Motion and constraint identification are the fundamental issue throughout the development of parallel mechanisms. Aiming at meaningful result with heuristic and visualizable process, this paper proposes a machine learning-based method for motions and constraints modeling and further develops the automatic software for mobility analysis. As a preliminary, topology of parallel mechanism is characterized by recognizable symbols and mapped to the motion of component limb through programming algorithm. A predictive model for motion and constraint with their nature meanings is constructed based on neural network. An increase in accuracy is obtained by the novel loss function, which combines the errors of network and physical equation. Based on the predictive model, an automatic framework for mobility analysis of parallel mechanisms is constructed. A software is developed with WebGL interface, providing the result of mobility analysis as well as the visualizing process particularly. Finally, five typical parallel mechanisms are taken as examples to verify the approach and its software. The method facilitates to attain motion/constraint and mobility of parallel mechanisms with both numerical and geometric features.