1
general::
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.
American Heritage Idioms
2
general::
Phrase(s): hinge (up)on someone or something
Fig. to depend on someone or something; to depend on what someone or something does. (Upon is formal and less commonly used than on.) • The success of the project hinges upon you and how well you do your job. • How well the corn crop does all hinges on the weather.
McGrawhill's American Idioms And Phrasal Verbs