What device is used to prevent twisting between the pulling rope and the cable?

The device used to prevent twisting between the pulling rope and the cable is known as a swivel. A swivel allows movement in multiple directions while keeping the two elements connected without allowing them to twist around each other. This is particularly important in various applications where a rope or cable needs to be pulled or maneuvered without becoming entangled or twisted, which could cause damage or reduce efficiency.

In contrast, a pulley primarily serves to change the direction of the force applied to the rope or cable, making lifting easier, but does not specifically address the issue of twisting. A clamp is utilized to secure or hold a cable or rope in place but does not facilitate movement or prevent twisting. A connector simply serves to join two components together but does not have any mechanisms to manage or reduce the potential for twisting. Therefore, the swivel is the most effective device for the purpose described in the question.