A family of power transmissions have three planetary gearsets each of which have first, second, and third members. A pair of fixed interconnecting members establish continuous connections between a member of the first planetary gearset and a member of the second planetary gearset, and between another member of the second planetary gearset and a member of the third planetary gearset, respectively. Each of the transmission family members has an output shaft, which is continuously connected with at least one member of one of the planetary gearsets and an input shaft, which is selectively connectible with at least two members of the planetary gearsets through respective first and second torque-transmitting mechanisms. Four other torque-transmitting mechanisms are provided to establish various interconnections between members of the planetary gearsets and/or members of the planetary gearsets and the transmission housing. The six torque-transmitting mechanisms are selectively engageable in combinations of four to establish at least seven forward speed ratios and one reverse speed ratio between the input shaft and the output shaft through the planetary transmission.