**The lead screw of a lathe with nut is a screw pair.**

**Explanation:**

A lathe is a machine tool used in metalworking operations to shape workpieces with the help of cutting tools. The lead screw is an important component of a lathe that is used to move the carriage or the tool post along the length of the lathe bed.

The lead screw-nut mechanism in a lathe is a screw pair. Let's understand the characteristics of a screw pair and how they apply to the lead screw-nut mechanism in a lathe:

1. **Screw Pair:**
- A screw pair consists of a screw and a nut that have helical or inclined surfaces.
- The screw has a helical thread on its outer surface, while the nut has a corresponding internal thread.
- The relative motion between the screw and the nut is a combination of rotary and translational motion.
- The rotary motion of the screw causes the nut to move linearly along its axis.

2. **Lead Screw-Nut Mechanism in a Lathe:**
- In a lathe, the lead screw is responsible for the longitudinal movement of the carriage or the tool post.
- The lead screw is connected to the carriage or the tool post, while the nut is fixed to the lathe bed.
- When the lead screw rotates, it causes the nut to move linearly along the length of the lathe bed.
- This linear movement of the nut translates into the longitudinal movement of the carriage or the tool post.

3. **Characteristics of the Lead Screw-Nut Mechanism:**
- The lead screw in a lathe has a helical thread on its outer surface, while the nut has a corresponding internal thread.
- The rotary motion of the lead screw causes the nut to move linearly, allowing the carriage or the tool post to traverse along the lathe bed.
- The helical nature of the lead screw and nut creates a mechanical advantage, allowing for precise control of the longitudinal movement.
- The lead screw-nut mechanism in a lathe exhibits the characteristics of a screw pair, making it an essential component for the functioning of the lathe.

In conclusion, the lead screw of a lathe with nut is a screw pair as it consists of a helical threaded screw and a corresponding nut that exhibit rotary and translational motion to facilitate the longitudinal movement of the carriage or the tool post along the lathe bed.

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