Large language models (LLMs) have recently emerged as a promising tool for automating robot design from high-level specifications, yet they remain ineffective for robots operating under complex physical interactions. This limitation stems from the gap between language-based reasoning and the physical consequences of embodiment, often resulting in designs with low physical validity. In this work, we propose a multi-layered framework, AID-SR, that establishes a closed loop by translating simulator-observed physical states into structured feedback for the LLM designer. Combined with semantic critique, human feedback, and iterative refinement, the framework promotes the generation of physically feasible and functionally meaningful robot designs. We evaluate our approach on tendon-driven continuum robots across a benchmark of 14 tasks spanning reaching, grasping, locomotion, and manipulation. The proposed framework achieves 96.2% rate for passing the simulation feasibility check and by applying a common reinforcement learning training, 26.7% robots can successfully fulfill the corresponding task. We then fabricate three designed robots of AID-SR that successfully complete the task in real-world. These extensive experiments across simulation and real-world environments demonstrate and break the wall of utilizing the LLMs for automated design of continuum robots. The source code and experimental resources are publicly available at https://github.com/UNITES-Lab/AID-SR.

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