Which assembly relationship defines the travel of an under-constrained component by relating it to a sketch?

The best choice is the Path relationship, which is specifically designed to define the movement of an under-constrained component in relation to a sketch or curve. This relationship allows the component to follow a defined trajectory within the assembly, effectively controlling how it moves along a specified path. Such a method is particularly useful in scenarios where precise motion along a predetermined route is necessary, such as with mechanical linkages or components that must traverse a specific trajectory.

In contrast, the other relationships serve different purposes. The Distance relationship is typically used to maintain a fixed separation between components, but it does not dictate movement along a particular path. The Angle relationship is focused on defining rotational relationships between components rather than movement along a sketch. A Fixed relationship is utilized to lock a component in place, which would not allow any movement at all. Therefore, when it comes to defining travel based on a sketch, the Path relationship is the only one that fits this specific requirement effectively.