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.