Language Models Refine Mechanical Linkage Designs Through Symbolic Reflection and Modular Optimisation Designing mechanical linkages is a complex engineering task that requires both selecting the right structural topology and fine-tuning continuous parameters to ensure the mechanism functions correctly. This paper introduces a new approach that uses language models to systematically improve these designs. By combining the creative exploration of language models with the precision of numerical optimisers, the researchers created a system capable of iterative design refinement that outperforms traditional monolithic methods. Bridging Generative AI and Engineering The core challenge in automated design is that language models often struggle with the precise numerical requirements of engineering. To solve this, the authors developed a "symbolic lifting operator." This tool translates raw data from a design simulator into a language the model can understand, such as qualitative descriptors, motion labels, and structural diagnostics. This allows the language model to act as an intelligent agent that interprets the design's performance and suggests improvements, while a separate numerical optimiser handles the mathematical adjustments to the linkage's parameters. How the System Learns The system operates through iterative design cycles. In each cycle, the language model evaluates the current design and proposes changes based on the symbolic feedback it receives. The researchers tested this architecture using three different open-source models: Llama 3.3 70B, Qwen3 4B, and Qwen3 MoE 30B-A3B. Remarkably, the models were able to acquire mechanical reasoning strategies without requiring any fine-tuning. The system demonstrated a sophisticated ability to diagnose specific mechanical failures, correctly identifying overconstraint issues in 56.3% of cases and underconstraint issues in 35.6% of cases, subsequently proposing grounded, actionable corrections. Performance and Results The modular architecture showed significant improvements over standard monolithic design baselines across six engineering-relevant motion targets. The system achieved a reduction in geometric error of up to 68% and improved the structural validity of designs by up to 134%. Furthermore, 78.6% of the refinement trajectories resulted in measurable improvements to the linkage designs. These results suggest that using symbolic abstraction is a highly effective way to bridge the gap between the generative capabilities of language models and the high level of precision required for mechanical engineering.