a variable ratio chain sprocket is disclosed wherein a plurality of chain engaging segments are slidingly affixed between a first pair of disks and are constrained to move in a radial direction with respect thereto . a second pair of disks , rigidly attached to a shaft , are disposed adjacent the first pair of disks and engage a projection on the segments in spiral slots . the torque applied to the sprocket controls the relative rotation between the first and second pair of disks and causes the chain engaging segments to move in a radial direction . the chain engaging segments have teeth movably attached thereto . the teeth are depressed radially inwardly when contacted on the top by a chain roller .