In woodworking, a driving tool is any tool used to push (drive) another object into the wood. Their general purpose is to connect two pieces of wood together, or to connect wood to another material.
An hammer is familiar tool available in all hardware stores, and is used for driving nails into wood. Different weights of hammer are available for different purposes and strengths of wood.
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A mallet is similar to a hammer, but larger and made of wood or rubber rather than metal, although sometimes metal is used in the center of the head to give greater weight. It is used when the heavier and stronger hammer is at risk of damaging the wood or other parts.
The punch is a steel cylinder with a slightly serrated edge. It is used to drive nail heads further into the wood than a hammer can to stop them from protruding, usually for safety or aesthetic reasons.
Another familiar tool, the screwdriver is used to drive screws into wood and other materials. Typically a screw with a sharp point, such as a wood screw, would be used.
A bench hold fast comes in several varieties. These tools are not used for driving directly, but are used to hold wood firmly to a bench, allowing them to be worked on with other tools. Some are simple hook shapes that press down on the wood, while others use a lever that is moved via an attached screw; this variety can push down with great force.