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We introduce Articulation-aware Normalized Coordinate Space Hierarchy (ANCSH) - a canonical representation for different articulated objects in a given category. As the key to achieve intra-category generalization, the representation constructs a canonical object space as well as a set of canonical part spaces. The canonical object space normalizes the object orientation,scales and articulations (e.g. joint parameters and states) while each canonical part space further normalizes its part pose and scale. We develop a deep network based on PointNet++ that predicts ANCSH from a single depth point cloud, including part segmentation, normalized coordinates, and joint parameters in the canonical object space. 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