Recent advances in generative models have produced strong results for static 3D shapes, whereas articulated 3D generation remains challenging due to action-dependent deformations and limited datasets. We introduce ArticFlow, a two-stage flow matching framework that learns a controllable velocity field from noise to target point sets under explicit action control. ArticFlow couples (i) a latent flow that transports noise to a shape-prior code and (ii) a point flow that transports points conditioned on the action and the shape prior, enabling a single model to represent diverse articulated categories and generalize across actions. On MuJoCo Menagerie, ArticFlow functions both as a generative model and as a neural simulator: it predicts action-conditioned kinematics from a compact prior and synthesizes novel morphologies via latent interpolation. Compared with object-specific simulators and an action-conditioned variant of static point-cloud generators, ArticFlow achieves higher kinematic accuracy and better shape quality. Results show that action-conditioned flow matching is a practical route to controllable and high-quality articulated mechanism generation.