Reaction force cancel system

A reaction force cancelation system provided in a stage device, the stage device comprising a surface plate having a plurality of plate surfaces with different heights from each other, and installed on a base via a vibration-isolating section, and a plurality of stages that are disposed on the plate surfaces respectively and move on the plate surfaces, the system configured to cancel a plurality of reaction forces generated in the surface plate upon movements of the stages, the system comprising:

• a first and a second application device configured to apply each of a first and a second force to the surface plate to cancel the plurality of reaction forces cooperatively;
• and
• a control device configured to control magnitudes of the first and second forces;
• wherein heights of action points of the first and second forces in the surface plate are different from each other;
• and
• wherein the control device is configured to controls the first and second forces so as to counterbalance the plurality of reaction forces as resultant forces and resultant moments based on a distance from a height of a center of gravity of the surface plate to a height of an action point of the plurality of reaction forces in each of the plurality of stages, a distance from the height of a center of gravity to a height of an action point of the first force, and a distance from the height of a center of gravity of the surface plate to a height of an action point of the second force.