When I tried to Re-Rigging my lamp, it is showing these kinds of unusual behaviors.
Unusual Behaviour:-
Armature Modifier:-
Vertex Groups:-
Bone’s Names:-
What I checked:-
Should I give you my project, So that you could easily understand the root of the problem in my lamp file?
That would probably help us find the issue if you can upload the blend file somewhere others can get it to look at.
Note:- There are two different scenes in my blend file. One is for modeling, and the second is for animation.
Blend file it’s empty.
Sorry, by mistake I uploaded the wrong blend file. Now I uploaded the correct blend file, please again have a look.
@FedPete and @NP5 , if you get some time, please have a look at my blender file because I am stuck at the end of the lamp section.
yes, but is still an empty project!
It is there now @FedPete
It seems to work perfectly well to me. No out of shape ‘bones to mesh’ when I move it by the look bone or the base control.
The problem is you do too much rigging.
Trying out all possibilities; limits, IK, etc.
Just keep it simpel. You don’t need IK or limits.
And if you do so, do it step by step.
configure one bone and test, and then a next one and test.
But I have a question, why my lamp is working totally fine before joining all the parts together. Please have a look at the above video link, in that video, you will see that before using the armature modifier to my lamp, it’s working fine, all the unusual things are happening afterward. And still, if the reason behind this problem is that I made the lamp in an inappropriate manner then should I re-setup the whole armature thing?
Why do you need the armature modifier?
As per the lecture Re-Rigging The Lamp, if we re-rig the lamp and combine everything into one, then we need to use an armature modifier on our model to change its pose of it on the basis of vertex groups.
Am I right?
Somehow you have messed up the mesh and bones.
I went into edit mode of the mesh and straightened them up a bit. Top down rotation.
Then I went to the armature in pose mode, rest position selected, and moved the bones to fit the positions needed to match the mesh.
Then it all worked.
Clearly, there was some accidental probably in the wrong mode, movements made to either or both parts.
I also tried the same thing after reading your reply and shockingly almost everything is fixed. Still my animation is not looking that great than it was looking before re rigging. And I am still so much confused that what was the main problem behind this mess and how can I fix this properly. But thanks a lot for helping me.
Oh, you fixed it so much correctly, it is almost the same as before. But I am still confused that how this happened. Maybe later in the blender journey, I will learn more about armature and its horrible problems. 
To be honest, I did not take detailed care to get it exact, doubtless, it can be tweaked to be exact. Try experimenting on your original following what I said above that I did. It is actually simple to do just some repositioning.
Happy to help get you going again. 
