Abstract: A gear system which includes a pinion and mating-gear forming a gear pair with a predetermined gear ratio (mG), center distance (C), face-width (Fw), and limiting stresses. The pinion has a pinion tooth number (N1) and a first plurality of teeth, each tooth having a first-tooth profile. The mating gear has a mating-gear tooth number (N2) satisfying the expression N2=mG·N1 and a second plurality of teeth, each tooth having a second-tooth profile. The relative curvature of the first-tooth profile and the second-tooth profile is given by the expression kc·Fc, where Fc is a relative reference curvature function given by the expression Fc=(N1+N2)2/(N1·N2·C), and kc is a relative curvature multiplier which is a function of the gear ratio (mG), the center distance (C), the face-width (Fw), and the limiting stresses.

Abstract: A gear and method for producing the gear. The gear has a gear tooth profile conjugate to a gear basic-cutter tooth-profile having an addendum with a convex portion having an addendum point proximal to a pitch line and a dedendum with a concave portion having a dedendum point proximal to the pitch line. The convex portion is complementary with a corresponding portion of a mating-gear basic-cutter tooth-profile dedendum. The concave portion is complementary with a corresponding portion of the mating-gear basic-cutter tooth-profile addendum. A transition zone between the addendum point and the dedendum point has a predetermined width. The gear basic-cutter tooth-profile has a predetermined half pitch relief at the pitch line and continuity of profile and continuity of slope at the addendum point.

Abstract: A gearing system which includes a pair of conjugate gears. The tooth profile of the first gear lies entirely within the pitch circle of the first gear, and the tooth profile of the mating gear lies entirely outside the pitch circle of the mating gear. The profile of the first gear is fully or partially concave, and the tooth profile of the mating gear is fully or partially convex. The profiles of the conjugate gear pair may have constant, or nearly constant, relative curvature. Alternatively, due to the shape of the profiles, constant, or nearly constant, contact stress results when the gears are in mesh.

Abstract: A gearing system which includes a pair of gears. The tooth profile of the first gear has three portions: a concave portion lying within the dedendum of the first gear, a convex portion lying within the addendum of the first gear, and a transition zone disposed between the concave and convex portions. Similarly, the tooth profile of the mating gear has three portions: a concave portion lying within the dedendum of the mating gear, conjugate to the convex portion of the tooth profile of the first gear; a convex portion lying within the addendum of the mating gear, conjugate to the concave portion of the tooth profile of the first gear; and a transition zone disposed between the concave and convex portions. The pair of gears may be designed such that no contact between meshing teeth is made along the transition zones. The tooth profiles of the gear pair have constant, or nearly constant, relative curvature.