English: Epicyclic Mechanisms for the Cosmos. Fixed gears are underlined; blue gears calculate synodic cycles; red gears calculate years; black gears are idler gears: all designated by their tooth counts. “ ~ ” means “meshes with”; “ + ” means “fixed to the same arbor”; “⨁” means “with a pin-and-follower, turning on the central axis” or “with a pin-and-slot on eccentric axes”—creating variable motion (turquoise). Followers are slotted rods that follow a pin on the epicyclic gear and turn on the central axis. For each mechanism, there is a fixed gear at the centre, meshing with the first epicyclic gear, which is forced to rotate by the rotation of b1 or the CP. (a) 4-gear epicyclic system for the Line of Nodes. (b) 3-gear direct model for the true Sun. (c) 5-gear direct model for an inferior planet for complex period relations, with variable motion calculated by a pin and slotted follower. (d) 7-gear indirect model for a superior planet for complex period relations, with variable motion calculated by a pin-and-slot on eccentric axes. (e) Period relations and gear trains on the Main Drive Wheel, b1; Mercury & Venus share fixed 51. (f) Period relations and gear trains on the Circular Plate, CP, sharing fixed 56; gears also shared between Saturn/true Sun and Mars/Jupiter (Supplementary Discussion S4).