Controlled Agentic Planning & Reasoning for Mechanism Synthesis

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).