Parametric Computer-Aided Design (CAD) of articulated assemblies is essential for product development, yet generating these multi-part, movable models from high-level descriptions remains unexplored. To address this, we propose ArtiCAD, the first training-free multi-agent system capable of generating editable, articulated CAD assemblies directly from text or images. Our system divides this complex task among four specialized agents: Design, Generation, Assembly, and Review. One of our key insights is to predict assembly relationships during the initial design stage rather than the assembly stage. By utilizing a Connector that explicitly defines attachment points and joint parameters, ArtiCAD determines these relationships before geometry generation, effectively bypassing the limited spatial reasoning capabilities of current LLMs and VLMs. To further ensure high-quality outputs, we introduce validation steps in the generation and assembly stages, accompanied by a cross-stage rollback mechanism that accurately isolates and corrects design- and code-level errors. Additionally, a self-evolving experience store accumulates design knowledge to continuously improve performance on future tasks. Extensive evaluations on three datasets (ArtiCAD-Bench, CADPrompt, and ACD) validate the effectiveness of our approach. We further demonstrate the applicability of ArtiCAD in requirement-driven conceptual design, physical prototyping, and the generation of embodied AI training assets through URDF export.