US Patent 7735396 Wave gear drive having negative deflection meshing tooth profile

A rigid internal gear and a flexible external gear of a wave gear drive are spur gears of module m. The number of teeth of the external gear is smaller by 2n (n is a positive integer) than that of the internal gear. The deflection of the major axis of the elliptical rim neutral line on the principal cross-section of the external gear is set at 2κmn (κ<1). On the principal cross-section, the meshing of both gears is approximated by rack meshing. The locus M of movement of a tooth of the external gear caused by the rotation of a wave generator is determined. A part AC of the locus M of movement from the inflection point A of the locus M of movement to the deepest position B of meshing is determined on the entering side of meshing of the teeth toward the major axis of the locus M of movement. A first similar curve FG generated by multiplying the curve part AC by &lgr; is employed as the tooth profile of the external gear, and a second similar curve DE generated by multiplying the curve part AC by (&lgr;+1) is employed as the tooth profile of the internal gear. The tooth whole depth is increased wherever possible so that the range of the tooth profile of the internal gear may be the greatest at which the tooth tip touches the locus M of movement of the tip of tooth of the external gear, thus realizing a wave gear drive of high ratcheting torque.