Abstract: Apparatus for underfiling curvelinear vanes of cast centrifugal impellers. Such vanes are cast with generally uniform thickness along their length; it is desirable to have the vanes taper in thickness such that the radially outward portions are thinner than the roots; also this provides a desired curve to each side of the blades.

Abstract: Cutting apparatus forms helical races in a workpiece defining a toroidal envelope having an axis of symmetry and a circular axis perpendicular to the axis of symmetry and defining a diametric plane through the envelope by rotating the workpiece about the axis of symmetry and continuously rotating a cutting tool about a second axis perpendicular to the axis of symmetry and coincident with the circular axis in synchronism with the workpiece rotation so as to form a series of helical grooves which extend all around the envelope. As the cutting tool is swung from the entrance end of each groove toward the diametric plane, the tool is rotated through a selected angle in one direction about its own longitudinal axis and, as the tool is swung from said diametric plane toward the exit end of each groove, it is rotated through said angle in the opposite direction about its said axis so as to produce a non-varying groove geometry when measured rectilinearly to the tangent of the lead angle of the groove.

Abstract: Programmable electric and hydraulic machine for shaping laps such as are used to form or polish opthalmic lenses, comprises vertically oscillatable, longitudinally displaceable arm carrying a point cutter which is functionally engageable by radially extensible, rotating lap carried by upstanding spindle. Alternately, spindle is operable by oscillating drive when lap is radially retracted. Toroidal or spherical laps having a large range of variance in two dimensions, i.e. curvatures, are thus obtained by using relevant cutter and lap locations, as well as appropriate drive settings. Concave laps are produced by exchanging locations of lap and cutter so workpiece is carried by vertical-moving arm.