How to Influence Mesh Positioning According to Bone Movement? The above gif summarizes this question. I'm not sure how it is done, though (but I do have the file of the gif, long story). 

The rods seem to elongate while keeping their thickness, and they are acting like they have "Track To" constraints. Could someone please help?

File attached below
If you want to "read" and understand your armature's behaviour, activate the second bone layer and the "X-rays" function in the armature properties panel, then select the colored bones and analyze the bone constraints (IK and damped track).



This Stretch setting is also important for this rig.