I see no very great difference between these two definitions:
11. to reach a particular state or condition; to make somebody/something/yourself reach a particular state or condition
18. to move to or from a particular place or in a particular direction, sometimes with difficulty; to make somebody/something do this
Definition 18 is just a special case of Definition 11 in which the “particular state or condition” which is achieved is location at or movement towards a particular place. The case you ask about, however, involves a posture rather than a place: Get on your hands and knees may be paraphrased “make yourself reach the condition of being on your hands and knees”.
It might very well be argued that Definition 11 is today the fundamental meaning of get: this sense underlies even the original sense of “obtain”, which may be paraphrased as “to reach or arrive at the state of possession of”. Definition 11 is remarkable in its generality, contemplating both non-agentive and agentive/causative uses.
Characterizing this as a linking verb is dubious to my mind. It is true that get ascribes the state defined by its complement to its subject; but get differs from the copula be in expressing not merely a state but a change of state. I’m not clear what useful purpose is served by grouping be with verbs like get and become.