Bending/Hinge upon Collision?

I am looking to have a piece of my assembly bend upon sliding down the surface of a cone face, extending as it rides down the cone. Setting slips for a liner hanger (downhole oilfield tool) will extend as they ride down the cone and dig and stick into the inside of the pipe it is going into allowing it to hang and hold the weight of whats underneath, is the jist of whats going on. I am thinking it is a certain type of mate or hinge command. PLEASE HELP!!. I have attached the files and assembly. THANKS!!

SolidworksAssemblies