Patent ID: 7117759

Claim:
A wave gear drive having a rigid internal gear, a flexible external gear and a wave generator that flexes the external gear into an elliptical shape so that the external gear meshes partially with the rigid internal gear and rotates meshing portions of the two gears circumferentially, the flexible external gear comprising a cylindrical body, a diaphragm extending radially outward or inward from one end of the cylindrical body, and external teeth formed around an outer periphery of an opening portion at another end of the cylindrical body, the cylindrical body being flexed radially into an elliptical shape by the wave generator with an amount of said flexing in the radial direction increasing substantially proportional to a distance to the opening portion from the diaphragm side, wherein the flexible external gear is a spur gear and a main portion of a tooth profile thereof is an arc, in a section of said opening portion of the flexible external gear perpendicular to the axis, a meshing center between teeth of the two gears is at a point away from a major axis of a center line of an elliptical rim of the flexible external gear, with θ as an angle of inclination of a tangent with the meshing center along a neutral line of the rim, z F and z C as numbers of teeth on the flexible external gear and rigid internal gear, respectively, h as a distance along a flexible external gear tooth body center line between a point at which a normal of the meshing center tooth profile intersects the tooth body center line and a point on the rim neutral line and r N as a radius of a rim neutral circle prior to deformation, an amount of flexing w of the opening portion is given by w = - b - b 2 - 4 ⁢ ⁢ a ⁢ ⁢ c 2 ⁢ a a = 3 ⁢ z F r n ⁢ cos ⁡ ( 2 ⁢ ⁢ θ ) b = ⁢ z C - z F + 3 ⁢ z F ⁢ r n + h r n ⁢ cos 2 ⁡ ( 2 ⁢ θ ) - z c ⁢ 1 + 3 ⁢ ⁢ cos 2 ⁡ ( 2 ⁢ ⁢ θ ) × ⁢ [ 2 ⁢ ⁢ sin ⁢ { tan - 1 ⁡ ( cot 3 ⁢ ⁢ θ ) + θ } - sin ⁡ ( 2 ⁢ ⁢ θ ) ⁢ cos ⁢ { tan - 1 ⁡ ( cot 3 ⁢ ⁢ θ ) - θ } ] c = ( r n + h ) ⁢ ( z C - z F ) ⁢ cos ⁡ ( 2 ⁢ ⁢ θ ) the rigid internal gear having a first tooth profile that is a tooth profile generated on the rigid internal gear by the arc tooth profile of the flexible external gear at the meshing center or a tooth profile that is an approximation thereof, and a second tooth profile that extends to a tooth crest adjoining the first tooth profile that is a tooth profile generated on the rigid internal gear tooth profile by the arc tooth profile of the flexible external gear or a tooth profile that is an approximation thereof in a section of the external teeth of the flexible external gear perpendicular to the axis at the diaphragm-side end.