Abstract: An actuator, with two independent degrees of freedom, rotates a stage about an axis and moves the stage along the axis, the range of motion defining a cylinder or cylindrical section. The stage is mounted on a hollow cylindrical plunger fitting in an annular well. A bearing allows the plunger to move axially and rotationally, in the preferred embodiment the bearing is an air bearing. The plunger has an array of permanent magnets on its external cylindrical face opposite coils in the well. Equal numbers of oppositely-polarized permanent magnets are arranged in a regular cylindrical pattern at 50% packing density forming rings and columns of like-polarity magnets, the rings of one polarity alternating with rings of opposite polarity and the columns of one polarity alternating with columns of opposite polarity. A set of Z-axis coils (for axial movement) curve around the plunger and are shaped to allow a current in them to produce an axial force with respect to the rings of magnets. A set of .phi.