= No-lift threshold of a wedge pinch
In the symmetric pinch geometry of <normal versus resultant force in a frictional pinch>, each inward <normal force> $N$ has downward vertical component $N\sin\alpha$, while limiting upward <static friction> contributes $\mu N\cos\alpha$. The maximum net upward support is therefore
$$
2N(\mu\cos\alpha-\sin\alpha).
$$
For $0\leq\alpha<\pi/2$, lifting a positive <weight> requires $\mu>\tan\alpha$. At equality the two vertical contributions cancel for every grip magnitude; below it, squeezing harder increases a downward resultant rather than supplying upward support.
The condition compares geometry with the <friction angle> $\arctan\mu$. It explains why a sufficiently steep outward-widening object cannot be raised by this particular symmetric squeeze alone. The conclusion assumes the stated face orientation and ideal contact law; a different surface orientation, an adhesive contact or a ledge changes the force balance.
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