Don't know if you have seen this ( Wiki is your friend ) but it does a good job of explaining the movements of Alpha Centauri A & B and shows how the PA and Separation change over time. When I first saw them through a telescope in the mid 60s' they were quite wide apart, about 12.0" I think and now they have closed to about 4.0". Just a game of patience and long memory but the spectroscopy angle for short period binaries looks interesting.
https://en.wikipedia.org/wiki/Alpha_Centauri