漸開線齒輪因為加工製作簡易且對裝配誤差不敏感的特點，已經廣泛地使用多年，但此漸開線僅是指在平面上形成的漸開線，其裝配軸必須平行才不會影響其嚙合特性，然而將平面漸開線應用於空間歪斜轉軸之螺旋漸開齒輪時卻失去對誤差不敏感之優點。Phillips於2000年提出了空間漸開線，定義出空間中的漸開線形式，設計出可裝配在歪斜軸上的空間漸開線齒輪對，且仍保有對裝配誤差不敏感之優點。但Phillips僅對空間漸開線齒輪主要的幾何建構形式與理論做解說，並沒有一套完整的設計方法，於是本文嘗試建立一套空間漸開線齒輪對與嚙合齒條之設計流程。
本文一開始先對空間漸開線齒輪之齒冠圓範圍使用齒輪干涉條件與Phillips提出的Wildhabor Cone進行設定，再利用Litvin提出的齒面接觸分析方法，得到空間漸開線齒輪對在嚙合過程中作用角與滑動軌跡之間的關係，藉由此關係可以建立一套設計流程來調整齒面寬以及齒數等參數，使其能符合設計需求。
本文接著將設計好之空間漸開線齒輪參數，配合Phillips以幾何觀念建構之齒條傳動方向來架設座標系與齒條齒面參數式，並對空間漸開線齒面與嚙合齒條齒面進行齒面接觸分析，得到在干涉範圍限制下，齒條齒面之限制範圍。
最後在SolidWorks軟體中合成空間漸開線齒輪對以及與其嚙合之齒條幾何模型，並進行運動模擬來驗證由此設計流程設計出的空間漸開線齒輪對以及與其嚙合之齒條能滿足設計需求，最後也驗證了當空間漸開線齒輪對裝配出現誤差時轉速比變化不敏感之特性。

Planar involute gears are widely used in industry because they are easy to manufacture and insensitive to assembly errors. Even though involute gears have such unique characteristic, the axes of gear pairs must be assembled parallel. In 2000, Dr. Jack Phillips proposed a new spatial involute curve and discovered spatial involute surfaces for designing the general spatial involute gears, which can be used in skew-axis transmission applications. However, his development of the general spatial involute gears is mainly based on geometric constructions. In this thesis, we seek to build solid models of the general spatial involute gears in CAD systems and investigate the process of designing a spatial involute gear pairs and its conjugate rack.
This thesis discusses the following. First, we use the condition of inference and the concept of wildhabor cone to design the addendum circle. Second, we use TCA technique to obtain the relationship between the slip track and the angle of action, which then leads to the calculation of contact ratios. We can then design the tooth face width and the numbers of teeth based on contact ratios. Third, we locate the position and direction of the rack that is conjugate to a spatial involute gear, and we use TCA technique to investigate the boundary of the rack plane. Finally, we build the models of spatial involute gears and its conjugate rack in CAD systems and demonstrate that spatial involute gears are indeed insensitive to assembly errors
This thesis provides mathematical and geometrical methods for the construction of solid models of the general spatial involute gears. We have demonstrated that the process presented in this thesis is helpful in designing the general spatial involute gears.

[1]Litvin, F. L., 1968, Theory of Gearing, 2nd edition, Nauka, Moscow.
[2]Litvin, F. L., 1994, Gear Geometry and Applied Theory, Prentice-Hall Inc., New Jersey.
[3]Phillips, Jack, 1999, “Some Geometrical Aspects of Skew Polyangular Involute Gearing,” Mechanism and Machine Theory, 34, pp. 781-790.
[4]Phillips, Jack, 2000, “From the Trailed Disc Plough with Ball to General Involute Gearing,” Proceedings of the Ball Symposium, July 9-12, Cambridge, UK.
[5]Phillips, Jack, 2003, General Spatial Involute Gearing, Springer-Verlag, Berlin.
[6]劉柏村，2006，空間漸開齒面之合成與接觸分析，國立成功大學機械工程研究所碩士論文。
[7]洪世杰，2006，共軛空間漸開線之研究，國立成功大學機械工程研究所碩士論文。