Derivation of the Specific and General Kinematic Laws of a Planetary Gear System with External Meshing: A Mathematical and Physical Framework Supporting Patent No. 6269

This research paper presents the formal mathematical and physical derivation of the MYM 2026 Law for planetary gear systems with external meshing. It establishes a new kinematic framework that addresses the limitations of traditional models (such as Willis's method) and provides the theoretical foundation for the efficient transmission and energy generation observed in the inventor's practical applications.The study provides a comprehensive analysis of specific and general kinematic laws, supporting the technical claims of Syrian Patent No. 6269 (Electric Power Generation Wheel). This work is a significant contribution to mechanical engineering and kinematics, offering a new perspective on torque cancellation and angular velocity relationships in complex gear assemblies.Key Innovation: The MYM Law (k - 2) for external meshing systems.Associated Patent: Syrian Patent No. 6269.