An appliance includes a linear hinge assembly that couples a door to a cabinet. The linear hinge assembly includes a bearing assembly mounted to the cabinet and an elongated shaft received within the bearing assembly for sliding along a translation axis. A cam is mounted to the door and is rotatably coupled to a distal end portion of the elongated shaft such that such that the door is rotatable about a pivot axis that extends through the distal end portion of the elongated shaft. A timing cable extends from a fixed location on the cabinet to a fixed location on a cam profile such that the timing cable wraps around the cam when the door is moved toward a closed position and unwraps when the door is moved toward an open position.