The call Flutterwheel starts from facing couples.
The dancers drop hands and the dancers on the right of each couple go in to meet each other with right hands. They turn using that hand until they are on the other side, where they extend their left hand to the other dancer who has been waiting there, and they join hands as a couple. Each couple continues the turning motion while facing the other couple, similar to a Circle Left, until they are back on the side where the dancer on the right originally started.
For this to happen smoothly, the dancers who are waiting must anticipate the circling motion. They should be ready to start moving to their left, with their right hands held out ready to form a couple.
Reverse Flutterwheel works the same way except that the dancers on the left meet each other with left hands, and then extend their right hand to the other dancer from the other side to bring that dancer back to their own side.