Greetings,
Let me help you, I have reviewed the information you provide; the orientation of the pieces, and their position, as well as the cones required by the design and compression of the springs. I realize that the springs would be hidden when making the assembly, so I would like to suggest that the top pan has a translucent effect for the visualization of the compressed springs.
The work I would do for you would be:
Add the cones in the assembly.
Integrate springs that can be compressed in the assembly with the specifications of your 3D drawings.
Perform the animation of the assembly and movement of pieces.
The files I would send you would be:
Assembly (Solidworks 2017)
File GIF animation
Sincerely,
Martin Gonzalez