Pink object has 3 degrees of freedom in its planar motion: two linear and one angular displacements.

Two white actuators deals with two linear ones.

See: "Planar motion control 1a"

Servo motor turns red shaft and controls angular displacement via a double parallelogram drive. Each of red and pink shafts has 2 eccentrics for overcoming dead positions of the parallelogram mechanisms. So the cyan shaft has 4 eccentrics. Transmission ratio between the red and pink shafts is 1/1. The pink shaft and the object are fixed together.

If the red shaft is immobile, the object doest not rotate when moving along Ox and Oy axes.

The video shows how the pink object moves along Ox axis, along Oy axis and then rotates.

The parallelogram drive can be applied for "Planar motion control 1b"

to control the pink object.