Language Models Refine Mechanical Linkage Designs Through Symbolic Reflection and Modular Optimisation

TL;DR

This paper demonstrates that language models can enhance mechanical linkage designs by combining symbolic reasoning with modular optimization, leading to significant error reduction and better structural validity.

Contribution

It introduces a modular architecture that enables language models to interpret symbolic representations and iteratively refine mechanical linkage designs without fine-tuning.

Findings

Reduced geometric error by up to 68%

Improved structural validity by up to 134%

78.6% of refinement trajectories showed measurable improvement

Abstract

Designing mechanical linkages involves combinatorial topology selection and continuous parameter fitting. We show that language models can systematically improve linkage designs through symbolic representations. Language model agents explore discrete topologies while numerical optimisers fit continuous parameters. A symbolic lifting operator translates simulator trajectories into qualitative descriptors, motion labels, temporal predicates, and structural diagnostics that models interpret across iterative design cycles. Across six engineering-relevant motion targets and three open-source models (Llama 3.3 70B, Qwen3 4B, Qwen3 MoE 30B-A3B), the modular architecture reduces geometric error by up to 68% and improves structural validity by up to 134% over monolithic baselines. Critically, 78.6% of iterative refinement trajectories show measurable improvement, with the system correctly diagnosing overconstraint (56.3%) and underconstraint (35.6%) failure modes and proposing grounded corrections. Models across all three families acquire interpretable mechanical reasoning strategies without fine-tuning, demonstrating that principled symbolic abstraction bridges generative AI and the numerical precision required for engineering design.