As a core component of modern mechanical transmission, rotary motion mechanisms and their drive systems have broad applications in aerospace, robotics, and other fields. This article systematically reviews the design principles, performance characteristics, and research progress of various rotary motion mechanisms and their driving technologies. The advantages, disadvantages, and applicable scenarios of traditional mechanisms such as gear mechanisms, drive belt mechanisms, sprocket mechanisms, cam mechanisms, ratchet and pawl mechanisms, and connecting rod mechanisms were analyzed in detail. The innovative design and application potential of new mechanisms, such as intermittent indexing mechanisms, magnetic gears, spherical gears, and multi-link mechanisms, were also explored. In addition, the paper provides a detailed comparison of the performance differences among electric, hydraulic, pneumatic, and other driving methods and summarizes the optimization directions for efficient driving systems. Research has shown that through material innovation, structural optimization, and intelligent control, there is still significant room for improvement in load capacity, accuracy, and reliability of rotary motion mechanisms, providing theoretical support and practical reference for future mechanical transmission technology development.