Multistep gear mechanism

A multi-stage transmission of a planetary design for a motor vehicle, the transmission comprising:

• a drive shaft (1),
• an output shaft (2),
• a housing (G),
• a first planetary gear set (P1), a second planetary gear set (P2), a third planetary gear set (P3), and a fourth planetary gear set (P4), each of the first, the second, the third, and the fourth planetary gear sets comprising:
• a sun gear, a carrier, and a ring gear,
• a plurality of rotatable shafts (1, 2, 3, 4, 5, 6, 7, 8, 9),
• a plurality of shift elements (03, 04, 16, 27, 58, 89), the plurality of shift elements comprising brakes (03, 04) and clutches (16, 27, 58, 89) whose selective engagement produces different transmission ratios between the drive shaft (1) and the output shaft (2),
• wherein the sun gear of the first planetary gear set (P1) is directly connected to a fifth shaft (5), the fifth shaft (5) is connected to the ring gear of the third planetary gear set (P3) and the fifth shaft (5) is detachably connectable, via a first clutch (58), to an eighth shaft (8),
• the eighth shaft (8) is connected to the carrier of the second planetary gear set (P2) and the eighth shaft (8) is detachably connectable, via a second clutch (89), to a ninth shaft (9),
• the ninth shaft (9) is directly connected to both the sun gear of the third planetary gear set (P3) and the sun gear of the fourth planetary gear set (P4),
• the drive shaft (1) is directly connected to the carrier of the first planetary gear set (P1) and the drive shaft (1) is also directly connected, upon engagement of a third clutch (16), to both a sixth shaft (6) and the ring gear of the second planetary gear set (P2),
• the sun gear of the second planetary gear set (P2) is directly connected to a third shaft (3), and the third shaft (3) is directly connected to the carrier of the third planetary gear set (P3) and the third shaft (3) is connectable, via a first brake (03), to the housing (G) of the transmission,
• the ring gear of the fourth planetary gear set (P4) is directly connected to a fourth shaft (4) and the fourth shaft (4) is connectable, via a second brake (04), to the housing (G) of the transmission, and
• the output shaft (2) is directly connected to the carrier of the fourth planetary gear set (P4) and the output shaft (2) is directly connectable, via a fourth clutch (27), to a seventh shaft (7), and the seventh shaft (7) is directly connected to the ring gear of the first planetary gear set (P1).