The motion of an articulated part in cluttered surroundings is constrained not only by an object’s intrinsic joint limits but also by extrinsic obstacles. However, existing approaches primarily consider object articulation properties alone. Here we present Motion Constraint Prediction Network (MoCo-Net), a two-stream neural network that jointly predicts the continuous motion ranges of articulated parts and obstacle heatmaps highlighting potential collision regions from partial view point cloud observation. By capturing both internal and external motion constraints, MoCo-Net produces more accurate feasible motion range prediction and obstacles recognition, improves generalization for novel objects in new scenes, and enables robots to construct a scene configuration space for efficient exploration of rearrangement actions. Our experiments show that MoCo-Net’s two-stream design enhances each other to deliver more accurate predictions, which subsequently form a compact configuration space for a customized planner to efficiently rearrange the scene.