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This study proposes a unified mathematical model based on the gear meshing law that can describe any gear profile along with its matching conjugate profiles. The model ensures proper meshing and enables geometric analysis, such as relative curvature and sliding ratio. This paper models involute, cycloidal, and novel circular-arc profiles, compares their curvature and sliding ratio, and outlines future research directions.

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A Parametric Mathematical Model for Spur Gear Tooth Profile Design

  • 会议论文

  • 发表日期：

    2026年

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  • Hung-Shuo Kuo,
  • Fang-Yi Lee,
  • Kuan-Lun Hsu

摘要

This study proposes a unified mathematical model based on the gear meshing law that can describe any gear profile along with its matching conjugate profiles. The model ensures proper meshing and enables geometric analysis, such as relative curvature and sliding ratio. This paper models involute, cycloidal, and novel circular-arc profiles, compares their curvature and sliding ratio, and outlines future research directions.