An automatic transmission includes a double-pinion planetary gearset and two single-pinion planetary gearsets. A first ring gear is held stationary. A second sun gear and a third ring gear are coupled to a first sun gear and a first carrier respectively, constituting first and second rotor units. An output is coupled to a third carrier. A first clutch selectively couples a second carrier to the first rotor unit. A second clutch selectively couples the second carrier to the second rotor unit. A third clutch selectively couples an input to the second carrier. A fourth clutch selectively couples a second ring gear to a third sun gear. A fifth clutch selectively couples the second ring gear to the third carrier. A sixth clutch selectively couples the input to the third sun gear. Nine forward gear ratios and one reverse gear ratio are obtained by simultaneous application of three of the clutches.