knife edge

the cutting edge of a knife.

anything very sharp.

a wedge on the fine edge of which a scale beam, pendulum, or the like, balances or oscillates.

Origin of knife edge

First recorded in 1810–20

This includes the case of a compound pendulum in which the knife-edge is replaced by a cylindrical pin.

Encyclopaedia Britannica, 11th Edition, Volume 17, Slice 8 |Various
The plane of the knife-edge wheel r is therefore always parallel to DB.

Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 |Various
He had hunted mountain sheep and imagined sun and frost had worn the rocks to something like a knife-edge.

Northwest! |Harold Bindloss
A touch of a knife-edge to the rope, and the girl would be saved.

Out of the Depths |Robert Ames Bennet

A keen wind which cut like a knife-edge blew steadily down from the highlands behind us.

On the Mexican Highlands |William Seymour Edwards

knife edge

the sharp cutting edge of a knife

any sharp edge

a sharp-edged wedge of hard material on which the beam of a balance pivots or about which a pendulum is suspended

a critical point in the development of a situation, process of making a decision, etc