I have this assignment to do and it has to with automatic and non automatic secondary articulators. This is my first time. I checked books at my disposals including Wikipedia, but none discussed anything about automatic and non automatic secondary articulators. Is that the title doesn't exist or what?
"Articulator" refers to a piece of anatomy, and an articulator could be active or passive (the tongue tip is active, the teeth are passive). Consonants are typically analyzed in terms of their "primary" place of articulation (defined by active and passive articulators), for example "labio-dental" ([f]). "Secondary articulation" refers to additional, typically vocalic articulations, such as palatalization or rounding.
There is also a phenomenon of coarticulation, having to do with the fact that the movement of an articulator may precede (or follow) the segment that triggers that articulator, so in "stool", the lips start protruding during [s], before the segment ([u]) which phonologically has rounding.
Only an action can be automatic vs. non-automatic, and a piece of anatomy (an articulator) can't be automatic. No piece of anatomy (articulator) is intrinsically secondary, but in combination with other articulations, one articulator could be used for secondary articulations. We don't say that it is therefore a secondary articulator. The best I can suggest is that you are supposed to be doing something with "automatic vs. non-automatic secondary articulations". The problem is figuring out what "automatic" could possibly mean in this context. Russian is an example of a language with "non-automatic" secondary articulations, because it has palatalization as a secondary articulation on consonants, and it is not always assigned by rule (it is not "automatic"). The problem is establishing that there is such a thing as an automatic secondary articulation. I suspect that the secondary coarticulation where in "stool" the lips protrude at some point before the vowel is an example. Necessarily, it takes some time to protrude the lips for the vowel [u], so it seems that that has to happen before you finish the consonant [t]. The "automatic" part would mean "this is what unavoidably happens, as a result of human physiology". But some languages have this kind of coarticulation and it starts much earlier that is absolutely physically necessary – there is a grammatical rule. So we don't know what the boundary is between "automatic, physically necessary" versus "language specific".
So another possibility is that the instructor means "the result of a rule" as opposed to "the result of a lexical specification. In that case, an example could be Russian, which has both lexically specified palatalization but also rule-governed palatalization before /-i/. However, Russian palatalization is a kind of third-rail topic because palatalization is not totally automatic except in the case of velars (as far as I know, nobody disputes that).
So it is a puzzle: "automatic secondary articulator" is at the very least non-standard terminology in linguistics.