Linear hinge for an appliance

An appliance, comprising:

• a cabinet;
• a door;
• a linear hinge coupling the door to the cabinet, the linear hinge comprising
• a bearing mounted to the cabinet;
• an elongated shaft received within the bearing such that the elongated shaft is slidable along a translation axis on the bearing, a distal end portion of the elongated shaft rotatably connected to the door such that the door is rotatable about a rotation axis that extends through the distal end portion of the elongated shaft;
• a pair of linkage arms, a first linkage arm of the pair of linkage arms rotatably connected to the bearing such that a first end portion of the first linkage arm is positioned at the bearing, a second linkage arm of the pair of linkage arms rotatably connected to the elongated shaft such that a first end portion of the second linkage arm is positioned at the distal end portion of the elongated shaft, the first linkage arm rotatably connected to the second linkage arm such that a second end portion of the first linkage arm is positioned at a second end portion of the second linkage arm,
• wherein the first linkage arm defines a length between the first and second end portions of the first linkage arm, the second linkage arm defines a length between the first and second end portions of the second linkage arm, and the length of the second linkage arm is oriented perpendicular to the translation axis when the door is closed, and
• wherein the distal end portion of the elongated shaft is spaced from the bearing by a gap along the translation axis when the door is closed, and a sum of the length of the first linkage arm and the length of the second linkage arm is greater than the gap, and
• wherein the length of the first linkage arm is greater than the length of the second linkage arm, and the length of the first linkage arm and the length of the second linkage arm are selected such that the door translates along the translation axis as the door rotates from a closed position towards an open position.