Abstract: A support structure for a lift car or elevator comprising two pairs of parallel rails and followers arranged in a horizontal parallelogram array between the lift car and support frame, such that compound movement of the followers on their respective rails allows the lift car to move in any horizontal direction to absorb transverse vibration due to misalignment of the vertical guide rails in the lift shaft. Also described are biassing devices arranged to lightly bias the lift car to a centralized horizontal position, and centralizing devices arranged to positively centralize the lift car for entry and egress at each floor.