Synchronizing movement between parts attached to telescoping arms fixed to a rotating disc?

Hello,

I'm trying to figure out if there's any possible way to mate my current assembly in a way so that each "slab" extends outwards at the same time as one another. I tried doing a rack & pinion mate between the middle disc and each of the five telescoping arms, but doing so messed up a lot of the mates as is.

Really not sure if this is possible, any help or advice would be greatly appreciated. I'll attach the zip file with everything at the bottom.

BTW I intend on this hopefully being a video render with multiple mechanisms like this alternating rotation, so it does not have to be realistic / mechanically feasible.

SolidworksModeling And Assemblies