What is a hinge mechanism? And what did Kempe prove?

For a long time, it was believed that Alfred Kempe proved (1876) a theorem about the possibility of plotting an arbitrary plane algebraic curve by parts using hinge mechanisms. However, at the end of the 20th century, specialists in algebraic geometry, having rediscovered and developed this result in modern language, began to assert that Kempe's reasoning contained significant gaps and errors. In the author's opinion, these charges are unfounded. In this paper, the author tries to substantiate this point of view. Moreover, the notions of a hinge mechanism and its configuration space are analyzed.