Source : Webster's Revised Unabridged Dictionary (1913)

Knife-edge \Knife"-edge`\, n. (Mech.)
   A piece of steel sharpened to an acute edge or angle, and
   resting on a smooth surface, serving as the axis of motion of
   a pendulum, scale beam, or other piece required to oscillate
   with the least possible friction.

   {Knife-edge file}. See Illust. of {File}.

Source : WordNet®

knife-edge
     n : a narrow boundary; "he lived on a knife-edge between genius
         and insanity"