Abstract: Embodiments provide for planetary gearing systems with ring gears comprising cylindrical tooth forms arrayed from a central axis and encompassing at least one planetary sprocket and a sun gear. The sun and ring gears have cylindrical tooth forms. The planetary sprocket teeth are aligned for engagement with at least one of the sun gear and ring gear cylindrical tooth forms at a contact radius from the central axis selected as a function of the sprocket tooth common involute gear shape, the sprocket radius, the sprocket tooth pitch, and of the pitch, gear radius and cylindrical form diameter of the selected at least one gear cylindrical tooth forms.

Abstract: Embodiments provide for planetary gearing systems with sun, planetary and ring gears, wherein the ring gears have generally cylindrical or elliptical tooth forms with a common shape and geometric parameters. The ring gear and a sun gear each engage one or more of planetary gears in respective mesh engagements, wherein the gear forms on each may be independently formed as a function of their respective geometries (sun or ring gear pitches, and sun or ring radii from a common central axis of the planetary gearing system), and as a function of the planetary gear tooth form shape and geometric parameters, planetary gear radius from the common central axis, and the planetary gear tooth pitch.

Abstract: Embodiments provide for planetary gearing systems with ring gears comprising cylindrical tooth forms arrayed from a central axis and encompassing at least one planetary sprocket and a sun gear. The sun and ring gears have cylindrical tooth forms. The planetary sprocket teeth are aligned for engagement with at least one of the sun gear and ring gear cylindrical tooth forms at a contact radius from the central axis selected as a function of the sprocket tooth common involute gear shape, the sprocket radius, the sprocket tooth pitch, and of the pitch, gear radius and cylindrical form diameter of the selected at least one gear cylindrical tooth forms.