How does the bevel gear on the shaft works?

How does the bevel gear on the shaft works?
The bevel gear on the input shaft turns two slightly larger bevel gears that spin freely on the vertical shaft. One is driven by the top of the input gear and the other by the bottom of it, so they rotate in opposite directions, but they are the same size as each other so they turn at the same speed.
Between the two gears is a sliding clutch assembly, shaped like two shallow cones mounted base-to-base on the shaft. Ridges called splines on the shaft and matching grooves in the clutch ensure that it can easily slide up and down, but can't turn without turning the shaft as well. Moving the gear lever slides the clutch up or down so that one of the cones engages into a matching hollow in one of the spinning gears, which locks that gear on to the shaft.
At the bottom of the shaft, a relatively small bevel gearbox engages with a much larger gear on the output shaft, to give a horizontal output, at a much lower speed of rotation.