There are demands for automobiles that have high fuel efficiencies because of environmental concerns.  Accordingly, improvements for fuel economy have been made on automatic transmissions which are incorporated in automobiles.  For example, speed ranges are arranged with multiple speed change ratios to transmit efficiently the output of the engine to wheels of the vehicle. 
As a method for designing an automatic transmission with multiple speed change ratios, for example, an automatic transmission is equipped with a planetary gear train whose gears are used in combination for establishing speed change ratios.  Also, as another example, an automatic transmission incorporates a plurality of gear trains that are disposed on a plurality of shafts arranged in parallel with one another (refer to, for example, Japanese Laid-Open Patent Publication No.  S60(1985)-4651 (pages 3 and 4 and FIG.  1)). 
However, the provision of multiple speed change ratios to an automatic transmission involves an increase in the number of gear intermeshing and also an increase in the number of elements that generate dragging torques, like clutches or brakes.  These increases present another problem that an automatic transmission designed in such a way can experience an impairment in the efficiency of power transmission.  It is possible to improve the transmission efficiency by designing a parallel shaft gear train type automatic transmission to have the least number of gear intermeshing.  In this case, however, a plurality of gear trains are required in the same number as the speed ranges to be endowed to the power transmission.  Therefore, this leads to an enlargement of the automatic transmission and impairs the mountability of the automatic transmission, for example, on an automobile.  On the other hand, if an automatic transmission is designed with a planetary gear train, then it is possible to compact the total size of the transmission.  However, the relatively large number of intermeshings inside the automatic transmission acts to increase the resistance in the power transmission and thereby decreases the efficiency of the power transmission.