If I understand the images, the flexures are solid bodies. This model should be simplified. Go into SpaceClaim and on the Prepare tab, in the Beams section click the Extract button then click on each of the solid flexures to convert them to beams. Then use the Midsurface button to extract a surface from the top disk.
Open this geometry in Mechanical. Under the Connections folder, Insert a Joint to connect the ends of the beam to the holes in the top disk using Fixed Joints.
You don’t need the bottom disk at all, suppress that. The bottom end of the beams can be connected to ground using either Fixed Joints or Translational Joints. Add a Joint Load of type = Displacement to the four beams to move the bottom end of those beams up to cause the top disk to tilt. In the image below, I suppressed two legs to save time building the model.
A different arrangement of six legs is called a Hexapod. The six legs meet at 3 points on the disk. The six legs start at six separate points on the ground. Each leg has a spherical joint on each end. As the leg length changes, the disk can be positioned in space at a wide range of angles. No bending is required, this is a well-known mechanism design.