Question

make a ball and socket joint

Answer 1

There are many joints in an animal body that have a ball and socket joint.

To make a model, take a ball of size 5 to 6 cm in diameter like a billiards ball. Then make a hemispherical socket by taking a rubber hollow ball, for example and cutting it in half.  Then this rubber socket, could be attached to a rod (wooden) say by an adhesive. The billiards ball could be attached to a wooden rod too.

Now the surface are of the hemispherical socket should be smaller than 50% of the sphere.  Then there will be more freedom for the ball & rod to move around in the space.