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since linear motors are too expensive I decided to buy a rotational motor and use some gears and a crank mechanism to get enough torque and translate rotation into linear motion.

I need to meet a certain force on the shaft though. The question is how do I calculate the resulting force on the shaft?

I do know the following formula: Torque = crossproduct( Radius, Force).

This is be the crank construction I am talking about:

I appreciate your help. God bless you all.