擺線減速機由於具有高減速比、高傳動效率、定位精度高等優點，已經被工業界應用一段時間。本論文內容主要為對一階擺線減速機中，具齒形修形的擺線齒輪進行分析，包括齒面接觸分析、齒輪受力分析、運動誤差分析與齒形最佳化設計。首先藉由坐標轉換與齒輪嚙合原理來推導出擺線齒形參數式，並依據工程上的需求對擺線齒輪的齒形進行修形；接著進行齒面接觸分析來得到輸出角度與針齒背隙，並利用其結果來計算擺線齒輪受力與運動誤差。本文最後將針對齒形做最佳化設計，並使用前述之分析方法來探討最佳化設計結果。

Cycloidal reducer, commonly used in industry for decades, is a speed reduction device with high speed ratio, high efficiency, and high locating precision. This thesis studies the force on a cycloidal speed reducer with midified teeth. Firstly the cycloidal gear profile is generated by using theory of gearing. To satisfy engineering requirements, the cycloidal gear profile is then modified. Second, the force performance and kinematic error are analyzed with the results of tooth contact analysis. Finally, an optimization design is discussed. The optimal results of tooth modification parameters are designed with the optimization processes.

摘要 I
Abstract II
目錄 III
圖目錄 VI
表目錄 IX
符號說明 X
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究動機與目的 6
1.4 論文架構 7
第二章 擺線齒形設計 8
2.1 前言 8
2.2 擺線齒形創成 8
2.2.1 坐標與參數設定 8
2.2.2 齒輪嚙合方程式 11
2.3 擺線齒形修形 15
2.3.1 轉角齒形修形 15
2.3.2 偏心量齒形修形 17
2.3.3 針齒位置齒形修形 18
2.3.4 針齒半徑齒形修形 19
2.3.5 齒形修形組合 20
第三章 具齒型修形之輸出角度 24
3.1 前言 24
3.2 齒面接觸點計算 24
3.2.1 坐標與參數設定 24
3.2.2 分析方程式設定與計算 25
3.3 輸出角度計算 28
3.4 針齒背隙計算 32
第四章 具齒型修形之力量分析 35
4.1 前言 35
4.2 赫茲接觸理論 35
4.3 受力與轉角變化計算 36
4.3.1 力平衡方程式 37
4.3.2 受力與變形關係 40
4.4 運動誤差 47
4.4.1 角位移誤差 47
4.4.2 減速比誤差 48
第五章 齒形修形最佳化 50
5.1 前言 50
5.2 最佳化設定 50
5.2.1 設計參數設定 50
5.2.2 邊界條件設定 51
5.3 減速比誤差最佳化 52
5.3.1 目標函數設定 52
5.3.2 正 與正 之齒形修形組合 53
5.3.3 負 與負 之齒形修形組合 57
5.3.4 負 與正 之齒形修形組合 61
5.4 本章結論 65
第六章 結論與未來方向 66
6.1 結論 66
6.2 未來方向 67
參考文獻 68
附錄 71

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