Infinitely variable multi-epicyclic friction transmission system including a main shaft, ball race discs, a splined tube, and twin planetary cone assemblies attached to a planetary carrier and disposed circumferentially around the splined tube. Each twin planetary cone assembly comprises a torque tube and a planetary cone-hemisphere structure comprising a planetary cone integral with hemisphere at its apex, wherein the planetary cone-hemisphere structure rolls inside the torque tube via the hemisphere, and wherein a slant height of the twin planetary cone assemblies is parallel to the main shaft. System also includes a series of spherical planets, a reaction ring disposed around the twin planetary cone assemblies configured to slide along the planetary cone assemblies to vary a gear ratio, and ball gear retaining rings. Each of the ball gear retaining rings is mounted on one of a plurality of ball gears which are mounted on the ball race discs.