本文針對具圓錐滾子之滾子輪式凸輪機構，以剛體運動軌跡的創成概念與微分幾何學的理論，提出可依滾子軸心直紋面的偏置曲面，建構凸輪曲面的幾何設計法則。
由於具半錐角的圓錐滾子與凸輪在嚙合過程中，滾子半徑隨滾軸高度而改變，造成滾子軸心到接觸點的嚙合向量不為單位法向量。因而需透過具嚙合角度特徵的三角形，求出嚙合向量並帶入剛體轉置法步驟，以推導出圓錐滾子之凸輪曲面。並可藉由所求得之通式，代入等速型與修正型正弦兩運動曲線，探討半錐角的變異對嚙合向量與扭曲角度的變動，及其所造成凸輪曲面特性的改變。

This thesis presents a geometry design method to generate the surfaces of the globoidal cam with the conical roller follower. Based on the trace of the rigid body and the theory of differential geometry, the conjugate surfaces can be the offset surfaces of the ruled surface.
With different roller’s axial height, its radius and the meshing vector also be changed. For this reason, the contact points on the outward roller are hard to find. To overcome this problem, we propose the triangular graph with meshing angle, it can present the vector quantity caused from the motion angle. We replace it into the procedures of the rigid body transformation method to derive the cam surfaces with the conical roller follower. Furthermore, two models with modified sine and constant velocity motion curves are generated and analyzed.

目錄 Ⅰ
圖目錄 Ⅲ
表目錄 Ⅵ
中文摘要 Ⅶ
Abstract Ⅷ

第一章 緒論
1-1 前言 1
1-2 文獻回顧 3
1-3 研究目的與研究方法 5
1-4 論文大綱 7

第二章 凸輪曲面建構理論
2-1 齊次座標轉換矩陣 9
2-2 曲線與曲面之微分幾何 12
2-3 直紋面與剛體轉置理論 17
2-4 包絡理論 21
2-5 螺旋理論 23

第三章 圓錐滾子之凸輪曲面求取
3-1 參數與座標系設定 26
3-2 單一運動方向與其嚙合向量 31
3-3 剛體轉置法步驟的介紹與推導 34
3-4 圓錐滾子之嚙合向量 39
3-5 三種曲面推導方法之比較 45
第四章 剛體轉置法的應用與討論
4-1 運動曲線與尺寸參數 49
4-2 滾子軸心線與其Frenet-Serret 三面體 53
4-3 圓錐滾子之半錐角對嚙合角度的影響 55
4-4 半錐角固定下的修正型正弦運動曲線 64
第五章 結論與建議
5-1 結論 69
5-2 發展與建議 70

參考文獻 71
附錄 A 74
附錄 B 79
附錄 C 84

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