Kinematic Effect of the Compliant Cup in Harmonic Drives

The paper and its companion [Dong et al., 2011, “Kinematic Fundamentals of Planar Harmonic Drives,” ASME J. Mech. Des., 133(1), p. 011007], which treats a harmonic drive without a cup, present the geometry-relevant operation of harmonic drives under an ideal little or no-load condition. This paper shows that the cup is essentially a compliant mechanism with the unique feature of transforming a set of different tooth rotations into a single rigid body rotation and demonstrates how the cup affects tooth conjugation and the conjugate tooth profiles. It proves and demonstrates that the conjugating tooth profile should be a three-dimensional surface because of the cup deformation. The use of spur gears on both flexspline and circular spline will cause excessive interference and excessive deformation will become necessary to overcome the interference. Since no-load geometry is clearly identified, excessive deformation and errors due to incorrect geometry can be removed or filtered and the loading effects can be identified. Contact ratio of a harmonic drive is also obtained through the range of conjugate positions. Although loading is not considered, the geometric error is. Eliminating or reducing geometric error will improve the performance.