With the rapid development of artificial intelligence (AI), it is foreseeable that the accuracy and efficiency of dynamic analysis for future power system will be greatly improved by the integration of dynamic simulators and AI. To explore the interaction mechanism of power system dynamic simulations and AI, a general design for AI-oriented power system dynamic simulators is proposed, which consists of a high-performance simulator with neural network supportability and flexible external and internal application programming interfaces (APIs). With the support of APIs, simulation-assisted AI and AI-assisted simulation form a comprehensive interaction mechanism between power system dynamic simulations and AI. A prototype of this design is implemented and made public based on a highly efficient electromechanical simulator. Tests of this prototype are carried out in four scenarios including sample generation, AI-based stability prediction, data-driven dynamic component modeling, and AI-aided stability control, which prove the validity, flexibility, and efficiency of the design and implementation for AI-oriented power system dynamic simulators.