Cone-twist constraint
A ball joint with limits: the limb may swing within a cone and twist a little around its own axis, and no further.
A bare ball-socket joint lets a ragdoll spin its head a full turn, which reads more as horror film than physics. The cone-twist constraint splits rotation into swing and twist: how far the limb points away from its rest direction, bounded by a cone, and how far it rolls around its long axis, bounded by a separate angle range. The cone can be elliptical, so an arm can be raised further forwards than backwards.
It goes on shoulders, hips and necks, while elbows and knees get a hinge joint. Bullet ships it as btConeTwistConstraint; PhysX builds the same thing from a spherical joint with a limit cone. The limits are enforced by the constraint solver, and a cone set too tight makes the character jitter.