Point at will solve your problem.

I selected small and object->point at and selected big, then big and pointed it at small and now they point at each other. I used point at=0.5 on small to keep it centered and it look nice.

You are limited to 20 degree rotate on up because small is short but you could make it longer, but that would also be true in real world. One idea might be to simply let small extend into down. A more detailed model would have a hole in down where big could rotate, it would also enable you to use a longer small.