What are the abilities and limits of a hexapod-based flight simulator?
What they can do.
Motion systems can produce accelerations that stimulate the acceleration sensors in our inner ear. Higher frequency acceleration can be sensed instantaneously in surge, sway and heave. From this answer:


  Motion systems can do a pretty good job at reproducing direct accelerations, until the actuator stroke runs out of course. So for short term accelerations.


This direct acceleration sensing is essential for pilot-in-the-loop motion control, that is why we have the sensors in the first place. The velocity information we get from our peripheral vision is an integrated signal and has 90° phase shift, causing a delay in sensing of motion.
What they cannot do.
Produce sustained accelerations. Six Degree of Freedom motion systems get by by tilting the sim, so that a component of gravity can be used for the feeling of sustained motion. But with some restraints on tilt velocity and angle, the tilt must happen imperceptibly and is of course also limited by the actuator stroke:


Imperceptively, by rotating at a rate below what the inner ear sensors can detect, and by not changing the visual image horizon.
Limited by stroke: in a 6-DoF system, using full tilt means that some of the other DoFs cannot be used. Full aft tilt has the front actuators fully extended, so linear surge cannot be actuated anymore.



Motion software contains a lot of fine balancing and frequency filtering code, to make optimal use of the available stroke and of the peculiarities of the inner ear acceleration sensors. Large stroke systems are essential for pilot-in-the-loop tasks in airliner and helicopter pilot training, and make the difference between being in an immersive simulated atmosphere, or being aware of the fact that you're inside some device firmly on the ground.