The apparatus of claim 2, further including a smooth transition region (60C) aligning the flank (60B) and face (60A) of the flexspline (26).The apparatus of claim 1, 2 or 3, wherein the transition region profile (60C) is a straight line.The apparatus of any preceding claim, wherein the tooth profile of the flank (60B) of the flexspline is a circular arc segment.A method of making a harmonic drive gearing apparatus for transmitting rotary motion from an input drive to an output drive, comprising the steps of:a) forming a circular spline (28) with gear teeth (32, 62) thereon having a face profile (62A) and a flank profile;b) forming a flexspline (26) with gear teeth (30, 60) thereon having a face profile (60A) and a flank profile (60B);c) orming a wave generator (12) having a major axis (35) and a minor axis (36) for deforming said flexspline when rotated, to generate relative motion between the flexspline and the circular spline; anddefining at least a face profile of the gear teeth of the circular spline (28) by an arc segment of known curvature while defining a face profile of the gear teeth of the flexspline by a curve which allows several flexspline teeth to remain in contact with the teeth on the circular spline;