Computational design and geometric characterization of S-shaped tooth profiles in harmonic gears: An emphasis on continuous dual conjugation

Abstract

To establish a systematic framework for harmonic reducer tooth profile design, this study proposes a novel methodology for developing S-shaped tooth profiles. First, by leveraging the geometric constraints between the tooth profile normal line and the centrodes, the proposed method directly generates continuous dual-conjugate profiles for the circular spline from the flexspline addendum, while defining precise boundaries for the design parameters. Subsequently, kinematic analysis is conducted to evaluate essential geometric characteristics, including the contact ratio, slip ratio, and curvature radius. The results demonstrate that the S-shaped profile achieves a high contact ratio and low slip ratios. Notably, comparative assessments of comprehensive curvature radii reveal that the gear pairs in the first conjugate interval exhibit superior load-bearing capacity. Finally, a dual-circular-spline harmonic reducer prototype was fabricated, and wear pattern analysis on the tooth surfaces experimentally validated the continuous dual-conjugation behavior. These findings provide a theoretical basis for parametric optimization and future research on tooth flank modifications.