Arky movements, in general, involve one set of active couples who are half sashayed working with the other two pairs who are in regular partner arrangement (lady on man's right). A great many Arky style movements will see men working with men and girls with girls. In some circles, the dancer in the man's position (on the left of a pair) is called a "Beau" while the dancer in the girl's usual position is called a "Belle."
This definition is from The Handbook of Modern Square Dancing by Jay King.
It is provided here for informational and educational purposes only.