Your Lamp “arms” design is very similiar to the one I did and I can see you have the same problems I did when I first tried to animate it 
The joint from the second to the first arm, is parented to the first instead of the second, which makes the second arm to “disconnect” from the Joint when moving. To solve this I had to parent the joint to the second arm and then using Constraints so it wouldn’t happen to rotate on Local Y.
My final result was this Lamp finds something strange on the Floor
It’s not so good, has too fast transitions… but maybe you can observe what I mean by the joint.