The rotator cuff was an anatomical term given to the group of muscles and their tendons that acted to stabilize the Human shoulder.
In 2371, Miles O'Brien tore his rotator cuff while playing darts with Syvar, necessitating surgery from Doctor Bashir. (DS9: "Shakaar")
O'Brien suffered the same injury four years later in a holosuite practice session while preparing for a baseball game against Captain Solok's team. Dr. Bashir again repaired the damage. (DS9: "Take Me Out to the Holosuite")