The family of transmissions has a plurality of members that can be utilized
in powertrains to provide at least seven forward speed ratios and one
reverse speed ratio. The transmission family members include three
planetary gear sets having six torque-transmitting mechanisms and three
fixed interconnections. The powertrain includes an engine and torque
converter that is not continuously connected to any of planetary gear
members. In some family members, the output shaft is continuously
connected with at least one member of the first or second planetary gear
set or continuously connected with a member of the third planetary gear
set and selectively connectable with at least one member of the first,
second or third planetary gear set. The six torque-transmitting mechanisms
provide interconnections between various gear members, the fixed
interconnections, the input shaft, the output shaft, and the transmission
housing, and are operated in combinations of three to establish at least
seven forward speed ratios and at least one reverse speed ratio.