LAUSR

Abstract Introduced are special evolutoid curves and spatial involutoid curves based on the special evolutoid curves. The special evolutoid is the striction curve to the family of constant pressure angle contact normals defined by a single transverse curve. Each axial position between the toe and heel of mating hyperboloidal pitch surfaces defines a unique transverse curve, and consequently, a special evolutoid and its spatial involutoid. The active tooth flank is comprised of a family of involutoid segments. This family of involutoid segments is used to define conjugate tooth flanks for hypoid gear sets. For hypoid gear sets, the pressure angle varies axially with each transverse curve. The generation of spatial involutoid curves is similar to the classical and well understood case of planar involute curves; the involutoid curve is obtained by the unwrapping of a taut chord from a planar and circular evolutoid. The line of action between the two conjugate flanks is simultaneously coincident with the input and output gear evolutoids. This process differs from the generation of planar involute curves in that the spatial involutoid curves are non-planar and there exists slip as the taut chord is unwrapped. Three gear sets are presented to showcase the process.