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.

翻译：设计机械连杆涉及组合拓扑选择与连续参数拟合。我们证明，语言模型能够通过符号表述系统性地改进连杆设计。语言模型代理探索离散拓扑结构，同时数值优化器拟合连续参数。符号提升算子将仿真轨迹转换为定性描述符、运动标签、时间谓词及结构诊断信息，使模型能在迭代设计周期中进行解读。在六个工程相关的运动目标以及三个开源模型（Llama 3.3 70B、Qwen3 4B、Qwen3 MoE 30B-A3B）上，该模块化架构相较于整体基线方法，将几何误差最多降低68%，结构有效性最多提高134%。关键在于，78.6%的迭代优化轨迹显示出可量化的改进，系统能够正确诊断过约束（56.3%）和欠约束（35.6%）失效模式，并提出基于现实的修正方案。所有三类模型在未经微调的情况下均获得了可解释的机械推理策略，这证明了原则性的符号抽象能桥接生成式AI与工程设计所需的数值精度之间的鸿沟。