The universe is expanding at 74 km/sec/Mpc (Mpc is a mega parsec which is 3.26 million light years). So let's take two heavy objects and place them far from any galaxy cluster or other influence and space them just one parsec apart (3.26 light years). Then they will effectively be moving apart at 7.4 km/sec. Now imagine that you have a monomolecular filament rope between the objects that puts a force on the objects that will decelerate the objects. Then during the time that they are decelerating you can extract work from the objects. That work per second comes from the force the rope is exerting being applied over the 7.4 cm/sec that the objects are moving apart. However, once the force causes their relative velocity to drop to 0, you won't be able to get any more energy from the objects since they are no longer moving apart. There will still be a constant force on your rope but you need to have a force applied over a distance to get work.
Now this is all from just the "Big Bang" expansion of space. Once the rope's force has gotten their relative velocity to zero, the two objects are like a gravitational bound system and it will stop "expanding". However, in addition to the "standard" expansion of space, we now know that there is dark energy which is causing an accelerating expansion of the universe. This means that the two objects are not just "moving" apart at constant 7.4 cm/sec but that this velocity is actually increasing with time. So if you setup your rope such that the force it is exerting on the objects results in an deceleration that is slightly smaller than this cosmic acceleration, you can extract work continuously and indefinitely. Unfortunately, I have not been able to convert the dark energy measurements into units of acceleration in this particular case of objects at one parsec. I suspect it is a small number but current estimates are that it is definitely positive. Note that if your rope exerts more force that causes a deceleration larger than the cosmic acceleration then the objects will eventually stop moving apart and the work you can extract will drop to zero again.
Note that from just the normal expansion of the universe you can only extract a finite total amount of energy, but that with the accelerated expansion you can extract a small but positive amount of energy per second forever. However, your rope needs to get longer and longer with time (at the rate of 7.4 cm/sec, in this example), so, as they say TANSTAFL (there ain't no such thing as a free lunch). The rope needs to get longer because you have to have your very small force applied to continuously moving objects to get work done. Since it will take continuous energy to make a continuously lengthening rope, and you cannot win this battle by starting with objects that are further apart since then the rope is lengthening at an even faster rate than the 7.4 cm/sec of this example. You can increase the energy per second you extract by making the objects more massive, but then the force on the rope increases so you need to make a thicker rope.
The bottom line is that I think this free energy project is impractical, even though it is theoretically possible. The problem that needs to be solved is the energy cost of the continuously lengthening rope.