A two-dimensional positioning mechanism, comprising a moveable platform (12), a first translating device (14) connected to the platform (12) to move the platform in a first direction, and a second translating device (16) connected to the platform (12) to move the platform in a second direction orthogonal to the first direction. The first translating device includes first (22) and second (24) links, each of which is pivotally connected to the platform (12), and a first linear actuator (26) pivotally connected to the first (22) and second (24) links to move those links in the first direction. The first (22) and second (24) links, the moveable platform (12) and the linear actuator (26) form a pivotal parallelogram structure to maintain the orientation of the platform substantially constant during movement thereof. Preferably, the positioning mechanism further includes a control system (20) connected to the first (14) and second (16) translating devices to control those translating devices to move the platform from a first position to a second position. This control system preferably also controls the translating devices to move the platform on a predetermined path as the platform moves from one position to the next.