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Part mobility analysis is a significant aspect required to achieve a functional understanding of 3D objects. It would be natural to obtain part mobility from the continuous part motion of 3D objects. In this study, we introduce a self-supervised method for segmenting motion parts and predicting their motion attributes from a point cloud sequence representing a dynamic object. To sufficiently utilize spatiotemporal information from the point cloud sequence, we generate trajectories by using correlations among successive frames of the sequence instead of directly processing the point clouds. We propose a novel neural network architecture called PointRNN to learn feature representations of trajectories along with their part rigid motions. We evaluate our method on various tasks including motion part segmentation, motion axis prediction and motion range estimation. The results demonstrate that our method outperforms previous techniques on both synthetic and real datasets. Moreover, our method has the ability to generalize to new and unseen objects. It is important to emphasize that it is not required to know any prior shape structure, prior shape category information, or shape orientation. To the best of our knowledge, this is the first study on deep learning to extract part mobility from point cloud sequence of a dynamic object.