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1. A strain wave gearing having a double-contact negative deflection tooth profile, the strain wave gearing comprising:
a rigid internally toothed gear, a flexible externally toothed gear coaxially disposed on an inner side of the internally toothed gear, and a wave generator fitted to an inner side of the externally toothed gear; the flexible externally toothed gear being made to flex into an ellipsoidal shape by the wave generator and external teeth of the ellipsoidally flexed flexible externally toothed gear being meshed with internal teeth of the rigid internally toothed gear at both ends in a major axis direction of the ellipsoidally flexed flexible external gear; the rigid internally toothed gear and the flexible externally toothed gear prior to ellipsoidal deformation both being spur gears having a module m;a number of teeth of the flexible externally toothed gear being 2n fewer than a number of teeth of the rigid internally toothed gear where n is a positive integer;
an amount of flexure with respect to a rim neutral circle prior to flexure being 2κmn, where κ is a flexure coefficient, at a major axis position in an ellipsoidal rim neutral line of the flexible externally toothed gear in an axially perpendicular cross-section at any position in a tooth trace direction of the external teeth; the external teeth having a negative deflection tooth profile with a flexure coefficient κ such that 0<κ<1; the internal teeth having an addendum tooth profile defined by a first homothetic curve and a dedendum tooth profile defined by a first-tooth-profile-creating curve; the external teeth having an addendum tooth profile defined by a second homothetic curve and a dedendum tooth profile defined by a second-tooth-profile-creating curve; the first and second homothetic curves being obtained on the basis of a movement locus of the external teeth relative to the internal teeth while the wave generator rotates, at different positions of the external teeth in the tooth trace direction, when the meshing of the external teeth and the internal teeth is approximated with rack meshing; the first homothetic curve being a curve segment from one vertex to the next bottom point of the movement locus, and a first curve segment from an inflection point to the bottom point in the curve segment being derived by scaling down by a ratio λ (0<λ<1) with the bottom point as the homothetic center; the second homothetic curve being derived by scaling, by a ratio (1-λ)/λ using an end point of the first homothetic curve BC as the homothetic center, of a curve obtained by 180 degree rotation of the first homothetic curve about the end point on the side opposite the bottom point in the first homothetic curve; the first-tooth-profile-creating curve being created in the internal teeth in the process of the addendum tooth profile of the external teeth, defined by the second homothetic curve, moving from the inflection point of the movement locus to the vertex in the movement locus; and the second-tooth-profile-creating curve being created in the external teeth when the addendum tooth profile of the internal teeth, defined by the first homothetic curve, moves from the inflection point to the vertex. |
