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Lathes that sit on a bench or table are called "bench lathes".
Machining can be done in-situ (on-car) or off-car (bench lathe).
For an off-car lathe, or bench lathe, the rotor is removed from the car and mounted to the lathe.
A machine tool may have several spindles, such as the headstock and tailstock spindles on a bench lathe.
The name bench lathe implies a version of this class small enough to be mounted on a workbench (but still full-featured, and larger than mini-lathes or micro-lathes).
Although a bench lathe has more than one spindle (counting the tailstock), it is not called a multispindle machine; it has one main spindle.
Turrets can be added to non-turret lathes (bench lathes, engine lathes, toolroom lathes, etc.) by mounting them on the toolpost, tailstock, or both.
The terms center lathe, engine lathe, and bench lathe all refer to a basic type of lathe that may be considered the archetypical class of metalworking lathe most often used by the general machinist or machining hobbyist.
The formative decades for this class of machine were the 1840s through 1860s, when the basic idea of mounting an indexable turret on a bench lathe or engine lathe was born, developed, and disseminated from the originating shops to many other factories.
Unlike bench lathes, engine lathes, and toolroom lathes, on which each tool change involved some amount of setup, and toolpath had to be carefully controlled by the operator, turret lathes allowed the multiple tool changes and toolpaths of one part-cutting cycle to be repeated with little time or effort.