Wedge Assembly Mate Problem

Hi,

  My challenge is to create the proper mates between the exterior conical faces of the wedges and the conical interior of the barrel.  The goal is to get all six wendges to seat in the barrel sliding down the interior of the cone and thereby moving closer to each other...in other words creating a smaller diameter between them.  Imagine a steel cable sliding through the assembley and suddenly getting caught by the six wedges.  That's the basic concept of the part.  Thanx,  Alex

   ps.  you'll notice the existing concentric mate in the assembly that I used to simply position the parts.  I realize this mate will not work towards my goal.