This seems to be what they are doing...

"Mature male dragonflies establish a territory from which he chases other males. He then produces sperm packets called spermatophores at the tip of the tenth segment of his abdomen. He then reaches the tip forward and places the spermatophores in a depression on the lower surface of the second abdominal segment."

"With the sperm receptacle filled the male grasps a female's head with his genitalia at the abdominal tip. (Each species' male genitalia fit the head of only the female of that species). In some dragonflies and damselflies, the shape of the male genitalia is the most constant and accurate identifier of the insect's species."

In summary from suite101

Incredible Photo!

Kinda poetic in it's shape!