An assisted-movement system is provided for an appliance, such as a dishwasher including a tub portion defining a forward opening, a door pivotally engaged therewith for selectively engaging the forward opening, and a rack movable into and out of the tub portion through the forward opening. A biasing device is operably engaged between the tub portion and one of the door, via a hinge mechanism, and the rack. The biasing device is extendable between contracted and extended positions. A position control device is operably engaged between the tub portion and one of the door, the rack, and the biasing device, and is configured to cooperate with the one of the door, the rack, and the biasing device to at least one of maintain the door in a closed position and maintain the rack within the tub portion, with the biasing device in the contracted position. Associated dishwashers are also provided.