From a line of four, the center two people move forward, working with the adjacent outside person who serves as a pivot or hinge, to turn as a couple the fractional part of a full turn indicated by the call. Finishes in lines facing out or in.
BACKGROUND NOTE: Cast Off has been a regular part of Contra Dancing and was being used long before modern square dancing reacquired the move. Before the name "Cast Off" was used, Jim York of Mill Valley, California in 1956 would have dancers perform the same move by using the more or less directional call, Ends Will Hinge. Another way of calling it in some areas was to say Centers Turn Out. There is still controversy about what to call a 3/4 arm turn by dancers in a wave formation (or two adjacent dancers with arms joined and facing in opposite directions.) The one-quarter arm turn is now generally termed "Hinge" or "Single Hinge" and the half arm turn is a "Trade." With regard to this "Trade" term--there is still no single call that will enable us to tell the end and adjacent dancer in a wave to swing half except by saying the actual words, "All Swing Half." Using the term "Neighbors" for these dancers would solve that problem (e.g., "Neighbors Trade"). The 3/4 arm turn is still usually called "Cast Off 3/4," but it is evident that it does not fit the definition of Cast Off. "Arm Turn 3/4" is descriptive enough as a call, but probably some other name will have to be coined and generally adopted.
This definition is from The Handbook of Modern Square Dancing by Jay King.
It is provided here for informational and educational purposes only.