Referred from another site: "汉语有些动词可以重叠使用，用来表示短时、尝试或反复多次，带有一种轻松的口气。" (http://www.chinaqw.com/hwjy/hykt/200806/11/119975.shtml)
I translate it as:
In Mandarin, some verbs can be used in an overlapping/repetitive way to signify short-time action, trying something or do something again and again, accompanied with a soft and relaxed tone.
For this ABAB-like structure, sometimes you can map it as "A+ed a bit/slightly", use -ed because it's a past action, besides the time period is really really short like in no time(practically or emotionally you want to de-emphasize the action).
甩了甩手 -> flicked his hand a bit/slightly.
他看了看手表 -> he took a quick look at his watch. (a quick look still has some meaning of 'slightly' to me)
奥巴马拉了拉领带 -> Obama slightly pulled his tie.
but 奥巴马 doesn't 打了打领带, 打领带 really takes time.
Jack 打了打篮球. -> I want to emotionally de-emphasize the action 打篮球 here, I think he didn't play for a long time, maybe made some shots and left and that's it.
And some opposite examples:
我吃了吃饭. also, 我喝了喝水, 我上了上班
Wrong, it violates the "short-time" action rule, since nobody can have dinner in no time, the same for work(上班)
So you only say 我吃（完/过）饭了. 我上（完/过）班了.
他正在眨了眨眼. 正在: be doing sth. 眨眼: blink
Wrong, ABAB usually don't fit the progressive tense, better as a past simple tense
So you can say: 他眨了眨眼
To comprehend ABAB structure, you will need a whole book, but hope these simple rules helps you out a bit.