Step 1: Recall how kinematic pairs are classified.
A kinematic pair is named according to the type and number of relative motions it allows between the two connected links, such as sliding along one axis, turning about one axis, or more complex combined motion.
Step 2: Work out the motion a ball and socket allows.
A ball sitting inside a matching socket can rotate freely about any axis passing through the centre of the ball, giving three independent rotational degrees of freedom rather than motion restricted to a single axis.
Step 3: Match this to the correct pair name.
A turning pair only allows rotation about one fixed axis, a rolling pair involves one body rolling over another without slipping, and a screw pair combines rotation with a proportional translation along a thread, none of which match the free multi-axis rotation of a ball and socket. That multi-axis rotation is exactly what defines a spherical pair.
\[ \boxed{\text{Spherical pair}} \]