A strain wave gearing with compound meshing that involves congruity of tooth surfaces, the strain wave gearing comprising:
- a rigid internally toothed gear;
- a flexible externally toothed gear disposed coaxially within the rigid internally toothed gear;
- and a wave generator fitted within the flexible externally toothed gear;
- wherein the flexible externally toothed gear is made to flex into an ellipsoidal shape by the wave generator, and external teeth of the flexible externally toothed gear mesh with internal teeth of the rigid internally toothed gear at both ends of the ellipsoidal shape along a major axis direction;
- a number of teeth of the flexible externally toothed gear is 2 n less than a number of teeth of the rigid internally toothed gear, where n is a positive integer;
- the rigid internally toothed gear and the flexible externally toothed gear before being flexed are spur gears of modulus m;
- an amount of flexure, relative to a pre-flexure rim-neutral circle on a major axis in an ellipsoidal rim-neutral curve of the flexible externally toothed gear in an axially perpendicular cross-section at an arbitrary position in a tooth trace direction of the external teeth, is 2 κmn, where κ is a deflection coefficient;
- and
- the deflection coefficient in a principal cross-section is set to 1, the principal cross-section being an axially perpendicular cross-section at a position on the external teeth midway in the tooth trace direction;
- and,
- wherein an addendum tooth profile of the internal teeth is prescribed by a first homothetic curve, and a dedendum tooth profile of the internal teeth is prescribed by a first tooth profile curve;
- an addendum tooth profile of the external teeth is prescribed by a second homothetic curve, and a dedendum tooth profile of the external teeth is prescribed by a second tooth profile curve;
- the first and second homothetic curves are obtained based on a movement locus through which the external teeth move relative to the internal teeth as the wave generator rotates at each position of the external teeth in the tooth trace direction, when the meshing of the external teeth and the internal teeth is approximated by rack meshing;
- the first homothetic curve is obtained by taking a curve segment of the movement locus from one apex to a next bottom point, and scaling down a first curve segment in this curve segment by λ (0<λ<1) using a second point as a homothetic center, the first curve segment extending from a first point to the second point, the first point being a point of an angle θA from 0 to π formed by a tangent of the curve segment and a major axis of the rim-neutral curve, and the second point being the bottom point of the curve segment;
- the second homothetic curve is obtained by multiplying a curve by (1−λ)/λ using a third point as a homothetic center, the third point being an end point on a side opposite from the second point in the first homothetic curve, and the curve being obtained by rotating the first homothetic curve 180 degrees about the third point;
- the first tooth profile curve is formed on the internal teeth in the course by which the addendum tooth profile of the external teeth, prescribed by the second homothetic curve, moves from the apex of the movement locus to arrive at the first point;
- and
- the second tooth profile curve is formed on the external teeth when the addendum tooth profile of the internal teeth, prescribed by the first homothetic curve, moves from the apex of the movement locus to arrive at the first point.