Which part of the lathe is located opposite the spindle and usually supports the workpiece?

The tailstock is located opposite the spindle on a lathe and serves the essential function of supporting the workpiece during machining. It provides stability and alignment, which are crucial for accurate cutting operations. The tailstock can also hold various tools, such as drills or reamers, making it versatile for different machining tasks. Its positioning allows it to complement the spindle, which is where the workpiece is secured and rotated. By supporting the opposite end of the workpiece, the tailstock helps prevent vibration and ensures a more controlled machining process. This configuration is vital in operations where precision is required, such as turning, drilling, and tapping.

In contrast, the toolpost is the part of the lathe that holds the cutting tool, while the carriage is utilized to move the cutting tool or workpiece in a controlled manner along the lathe bed. The headstock houses the spindle and is the driving force for rotation. Thus, the tailstock's role in workpiece support distinctly sets it apart from these other components.