Large Language Models and their Awareness of Mechanics and Spatial Geometry

Abstract

Large Language Models (LLMs) perform well on established code-generation and mathematical-reasoning benchmarks, but their capabilities in mechanics and spatial geometry, here denoted as mechanical engineering awareness, has not been quantified systematically. We present MecEng, a fully automated benchmark that evaluates LLMs on the creation of multibody simulation models from parameterized textual descriptions. The benchmark comprises 84 generic tasks on three difficulty levels, ranging from rigid-body systems with joints and contact to flexible multibody systems that require exact 3D geometry generation, tetrahedral finite-element meshing, and Hurty-Craig-Bampton model order reduction of machine parts. A dedicated pipeline with LLMs generates simulation-ready geometry from text using Netgen, and builds multibody system models for the code Exudyn, which are then verified against expert ground truth on several levels: system-graph isomorphism including graph node annotations, numerical solutions, and part-specific measures such as mass, geometry, and eigenfrequencies. In total, 32 open-weight and two proprietary LLMs are evaluated. On rigid-body tasks, the best open-weight model obtains an overall success rate of 86.0%, compared to 91.4% for the strongest proprietary model, while flexible multibody tasks remain considerably harder. Additional studies quantify the influence of sampling temperature, reasoning, prompt design, model size, and LLM-release date. The results indicate rapidly improving, but still error-prone, mechanical engineering awareness of current LLMs.