Planetary gear-cam mechanisms (PGCMs) are mechanisms that combine planetary gears and cams. Despite the fact that these systems have the ability to achieve a wide variety of periodic motions of the output link, they have received little attention. To generate and classify PGCMs, structural properties must first be identified. The classification of gear-cam mechanisms is studied, as are their functional, structural, and graph representations. PGCMs are classified based on their number of degrees of freedom, number of links, and joint types. They are synthesized utilizing the spanning tree-based approach to build the entire set of gear-cam graphs. The relation between graphs and PGCMs is investigated and many graph fundamentals are converted into PGCMs. The atlas of five-vertex graphs is obtained, allowing the development of a large number of mechanisms. The precise results of the 5-link PGCM graphs have been confirmed to be 12. The application and significance of this approach in producing a variety of non-uniform motions, developing better alternatives, and creating new designs for variable-speed output mechanisms are demonstrated.