A screw-cutting lathe is a machine (specifically, a lathe) capable of cutting very accurate screw threads via single-point screw-cutting, which is the process of guiding the motion of the tool bit in a precisely known ratio to the rotating motion of the workpiece. This is accomplished by gearing the leadscrew (which drives the tool bit's movement) to the spindle with a certain gear ratio for each thread pitch. Every degree of spindle rotation is matched by a certain distance of linear tool travel, depending on the desired thread pitch (English or metric, fine or coarse, etc.).
The name "screw-cutting lathe" carries a taxonomic qualification on its use—it is a term of historical classification rather than one of current commercial machine tool terminology. Early lathes, many centuries ago, were not adapted to screw-cutting. Later, from the Late Middle Ages until the early nineteenth century, some lathes were distinguishable as "screw-cutting lathes" because of the screw-cutting ability specially built into them. Since then, most metalworking lathes have this ability built in, but they are not called "screw-cutting lathes" in modern taxonomy.
The screw has been known for millennia. Archimedes devised the water screw, a system for raising water. Screws as mechanical fasteners date to the first century BCE. Although screws were tremendously useful, the difficulty in making them prevented any widespread adoption.
The earliest screws tended to be made of wood, and they were whittled by hand, with or without the help of turning on a lathe with hand-controlled turning tools (chisels, knives, gouges), as accurately as the whittler could manage. It is likely that sometimes the wood blanks that they started from were tree branches (or juvenile trunks) that had been shaped by a vine wrapped helically around them while they grew. (In fact, various Romance words for "screw" come from the word root referring to vines.) Walking sticks twisted by vines show how suggestive such sticks are of a screw.