What is the pipe connection in which a ball is held in a cup-like that allows movement in every direction?

The concept being referenced is the ball joint, which is a connection that consists of a spherical ball encased in a cup-like socket. This design allows for movement in multiple directions, making it highly versatile and useful in applications where flexibility and adjustment are required. Ball joints are often found in various mechanical systems, including automobiles, where they enable smooth rotation and pivoting.

In this context, the ball joint's structure permits it to accommodate changes in alignment and angle, which is essential for maintaining proper function in dynamic systems. The ability to move in all directions enhances the joint's capability to absorb shocks and supports the overall stability of the connected components.

Other options, while they may also refer to types of joints or connections, do not specifically facilitate the same level of multi-directional movement that is characteristic of ball joints. This specificity is what makes the ball joint the correct answer to the question presented.