grab sb "by" the arm?

[simile]

A sentence goes like this:
The mother grabbed her son by the arm to keep him from falling down the stairs.
I just wonder why there's a "by" after "grab"?

According to Longman Dictionary (from the iPad version):
grab somebody's arm (= take hold of it with a sudden violent movement)
　ex: 'Wait', he cried, grabbing her arm.
take somebody by the arm (= lead someone somewhere holding their arm)
　ex: 'It's this way' he said, taking me by the arm.

I feel quite confused! The translation in Chinese for the sentence "The mother grabbed her son by the arm to keep him from falling down the stairs." indicates that the meaning of the expression used here is "to grab her son's arm" in order that her son won't fall down.
Then why not just use "grab her son's arm"? There seems no need for the use of "by".

 

[Hedwig]

It's a question of emphasis, I should say. Perhaps I'm getting too "psychological" here, but in "the mother grabbed her son's arm" the writer's mind is focused simply on the action of grabbing the arm. On the other hand, in "the mother grabbed her son by the arm" they are focused more on the idea of getting hold of the child to stop him from falling. And how does she do it? By grabbing him by the arm.

Hedwig
Not a teacher