諧波齒輪減速機廣泛應用於半導體設備、醫療設備、機械手臂等，這些減速機具有體積小、零背隙和高速比的優點，由於工業自動化的發展，對諧波齒輪減速機的需求越來越大。
該減速器由三個基本部件組成：通常帶有橢圓凸輪的波產生器、作為可彈性變形的杯形且其開口端具有外齒的柔輪(FS)和作為剛性內齒輪的剛輪(CS)。其中剛輪是一個與柔輪嚙合的剛性內齒輪，由波產生器的旋轉驅動，柔輪與剛輪的全共軛齒面可以從齒輪理論推導出來，然而，考慮到柔輪的變形，其理論齒形不能滿足實際上的需求。
因此，本研究採用有限元方法(ANSYS)分析負載作用下三個部件的應力。首先，使用二維ANSYS應力分析評估兩個柔輪的設計參數（中性線的位置係數和偏差係數）以獲得齒輪輪廓的最佳值，然後，使用三維ANSYS應力分析評估波產生器、柔輪以及剛輪的變形和應力。於此，在齒輪上加入齒隙、齒面修形和齒頂修形的設計，以避免齒輪干涉並提高齒輪接觸性能。

The harmonic gear reducers are widely applied in semiconductor equipment, medical equipment, robotic arms, et cetera. These reducers have excellent advantages of small size, zero backlashes, and high gear ratio. The demand for harmonic gear reducers is increasing due to the development of industrial automation.
This reducer comprises three essential components: a wave generator with an elliptical cam normally, a flex spline (FS) which is an elastically deformable cup and its open end having external teeth, and a circular spline (CS) which is a rigid internal gear. Its CS is a rigid internal gear engaged with a FS, driven by the wave generator’s rotation. The full-conjugated tooth surfaces of FS and CS can be derived from gear theory. However, the perfect tooth surfaces cannot satisfy the application considering the deformation of FS.
Therefore, this research uses the finite element method (ANSYS) to analyze the stresses of three components under loading. Firstly, two FS’s design parameters (position coefficient of the neutral curve) and (coefficient of deviation) are evaluated to obtain the optimal values for better gear profiles using two-dimensional ANSYS stress analysis. And then, the deformation and stresses of a wave generator, FS, and CS are assessed using three-dimensional ANSYS stress analysis. Here, backlash, tooth flank modification, and tip relief of gear pair are applied to gear design to avoid tooth interference and improve tooth contact performance.

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