Abstract: Apparatus for generating a lobular polygonal form comprises a first device rotatable about an axis, a second device including a member eccentric to the axis and movable in an orbit thereabout, and a third device responsive to said combined movement of the first and second device for tracing a lobular polygonal form (1) which has an odd number of sides capable of maintaining approximate tangency with two parallel planes upon rotation of said form or (2) which has an even number of sides capable upon rotation of the form of maintaining approximate tangency with three circles of equal diameter and having equidistant centers. The generated lobular form may be traced by a metal-working tool that forms a die cavity in a workpiece. A novel lobular screw blank may be formed in the die cavity.

Abstract: A self-threading fastener has circumferentially spaced thread-forming lobes on its thread and with the thread depth at a maximum at the lobes and a minimum circumferentially between the lobes. A lobe in one turn is circumferentially offset from a lobe in an adjacent turn. The fastener is made on roll-threading dies each having grooves sinusoidally varying in depth frm a maximum at one region to a minimum at a second region. The spacing of the regions is equal to a fraction of the thread pitch multiplied by the cosecant of the thread helix angle.

Abstract: A self-threading fastener has circumferentially spaced thread-forming lobes on its thread, and with a thread depth at a maximum at the lobes and a minimum circumferentially between the lobes. A lobe in one turn is circumferentially offset from a lobe in an adjacent turn. The fastener is made on roll-threading dies each having grooves sinulsoidally varying in depth from a maximum at one region to a minimum at a second region. The spacing of the regions is equal to a fraction of the thread pitch multiplied by the cosecant of the thread helix angle.