Kinematical approach to the drilling mechanisms for n-sided polygonal holes

The present analysis addresses the generation of regular polygonal paths with any number of sides, odd or even, using special rotors revolving with uniquely prescribed motions inside fixed guidance polygons, which are coincident or similar to the trajectories to be traced. The whole rotation motion of the rotor is considered composed of a succession of Cardan motions so that the active profile of contact is formed by a polycentric sequence of circular arcs. It is shown and proved that the guidance polygon and the target polygon may coincide in the hypothesis of an odd number n of sides, whereas the guidance profile must necessarily be larger than the one to be generated for n even, in which case two equal concentric polygons rotated of θ/n between each other may be simultaneously generated by two particular points of the rotors. These devices are very useful to drill blind polygonal holes, providing the rotors of proper cutting tools and driving them by constant-speed motors through homokinetic joints.