speed of the ring gear with weighting factors determined by the number of teeth on each gear similar speed relationships are imposed by other known types of fixed gearing arrangements for example a double pinion planetary gear set constrains the speed of the ring gear to be a weighted average between the speed of the sun gear and the speed of the carrier gear sets 30 40 and 50 are similarly structured a suggested ratio of gear teeth for each planetary gear set is listed in table 1 in the transmission of fig1 sun gear 26 is fixedly coupled to sun gear 36 by intermediate shaft 72 ring gear 28 and carrier 32 are fixedly coupled to ring gear 58 sun gear 46 is fixedly coupled to sun gear 56 ring gear 48 is fixedly coupled to carrier 52 and output shaft 12 is fixedly coupled to carrier 42 intermediate shaft 72 is selectively held against rotation by brake 66 and selectively coupled to input shaft 10 by clutch 64 carrier 22 is selectively held against rotation by brake 70 input shaft 10 is selectively coupled to ring gear 38 by clutch 68 and selectively coupled to ring gear 48 and carrier 52 by clutch 62 sun gears 46 and 56 are selectively held against rotation by brake 60 the combination of gear set 20 and brake 70 selectively impose a speed relationship between ring gear 58 and intermediate shaft 72 specifically intermediate shaft 72 and ring gear 58 rotate.