An actuation device is described, comprising: an actuator (1) having a movable actuation element (3,8); at least a transmission element (23) being capable of moving from a respective first operating condition to a respective second operating condition under the action of said actuation element (3,8). According to the invention, actuating means (21F,23D,24,26) are provided, which are made operative by said actuation element (3,8) during a displacement of the latter, for inducing to said transmission element (23) a movement which occurs at least in part with a speed being higher than the speed of said displacement of said actuation element (3,8). The device has an advantageous use in the realization of systems for blocking in a determined position the drum of a machine for washing and/or drying laundry.