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 via a pantograph (two violet and two blue bars). For more about pantograph see: "Planar motion control 1b"

Servo motor turns red gear and controls angular displacement via 4 bevel gear drive.

Four gears have the same tooth number.

Transmission ratio between the red and pink gear is 1/1.

If the red gear 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 4 bevel gear drive can be applied for "Planar motion control 1a" to control the orange object.