If you attach an archive of your model, it will be easier to see in detail what you have and make suggestions. To create an archive in Workbench, Clear Generated Data on the Model item and save the Project. Then click File, Archive... and save a .wbpz file. You can use the Attach button to your first post to upload that file if it is < 120 MB. Please edit your post and add which version of ANSYS you are using (17.2, 18.2 etc).
You say you need to simulate the buckling load factor. Does that mean you have a Static Structural model that solves? Is the line of the remote force pointed up in a stable direction?
You also say "I can't constrain the axial movement of the pins." Do you mean you tried to do it and ANSYS wouldn't allow it, or that you don't know how to?
The bushings are bonded to the links, is that because they are a press fit?
What is the ID of the the bushing? What is the OD of the pin?
If there is a clearance, is the centerline of the pin coaxial with the centerline of the bushing?
That would be typical of most CAD design layouts, but is not appropriate for analysis.
In the figure below, I show (exaggerated) a hole that represents the ID of the bushing and the pin.
What you want for analysis is for the clearance between the parts to be taken up in the way they would be in a physical sample under load (reality).
The buckling load will be sensitive to the location of load paths through the parts and it matters if the load is on the inside or the outside of the thickness of a part.