)