**Explanation:**

The correct answer is option D, which states that a half nut is a mechanism that locks the lathe carriage to the lead screw for thread cutting.

A half nut is an essential component in a lathe machine, which is used to cut threads on a workpiece. It is a mechanism that engages with the lead screw, allowing the carriage to move along the length of the bed and cut threads accurately. Here is a detailed explanation of how the half nut works:

**1. Purpose of the Half Nut:**
The half nut is responsible for engaging and disengaging the carriage from the lead screw. When the half nut is engaged, it locks the carriage to the lead screw, allowing the carriage to move along with the rotating lead screw. This movement is used to cut threads on a workpiece.

**2. Half Nut Design:**
The half nut is designed as a split nut, which means it is divided into two halves. These halves are hinged together and can be opened or closed around the lead screw. The nut has internal threads that match the pitch of the lead screw.

**3. Engaging the Half Nut:**
To engage the half nut, the operator brings the carriage close to the desired starting position for thread cutting. Then, the operator manually closes the two halves of the nut around the lead screw. This action aligns the internal threads of the nut with the threads of the lead screw.

**4. Locking the Carriage:**
Once the half nut is engaged, the operator locks the carriage to prevent it from moving freely along the bed. This is done by tightening a locking lever or knob that secures the half nut in place. With the half nut locked, the carriage is now connected to the lead screw and will move along with it during thread cutting.

**5. Disengaging the Half Nut:**
After completing the thread cutting operation, the operator must disengage the half nut to allow the carriage to move freely again. This is done by loosening the locking lever or knob, which releases the pressure on the half nut and allows it to open up, disengaging from the lead screw.

In summary, a half nut is a mechanism in a lathe machine that locks the carriage to the lead screw for thread cutting. It is a split nut that engages with the lead screw and is locked in place to ensure accurate thread cutting.

D