現今的面滾式切製法為螺旋傘齒輪和戟齒輪的主要製造方法之一，此方法採連續分度雙齒面切削，因此加工速度快，且製造之齒形具有高精度與較佳的齒面接觸性能等優點，然而其齒線為延伸外擺線，無法直接運用於直傘齒輪的加工。本論文利用內擺線運動中特殊的直線運動機構，亦即當滾動圓半徑等於基圓半徑的一半時，其運動軌跡會退化為直線，透過泛用型搖台式切齒機之坐標系統，推導面滾式直傘齒輪齒面數學模式，包含三個模組，分別為面滾式刀盤、平面假想產形輪，以及工件齒輪與平面假想產形輪之間的相對運動。對推導出的面滾式直傘齒輪齒面數學模式，進行齒頂變尖檢查與齒底過切分析，以及對面滾式直傘齒輪對進行齒面相對修形拓樸與齒面接觸分析，觀察其齒面接觸的情形與性能，接著說明使用齒輪專用量測機進行傘齒輪齒面拓樸量測之流程，並產生量測所需之齒面量測點資料，最後提出一數值範例說明並驗證本論文推導之面滾式直傘齒輪齒面數學模式之正確性，以及利用市售直傘齒輪齒面拓樸量測實驗驗證本論文產生之齒面量測點資料的可用性。

The face-hobbing method is one of the leading methods for manufacturing spiral gears and hypoid gears. Because it is a continuous-indexing and double flank cutting process, it supports high productivity, precision, and cutting gears with better contact bearing. Since this method generates extended epicycloidal flanks of bevel gears, so it is not suitable for cutting straight bevel gears. In this thesis, a special straight line mechanism of hypocycloidal motion is utilized to fabricate straight bevel gears by setting the radius of a rolling circle equals to half of the radius of a base circle. The mathematical model of a straight bevel gear is developed based on a universal face-hobbing bevel gear generator. This model contains three modules: a face-hobbed cutter, an imaginary generating gear, and the relative motion between an imaginary generating gear and the work gear. The tooth tapering and undercutting conditions of the face-hobbed straight bevel gear are checked, and the contact conditions of the designed gear pairs are investigated by ease-off topography, as well as the TCA.
In the thesis, the operating procedure for the tooth topographic measurement of bevel gears by gear measuring center is interpreted, and the nominal data are also generated. A numerical example of the face-hobbed straight bevel gears without a cutter tilt, in the essay, is presented to validate the proposed mathematical model, and then the experiment for measuring straight bevel gears is implemented to validate the nominal data.

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