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).

Designing mechanical mechanisms to trace specific paths is a classic yet notoriously difficult engineering problem, characterized by a vast and complex search space of discrete topologies and continuous parameters. We introduce MechaFormer, a Transformer-based model that tackles this challenge by treating mechanism design as a conditional sequence generation task. Our model learns to translate a target curve into a domain-specific language (DSL) string, simultaneously determining the mechanism's topology and geometric parameters in a single, unified process. MechaFormer significantly outperforms existing baselines, achieving state-of-the-art path-matching accuracy and generating a wide diversity of novel and valid designs. We demonstrate a suite of sampling strategies that can dramatically improve solution quality and offer designers valuable flexibility. Furthermore, we show that the high-quality outputs from MechaFormer serve as excellent starting points for traditional optimizers, creating a hybrid approach that finds superior solutions with remarkable efficiency.

Mechanisms are essential components designed to perform specific tasks in various mechanical systems. However, designing a mechanism that satisfies certain kinematic or quasi-static requirements is a challenging task. The kinematic requirements may include the workspace of a mechanism, while the quasi-static requirements of a mechanism may include its torque transmission, which refers to the ability of the mechanism to transfer power and torque effectively. In this paper, we propose a deep learning-based generative model for generating multiple crank-rocker four-bar linkage mechanisms that satisfy both the kinematic and quasi-static requirements aforementioned. The proposed model is based on a conditional generative adversarial network (cGAN) with modifications for mechanism synthesis, which is trained to learn the relationship between the requirements of a mechanism with respect to linkage lengths. The results demonstrate that the proposed model successfully generates multiple distinct mechanisms that satisfy specific kinematic and quasi-static requirements. To evaluate the novelty of our approach, we provide a comparison of the samples synthesized by the proposed cGAN, traditional cVAE and NSGA-II. Our approach has several advantages over traditional design methods. It enables designers to efficiently generate multiple diverse and feasible design candidates while exploring a large design space. Also, the proposed model considers both the kinematic and quasi-static requirements, which can lead to more efficient and effective mechanisms for real-world use, making it a promising tool for linkage mechanism design.