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How will this be used?

 

Always start by asking yourself:
"Where have you ever seen anything that works like this?"
Probably nowhere, this is not a viable scheme for a linear actuator.

 

Why not use a simple lever to convert a short stroke into a longer one? You need more force on the solenoid side of the lever, but that's less a problem than such a long throw.
I think a motor turning a wheel would be better still.

 

If You would simply explain what it is that You are trying to accomplish,
You would probably get some much more useful answers.
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