A cable transportation installation, including an aerial hauling cable, a vehicle having an attachment device to attach the vehicle to the hauling cable, a structure on which at least one sheave is mounted movable between a first position in which the at least one sheave is in contact with the hauling cable and a second position in which the at least one sheave is separated from the hauling cable, and at least one actuating device coupled to the at least one sheave and configured to exert a first force on the at least one sheave in order to move the at least one sheave to the first position, and to exert a second force on the at least one sheave in order to move the at least one sheave to the second position.