本論文旨在進行一單階螺旋齒輪減速機之特性分析。利用齒輪原理，建立具有線性齒頂修整(Linear Tip Relief)、導程修整(Lead Crowning)與轉位(Profile Shift)之螺旋齒輪齒面數學模式，進行該齒輪對之齒面接觸分析，包含傳動誤差(Transmission Error，TE)與接觸齒印(Contact Pattern)等，並探討組裝誤差對系統的影響。再利用有限元素分析軟體搭配自行撰寫的自動化網格分割程式，進行五齒對之負載下齒面接觸分析，將所得結果與機械設計分析軟體進行比對，驗證分析結果的正確性。根據齒頂修整相關規範及機械設計分析軟體建議值，提出針對齒頂修整參數之優化設計。 動態模擬部分，建立齒輪系統動態模型，將齒面接觸分析與機械設計分析軟體所得之靜態傳動誤差與嚙合剛性(Meshing Stiffness)代入，利用龍格-庫塔法(Runge-Kutta Methods)求解動態方程式，取得動態傳動誤差(Dynamic Transmission Error，DTE)與模擬振動訊號，分別透過均方根值計算(Root Mean Square，RMS)及快速傅立葉轉換(Fast Fourier Transform，FFT)探討優化前後之平均振動量與嚙合頻能量變化，模擬結果顯示，優化設計可成功降低齒輪系統的振動量。 ;The purpose of this study is to analyze the meshing characteristics of a single-stage helical gear speed reducer. The mathematical model of a helical gear pair with linear tip relief, lead crowning and profile shift was developed based on the theory of gearing and differential geometry. The transmission errors and contact patterns were calculated by tooth contact analysis. The effects of assembly errors on the contact stress and contact patterns were also investigated and discussed. An auto-mesh-generation computer program was developed based on the mathematical model. Finite element analysis and a commercial machine design package were used in the loaded tooth contact analysis. Based on the standards of tip relief and suggestions of commercial machine design package, an improved design was attained. In the dynamic simulation aspect, the dynamic model of a modified helical gear pair was developed. Based on the results of loaded tooth contact analysis, including the static transmission errors and meshing stiffness, the dynamic transmission errors (DTE) and vibration signals were solved by using Runge-Kutta method. Furthermore, the energy level of meshing frequencies and average energy of DTEs were evaluated by Fast Fourier Transform (FFT) and Root Mean Square (RMS) method. The results from original design and improved design were compared and discussed. The simulation results show that the improved design can reduce the amount of vibration.