Практическая грамматика

2. Auxiliary verbs are those which have lost their meaning and are used only as form words, thus having only a grammatical function. They are used in analytical forms. Here belong such verbs as to do, to have, to be, shall, will, should, would, may.
Have you spoken to him?
I haven’t had the chance yet.
You will realize soon that he is always like this.
They are coming tomorrow.
3. Link verbs are verbs which to a smaller or greater extent have lost their meaning and are used in the compound nominal predicate: to be, to turn, to get, to grow, to remain etc.
The house was too big. (Galsworthy)
The old face looked worn and hollow again. (Galsworthy)
It’s getting dark outside.
He didn’t seem tired. (Snow)
In different contexts the same verb can be used as a notional verb and an auxiliary verb or a link verb:
She turned her head sullenly away from me. (notional verb)
She turned deadly pale. (link verb)
No one was there to meet him. (notional verb)
She was not a ten-year-old girl any more... (link verb)
This evening she was unusually excited, her red cheeks and lips contrasting lustrously with her shadowy hair. (link verb)
There is a special group of verbs, which have no independent function in the sentence, though they preserve a meaning of their own. They are often referred to as semi-auxiliary verbs. These are modal verbs such as can, may, must, ought etc.
I can’t walk any further, my feet ache.
I suppose I ought to say a word or two about myself (Rendell)
The same verb in different contexts can be modal and auxiliary.
I crouched against the wall of the gallery so that I
should not be seen. (Du Maurier) (auxiliary verb)
I don't honestly think Lady Crowan was exaggerating when she said something should be done in your honour. (Du Maurier) (modal verb)
I had no idea she would do that. (Du Maurier) (auxiliary verb)
He needed a cook. Why couldn't she apply for the job? But Morris would not hear of it. (Prichard) (modal verb)