In a two-speed gearbox (Figure P8.27, see on page 404), the lower shaft has splines, and...

In a two-speed gearbox (Figure P8.27, see on page 404), the lower shaft has splines, and it can slide horizontally as an operator moves the shift fork. Design the transmission and choose the number of teeth on each gear to produce velocity ratios of approximately 0.8 (in first gear) and 1.2 (in second gear). Select gears having only even numbers of teeth between 40 and 80. Note that a constraint exists on the sizes of the gears so that the locations of the shaft’s centers are the same in the first and second gears.