Abstract: A W-N gear which has a surface strength at least nearly maximized for a given addendum and minimum pressure angle is realized by selecting a mean radius for the convex and concave circular arcs of the tooth profile in an appropriate range. Also, a dual=line mesh W-N gear of the character described which has a requisite face width minimized is obtained by selecting a mean arc radius which lies in the range referred to above and enables the addendum and dedendum points of meshing contact to appear at equal angle intervals.

Abstract: A single-flank or double-flank type W-N gear each of the convex or concave tooth flanks of which is formed of a plurality of circular arcs (which participate in meshing engagement and) the centers of which (arcs) are arranged on the pitch line or in the vicinity thereof in spaced-apart relation to each other and an intermediate curved line or lines interconnecting the circular arcs. Meshing contact at any instant is obtained at different locations mutually spaced in the direction of tooth trace and stress concentration at the root of the teeth is minimized.

Abstract: W-N gears of novel basic rack tooth profile designed to have at all times two points of meshing contact located in the same reference plane, one on an addendum arc of first tooth and the other on the dedendum arc of a second tooth neighboring the first tooth on its side opposite to the addendum arc, so that at the respective points of contacts the addendum and dedendum arcs have lines of radius aligned with each other. Such dual tooth contact enables much smoother and quieter gear operation, the points of contact proceeding in the direction of tooth trace.