To increase transmission torque by automatically strengthening a magnetic field imparted to a magnetic viscous fluid, when a rotating speed of a rotary shaft of becoming the input side becomes a rotating speed of a certain constant value or more, with a simple structure.

A rotation braking device includes first torque transmission members relatively nonrotatably arranged to a rotary shaft 10, second torque transmission members relatively rotatably arranged to the first torque transmission member, a magnetic viscous fluid interposed in clearances between the first torque transmission members and the second torque transmission members, and permanent magnets 50 having magnetic poles on both outside in the axial direction of the first and second transmission members and generating a magnetic field of penetrating through the magnetic viscous fluid of interposing in the clearances, and includes movable members 60 constituted of a magnetic substance relatively nonrotatably arranged to the rotary shaft 10 and slidably arranged in the radial direction, springs 80 for energizing the movable members 60 to the axial side, and movable member entering spaces for making the movable members 60 enter when the rotating speed of the rotary shaft 10 becomes the rotating speed of the certain constant value or more and arranged between the magnetic poles.