at least one opening in said shroud disposed circumferentially from said centered, longitudinal axis, said at least on opening being operable for an end portion of a suitable animal's nail to be put through said at least one opening, said at least one opening comprising a first component of an effective holding point system for said suitable animal's nail;

a rotary grinder contained within said shroud, the rotary grinder having a rotational axis and configured to rotate generally towards said first holding point system component, said first holding point system component being a boundary portion of said at least one opening, said opening boundary portion being configured to have an apex, said apex is configured to be a point or segment in said opening boundary portion that is further away from the rotary grinder rotational axis than neighboring points or segments to the left or right of said apex, said opening boundary portion being further configured to have a shape that generally converges towards said apex from left or right, the rotary grinder being located such that at least a portion of its grinding surface is directly under said apex; the rotary grinder being further configured to have the rotational axis different from said shroud centered, longitudinal axis, yet substantially parallel thereto, the difference between said grinder rotational axis and said shroud centered, longitudinal axis thereby providing an offset alignment of said rotary grinder in a direction perpendicular to said rotational axis, said offset alignment being configured to provide a sufficiently small distance between said first holding point system component and the rotary grinder grinding surface to enable an end portion of the suitable animal's nail, when put through said at least one opening, to contact the grinding surface of the said rotary grinder at a grinding contact location and achieve a suitable nail filling relationship with the suitable animal's nail at said grinding contact location, said offset alignment being further configured to provide a sufficient gap between said grinding contact location and said shroud or at least one opening to allow substantially all the nail debris grinded away at said grinding contact location to be transported to and contained within said shroud debris containment space, said grinding contact location being a second component of said effective holding point system, said shroud being further configured to be at least sufficiently transparent at a suitably located region to thereby enable external visual inspection of said grinding contact location by a human operator of said rotary nail filing apparatus, said second holding point system component operating to frictionally grab the suitable animal's nail end portion and, as the rotary grinder rotates, pull the suitable animal's nail generally towards said first holding point system component, said first holding point system component thereby operating in cooperation with said second holding point system component to converge the suitable animal's nail towards said apex, said converting shape of said first holding point system component further operating to likewise maintain the suitable animal's nail terminally towards said apex and thereby enabling the holding point system to automatically hold the suitable animal's nail in a generally stable pivoting point that enables the human operator of said rotary nail filing apparatus to three dimensionally file the suitable animal's nail end portion in a more controlled fashion.