Controlling Two Linear Motions of an Object

The motion of pink object along two perpendicular horizontal axes is controlled by two grounded violet actuators.
Orange vertical bar has spherical joints with blue and green pistons, point on line (sphere in cylindrical hole) joints with the white base and the pink object.
For the orange vertical bar, the middle sphere is at the bar center (distances between two adjacent spheres are the same).
Position of the pink object in the horizontal plane is determined by the displacements of two pistons.
Approximately, the displacement of the blue piston is equal to the one of the pink object along the yellow slider. The displacement of the green piston is equal to the one of the yellow slider along the base white runway.

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