I'm looking for a word for the thingy that's in the blue circle - ideally something not too complicated for a 3-year-old buddy. :)
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I like the word connector. It's generic enough that it would work for the ball or the socket, and also for the male and female ends of the other track pieces.
I don't think connector is too advanced for a 3-year-old. A connector connects two things together. If the child doesn't already know its meaning, it's an age-appropriate vocab word.
I might wait awhile, though, before using male and female to describe the other joints.
This is known as a "ball joint". They're often seen in puppets, armatures, and other toys, as well as in the human body.
Edit: Just saw the updated question. tchrist's suggestion of knob works great, and in describing how it works, you can simply say it plugs in or connects another piece. Although I think there's nothing wrong with exposing a 3-year-old kid to "advanced" terminology like joint.
Pictured: a LEGO Bionicle Ball Joint
Edit #2: Jon Hanna made a good point in the comments below. Upon closer inspection, it may be more accurate to describe the track as using a "pivot joint" (#5 in the picture below). I mistakenly assumed that the ball would plug into the next section of track rather than lay in the cut out groove.
I won't be miffed if another answer is now accepted instead as I think they're both excellent alternatives!