This work presents a dual-agent \ac{llm}-based reasoning framework for automated planar mechanism synthesis that tightly couples linguistic specification with symbolic representation and simulation. From a natural-language task description, the system composes symbolic constraints and equations, generates and parametrises simulation code, and iteratively refines designs via critic-driven feedback, including symbolic regression and geometric distance metrics, closing an actionable linguistic/symbolic optimisation loop. To evaluate the approach, we introduce MSynth, a benchmark of analytically defined planar trajectories. Empirically, critic feedback and iterative refinement yield large improvements (up to 90\% on individual tasks) and statistically significant gains per the Wilcoxon signed-rank test. Symbolic-regression prompts provide deeper mechanistic insight primarily when paired with larger models or architectures with appropriate inductive biases (e.g., LRM).

翻译：本研究提出了一种基于双智能体大语言模型的推理框架，用于自动化平面机构综合，该框架将语言描述与符号表示及仿真紧密耦合。系统从自然语言任务描述出发，组合符号约束与方程，生成并参数化仿真代码，并通过包含符号回归与几何距离度量的批判驱动反馈迭代优化设计，从而构建了一个可执行的语言/符号优化闭环。为评估该方法，我们引入了MSynth基准测试集，其中包含解析定义的平面轨迹。实验表明，批判反馈与迭代优化带来了显著改进（单项任务提升最高达90%），且根据Wilcoxon符号秩检验，其增益具有统计显著性。符号回归提示能够提供更深入的机构学洞察，这主要在与更大规模模型或具有适当归纳偏置的架构（如LRM）结合时尤为明显。