What is the motivation of pinhead in hellraiser?

Answer 1

Pinhead (who initially had no name in the original story) is no human being. Thus he has no real psychological structure which could give him something that you could call a "motivation" (or better said, something that any human being could understand without going insane).

It is more a process of transcending the self in which Pinhead aids the user. People finding the puzzle box have been looking for it in the first place (sometimes their whole life). It is a subconscious process in which solving the puzzlebox is the last and final step into leaving the mundane world (and the body which binds the user to it) behind and reaching out for new grounds.

Thus you can see Pinhead as an enhanced (even outsourced) "motivation" of the puzzlebox user. Pinhead is a tool as the puzzle box is one. But with one difference. The puzzlebox gives the user a choice.