Wave gear (1) with a ring-shaped, fixed, internally toothed gear (2), a flexible, externally toothed gear (3) arranged inside the internally toothed gear (2), and a wave generator (4) which is inserted into the externally toothed gear (3), wherein the flexible, externally toothed gear (3) has a flexible, cylindrical
body region (301) and an annular membrane (302) extending radially from a rear end (301a) of the cylindrical
body region (301), and wherein a toothed region formed in a region of the cylindrical
body region (301) near an open region at the front end (301b) is deformed into an elliptical shape by the wave generator (4) over a region extending from a rear end region near the diaphragm (302) to a front end region near the opening, such that the deformation is substantially proportional to the distance from the diaphragm (302), wherein the wave gear (1) has a compound tooth profile which is engaged during positive deformation, wherein: the fixed, internally toothed gear (2) is designed as a
spur gear with a module (m); the flexible, externally toothed gear (3) is designed as a
spur gear with a module (m); a number of teeth of the flexible, externally toothed gear (3) is smaller by the size 2n, where n is a positive integer, than the number of teeth of the fixed, internally toothed gear (2); the deformation of a principal axis of an elliptical boundary
neutral line of the flexible, externally toothed gear (3) in a cross-section which is perpendicular to an axis and is hereinafter referred to as the principal cross-sectional area, and which is selected at a predetermined position of the toothing of the flexible, externally toothed gear (3) in a tooth path direction, is set to 2κmn (κ>1); the engagement of the teeth of the fixed, internally toothed gear (2) and the flexible, externally toothed gear (3) in the main cross-sectional area is approximated by rack engagement in order to calculate a motion position curve (M) of the teeth of the flexible, externally toothed gear (3) in relation to the teeth of the fixed, internally toothed gear (2) in connection with a rotation of the shaft generator (4); characterized by the fact that a curve region (AB) is obtained from a region of the motion position curve (M) extending from the main axis of the deepest engagement position of the two gears (2, 3) to a side where the engagement of the teeth is disengaged, such that the curve region (AB) begins at position (A) of the deepest engagement of the two gears (2, 3), which is the position where the inclination angle is 90°, and reaches a position (B) where the inclination angle of the motion position curve (M) relative to a
radial line of the fixed, internally toothed gear (2) is α° (0°<α°<30°); and a main area of the tooth profile (30) of the flexible, externally toothed gear (3) is defined by a first similarity transformation curve (AC) in which the curve area (AB) is enlarged by a multiple of λ, and by a straight line (33) smoothly connected to an endpoint of the first similarity transformation curve (AC); a main region of a tooth profile (20) of the fixed, internally toothed gear (2) by a second similarity transformation curve (AD) in which the curve region (AB) is enlarged by a multiple of (λ+1), and is defined by a straight line (24) smoothly connected to an endpoint of the second similarity transformation curve (AD); and a value of λ is less than a maximum value of λ, where the maximum value of λ is obtained when the curve region (AB) is subjected to a similarity transformation with the factor (λ+1), where the origin of the similarity transformation of the curve region (AB) is placed at the position of the deepest intervention (A), such that a remote end of the second similarity transformation curve (AD) is arranged on the motion position curve (M).