雙包絡減速機具有高扭力與高精度等優點，在工業上常被廣泛使用。首先，本文介紹兩種雙包絡蝸桿曲面之求取方法，分別為接觸法與剛體轉置法，再依不同刀具幾何(錐型刀具與兩線刀具)來推導出雙包絡蝸桿曲面方程式。

依照國際標準規範，求出雙包絡蝸桿偏置曲面所需要之刀具幾何尺寸參數。最後架設雙包絡蝸桿曲面量測平台，利用CMM紀錄探針球在碰觸雙包絡蝸桿曲面時之中心點位置，再與兩種刀具所產生的雙包絡蝸桿偏置曲面之理論值比較。其結果為錐型刀具所推得之雙包絡蝸桿偏置理論曲面值與量測值較接近，判斷其雙包絡蝸桿可能為錐型刀具所加工而成。

Double-enveloping reducer is widely used in the industry due to its high transmission torque and high accuracy. The screw theory and the rigid-body transformation method are introduced and applied in this thesis to the determination of the worm surface. The equation of the worm surface is derived by the two methods based on different geometries of cutting tools (conical cutter and fly cutter).

According to the Standards of American Gear Manufacturers Association (AGMA6030 C-87), the size and the shape of the cutters can be determined to conform the worm offset surface. Moreover, a measuring system is set up with a CMM (coordinate measuring machine) to measure and record the center point of the touch probe when it contacts with the surface of the double-enveloping worm. Finally, comparisons of measured results with different theoretical worm offset surfaces obtained from two types of cutting tools are made in this study. Geometric errors of the measured worm offset surface shows that the worm used in this thesis was machined by cutters with a conical form.

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4
1.4 論文架構6
第二章 雙包絡蝸桿曲面方程式及曲面參數推導
2.1 雙包絡蝸桿曲面方程式推導 7
2.2 雙包絡蝸桿蝸輪部位名稱與設計尺寸15
2.3 雙包絡蝸桿曲面參數20
2.4 探針球中心點曲面參數22
第三章 雙包絡蝸桿曲面量測規劃
3.1 量測台設定與三次元量床精度檢測24
3.2 蝸桿量測之座標及工件工作原點設定27
3.3 蝸桿曲面量測旋轉程序30
3.4 蝸桿曲面量測區與資料點數規劃32
3.5 蝸桿空間旋轉偏擺補正33
第四章 量測結果與分析
4.1 雙包絡蝸桿曲面誤差表示36
4.2 蝸桿軸心偏擺補正後之蝸桿曲面誤差結果38
4.3 結果與討論51
第五章 結論52
參考文獻53
附錄56

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