Which type of machine operates by pushing or pulling a toothed tool through a workpiece?

The correct answer is a broaching machine. This type of machine operates by using a toothed tool, known as a broach, which is pushed or pulled through a workpiece to remove material and create a desired shape or finish. The teeth on the broach progressively cut into the material as it moves, allowing for precise machining of complex profiles, holes, and surfaces.

Broaching is particularly effective for producing features such as keyways, splines, or gear teeth, where accuracy and surface finish are crucial. The capability to machine in one stroke, as opposed to multiple passes, makes broaching an efficient method for mass production of parts.

Other options like stamping machines and forging machines operate on different principles—stamping involves shaping materials through compressive forces, while forging uses localized compressive forces to deform metal. Workholding stations are not machines that process materials but rather setups to hold workpieces securely during machining operations.