The other end
The diagrams show, as you state, a machine that will generate a linear force from rotational movement. The notation seems a little out of my experience as you seem to indicate that the centre of the 2nd moment of area is at the shaft, when it is surely nearer the weight.
Can you please elaborate the method by which you will create the torque to accelerate and decelerate the rotational motion. How will you stop this being transferred (every action has an equal and opposite reaction) to the body of the inertia machine.