A mechanism is disclosed for controlling the position of a heavy object, such as a part of a vehicle, in an x, y, z coordinate plane. The mechanism includes linear positioners, such as rail-guided carriage assemblies spanning the width of the mechanism, as well as longitudinal rails and blocks running the length of the mechanism. A lift table is mounted to the linear positioners such that the mechanism can be used to move the heavy object to virtually any desired position and orientation in the x, y, z coordinate plane.