The line of contact T, therefore, on the surface of the cylinder bbb, is for the instant at rest, and is the instantaneous axis FIG.
If P is in the circumference of bbb, that path becomes an epic ycloid.
The line T on the surface bbb has also for the instant no velocity in the plane AB; for it has just ceased to move towards the fixed surface aaa, and is just about to begin to move away from that surface.
Sorry BBB I disagree with your " proven formula to ignore scare mongers " .
The whole of the foregoing reasonings are applicable, not merely when acm and bbb are actual cylinders, but also when they are the osculating cylinders of a pair of cylindroidal surfaces of varying curvature, A and B being the axes of curvature of the parts of those surfaces which are in contact for the instant under consideration.