Patent ID: 8555505

Claim:
A flat wave gear device, comprising: a D-side rigid internally toothed gear; an S-side rigid internally toothed gear disposed in parallel in a coaxial state with the D-side rigid internally toothed gear; an annular flexible externally toothed gear disposed in a coaxial state within the D-side and the S-side rigid internally toothed gears; and a wave generator for causing a cross-section of the flexible externally toothed gear given perpendicularly with respect to an axis thereof to flex elliptically and the resulting shape to rotate; a number of teeth on the D-side rigid internally toothed gear being the same as a number of teeth on the flexible externally toothed gear, and a number of teeth on the S-side rigid internally toothed gear having 2n more teeth, n being a positive integer, than the number of teeth on the flexible externally toothed gear; the flat wave gear device having a tooth profile derived from the following method: using both the flexible externally toothed gear and the S-side rigid internally toothed gear as spur gears of module m; setting κmn, wherein κ≦1, and −κmn as a degree of radial flexing on, respectively, a major and minor axis of an elliptically shaped rim neutral line of the flexible externally toothed gear, a line passing through the center part along a thickness direction of a tooth root rim when the flexible externally toothed gear is deformed into an elliptical shape, in the cross-section of the flexible externally toothed gear given perpendicularly with respect to the axis; determining a rack-approximated movement locus of the flexible externally toothed gear with respect to the S-side rigid internally toothed gear accompanying rotation of the wave generator; taking ρ OPT as a minimum value of a radius of curvature of the movement locus; and using a convex arc having a radius ρ, wherein ρ≦ρ OPT , on a main part of a tooth profile of the flexible externally toothed gear; wherein the method for setting the tooth profile in the flat wave gear device further comprises: determining the movement locus using formula (1); determining an evolute of the movement locus using formula (2); and determining the radius of curvature ρ OPT using formula (3), with θ=π in formula (2) ⁢ x = 0.5 ⁢ mn ⁡ ( θ - κ ⁢ ⁢ sin ⁢ ⁢ θ ) ⁢ ⁢ ⁢ y = - κ ⁢ ⁢ mn ⁡ ( 1 - cos ⁢ ⁢ θ ) ( 1 ) x = mn ⁡ [ 0.5 ⁢ ( θ - κ ⁢ ⁢ sin ⁢ ⁢ θ ) + 2 ⁢ { 0.25 ⁢ ( 1 - κ ⁢ ⁢ cos ⁢ ⁢ θ ) 2 + κ 2 ⁢ sin 2 ⁢ θ } 1.5 κ ⁡ ( κ - cos ⁢ ⁢ θ ) ⁢ cos ⁢ { tan - 1 ⁢ 0.5 ⁢ ( 1 - κ ⁢ ⁢ cos ⁢ ⁢ θ ) κ ⁢ ⁢ sin ⁢ ⁢ θ } ] ⁢ ⁢ y = mn ⁡ [ κ ⁢ ⁢ cos ⁢ ⁢ θ - 1 + 2 ⁢ { 0.25 ⁢ ( 1 - κ ⁢ ⁢ cos ⁢ ⁢ θ ) 2 + κ 2 ⁢ sin 2 ⁢ θ } 1.5 κ ⁡ ( κ - cos ⁢ ⁢ θ ) ⁢ sin ⁢ { tan - 1 ⁢ 0.5 ⁢ ( 1 - κ ⁢ ⁢ cos ⁢ ⁢ θ ) κ ⁢ ⁢ sin ⁢ ⁢ θ } ] ( 2 ) ⁢ ρ OPT = 0.25 ⁢ mn ⁢ ⁢ ( 1 + κ ) 2 κ . ( 3 )