In a roll rotation mechanism (1) for continuously causing a film-rolling roll to rotate at a constant rate, an Oldham coupling (4) is interposed in a transmission path between a wave gear reduction mechanism (3) and a roll (10). The Oldham coupling (4) forms a connection between a gear rotation output shaft (34) and a roll rotation shaft (11) in a state in which latitude of movement α is present about a central axis line (4a). When a roll (10) is continuously rotated at a constant rate, the Oldham coupling (4) is held in a state in which no latitude of movement is present in a rotation direction R and latitude of movement α is present in a direction opposite the rotation direction; and rotation torque is transmitted. Due to the presence of the latitude of movement α, a vibration transmission path is blocked in the Oldham coupling (4), vibrations are not transmitted from the wave gear reduction mechanism (3) to a roll (19), a vibration system does not resonate, and no incidence of large rotational fluctuation occurs in the roller.