Ok, look at this vowel diagram of English language, you will see
/ɜ/ are the central vowel. Both has the middle of the tongue raising in the middle of the mouth, except that
/ə/ has to raise a bit higher than
Now if we have
/r/ right after these vowel, then the tip and the blade of the tongue must be curved up, but not touching the roof of the mouth.
So, for the /ɚ/ (farmer /ˈfɑːr.mɚ/) & /ɝ/ (bird /bɝːd/), I think we have to do like the following, but please correct me if I am wrong:
So, basically, /ɚ/ & /ɝ/ have the same position of articulation, except that the central of the tongue of the /ɚ/ is just a little bit higher than /ɝ/ as showed in the 2 above pictures.
Note that: since we got
/r/, so the tip and the blade of the tongue must be curved up.
So, do I get anything wrong here?