On a lathe, the top and the swivel are the two main parts of which component?

The correct answer is the compound rest. The compound rest is an essential component of a lathe that allows for precise control of the positioning and movement of the cutting tool. It consists of multiple parts, including the top slide and the swivel base. The top slide can be adjusted for angular cuts, while the swivel base allows the operator to set the tool at various angles to the workpiece.

This functionality is crucial for tasks such as taper turning or making intricate cuts, enhancing the lathe's versatility beyond straight turning. The compound rest's design facilitates smooth and accurate adjustments, which is why it is a fundamental feature in lathe operations. Therefore, recognizing the compound rest's importance and its distinguishing characteristics provides insight into its role in machining processes.