曲齒聯軸器目前已經廣泛的應用在工業界，其生產設備大部分是利用美國格里森公司(Gleason Works Co.)所發展的Gleason No.120型專用磨床機。所以為了要提高國內生產曲齒聯軸器的設計及製造之自主能力，本研究發展出另一種曲齒聯軸器齒形製造方式。
本研究為了探討該齒形之幾何形狀特性。首先，利用空間座標轉換矩陣理論，配合磨輪加工路徑與刀具之位置關係，推導出製造曲齒聯軸器之刀具輪廓方程式，再根據創成刀具之運動軌跡方程式，配合刀具與工件之嚙合方程式，求出刀具創成出齒形之包絡面，也就是曲齒聯軸器之幾何數學模式。最後，依據推導的齒面數學模式，建構實體模與使用Gleason No.120型專用磨床機加工方式的齒形作比較，並針對其中加工參數的變化建構圖表，分析其齒面性質，以作為後續依不同應用場合選擇適當設計參數之研究基礎。

Curvic couplings have been widely applied to various industrial applications. Presently the Gleason No.120 special grinding machine developed by Gleason Works Co. is one of the commonly used machine tool for the curvic coupling manufacturing. On the other hand, in response to the issue of improving the domestic design and manufacturing ability, an alternative manufacturing method of curvic coupling is introduced in this study.
In this study the geometrical characteristics of the novel gear profile are investigated. Firstly, applying the spatial transformation matrix theorem to the relationship between the cutting tool path and the cutting tool position, the cutting tool profile equation of curvic coupling is successfully derived. Secondly, the mathematical model of the envelope surface of the generating tool, or generally being called the gear surface, is constructed based on the trajectory equation of the generating tool motion and the tool-workpiece meshing equation. Finally, the solid model is established based on the obtained mathematical model, and the comparison works with the conventional curvic coupling are also carried out. The analysis of gear surface is graphically depicted with respect to the various machining parameters. It is believed that this thesis provides a useful tool for the following studies of curvic couplings for the different demand of application fields.

摘要 I
Abstract II
目錄 III
圖目錄 V
表目錄 VIII
符號說明 IX
第一章 緒論 1
1-1 研究背景及目的 1
1-2 文獻回顧 2
1-3 論文組織與章節 4
第二章 創成曲齒聯軸器之刀具數學模式 5
2-1 聯軸器種類 5
2-2 曲齒聯軸器簡介 6
2-3 格里森曲齒聯軸器加工方式 7
2-4 研究流程 9
2-5 本文發展的曲齒聯軸齒形製造方式 10
2-5-1 創成刀具之數學模式 13
2-5-2 刀具之實體模型建構及刀具設計探討 22
第三章 曲齒聯軸器之齒面數學模式 25
3-1 包絡理論 25
3-2 嚙合方程式 27
3-2-1 刀具曲面之法向量 29
3-2-2 相對速度 32
3-2-3 嚙合方程式 36
3-3 刀具軌跡方程式 37
3-4 曲齒聯軸器之數學模式 42
第四章 曲齒聯軸器之實體建構及探討 44
4-1 齒面建構 44
4-2 本文製造方式與格里森製造方式的曲齒聯軸器齒形之比較 48
4-2-1 齒形之比較 48
4-2-2 齒形加工量 54
4-2-3 齒形邊緣分析 64
4-2-4 應用 71
第五章 結論與建議 72
參考文獻 74
附錄A 擺線軌跡方程式 77
附錄B 曲齒聯軸器之齒面方程式 87

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