The common screws which we use, are right handed helices, the simplest parametric equations of which are:- $$x(s)=\cos(s),y(s)=\sin(s),z(s)=s$$, with $z$-axis as the axis of the helix.
My question is:-
Why does a screw move forward or backward (forward for clockwise rotation of a right-handed helix), on applying a pure rotational torque?
Even if we provide only torque for rotation, i.e. force perpendicular to the axis, it moves along the axis. What force acting on it propels it forward? if it is a component of the normal reaction of the material it is driven into, what is the action-reaction pair for this normal reaction?