This mod is particularly valuable when attempting to solo a mission, as knockdowns and the long period of helplessness they cause are one of the most common causes of death when you have no teammates to back you up.
Unranked Handspring speeds up the recovery animation without changing the animation (like Constitution).
If stacked with ranked Constitution, the recovery animation may change to the flip-up animation if the recovery time is short enough.
Maxed (and other ranks) Handspring speeds up the recovery animation by changing it to a flip-up animation.
The flip-up animation is similar, if not identical, to that of MOA's kick-up.
The animation depicted in the mod's picture is actually Back Handspring's animation.
Maxed Handspring does not stack with Constitution. Unranked mod will stack, and other ranks may stack (further testing is needed)