There is disclosed a torque transmitting or couplling arrangement for a fastener drive system or the like, wherein the respective externally configured and internally configured components are provided with a series of mating, elliptically curved flutes and lobes. f In both the externally and internally configured components, the flutes and lobes are defined by a first series of elliptically curved surfaces which alternate with a second series of elliptically curved surfaces, with the respective surfaces merging smoothly and generally tangentially to define the alternating flutes and lobes on each said component. One of the components, either the externally configured or the internally configured component will preferably have the flutes and lobes thereon generated from ellipses of substantially equal dimension. The other component, of necessity, will have the flutes and lobes generated from ellipses of differing dimensions. It is appreciated of course, that the flutes and lobes on both the internally and externally configured components may be generated from ellipses of unequal dimensions. In addition, in the preferred embodiment, the centers of the various . ellipses which define the flutes and lobes fall at the apexes of regular hexagons. Also, the centers for both series of ellipses will fall on substantially the same circle. There is also disclosed the tools which can be employed to form both the external and internal configurations in accordance with the invention.
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