Also, hinge upon. Depend or be contingent on, as in This plan hinges on her approval. This expression employs the verb hinge in the sense of “to hang,” as a door would hang on a hinge, a usage dating from the early 1700s.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.