An English Boxford VSL lathe showing the clever but simple lever-operated "tumble-reverse" mechanism by which means the direction of drive to the leadscrew (and power-shaft if fitted) can be reversed and the carriage caused to move either towards or away from the headstock.
In its neutral, central position it allows the headstock spindle to revolve without driving any of the gears. Moving the engagement lever up or down (the spindle must be stationary of course) engages one or other of a pair of tumble gears below the spindle gear causing the next gear in the train to revolve either clockwise or anticlockwise. The lever is usually, but not always, spring loaded in some way, with a plunger that engages in one of three holes in either the front or side face of the headstock.
On all types, the stud gear is made removable, allowing it to be part of the screwcutting train.
See below for other examples of tumble-reverse units.

The same type of tumble-reverse mechanism on an American "Craftsman" lathe.

Another "Craftsman" lathe - but this time the tumble-reverse operating lever has to be unbolted before it can be moved.