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 thereforeFor $0\le \alpha <\pi /2$, 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.