An operator cab for a machine such as a motor grader includes an access door coupled to a frame by way of a hinge mechanism. The hinge mechanism has abutting cam and follower surfaces with geometry to control the swinging of the access door such as under the force of gravity. The cam surface has a double-sloped profile of rotation about the pivot axis of the hinge mechanism so that the access door swing is controlled in either of a first or a second swing direction toward a dwell location of the access door.