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研究生： 施偉翔
Shih, Wei-Hsiang
論文名稱： 運用極心改換速度於無四桿迴路平面連桿組之加速度分析
Acceleration Analysis of Planar Linkages without Four-Bar Loops Using Pole Changing Velocity
指導教授： 黃文敏
Hwang, Wen-Miin
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2008
畢業學年度： 96
語文別： 中文
論文頁數： 105
中文關鍵詞： 雙蝴蝶八連桿組 、運動複雜性機構 、加速度分析 、路徑曲率中心 、虛擬連桿組 、極心改換速度 、運動不確定性
外文關鍵詞： center of path curvature, acceleration analysis, pole changing velocity, virtual linkage, kinematically complex mechanism, kinematic indeterminacy, double butterfly eight-bar linkage
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    • 本文利用一套幾何作圖法進行平面連桿組的加速度分析，此分析方法包含四個步驟。首先，以速度輔助點法求出連桿組之速度極心，並完成速度分析。其次，利用求解連桿組速度極心位置時所繪製之輔助線，建構一虛擬連桿組，再以此虛擬連桿組進行極心改換速度之分析。然後，以極心改換速度搭配Hartmann 定理，求出特定耦桿點之瞬時路徑曲率中心，藉以將原複雜連桿組拆解成多組等效四連桿組。最後，利用等效四連桿組與原連桿組耦桿的角速度與角加速度相同之特性，完成原複雜連桿組之加速度分析。
    此分析方法之關鍵在於極心改換速度之求解，然而，具運動不確定性之連桿組，其極心改換速度無法依一般方法求出。針對此問題，本文提出一種幾何法，先以虛擬連桿組之運動拘束關係，求出輔助點與其正交速度前端點兩者之改換速度，再求出各速度極心之改換速度，藉以完成整個加速度分析之流程。
    本文針對三個不具任何四桿迴路之連桿組，分別是雙自由度五連桿組、雙蝴蝶八連桿組、三自由度八連桿組，套用此加速度分析程序，完成各連桿組之加速度分析，並使用工程分析軟體驗證其結果之正確性。

    This article provides a geometrical method to analyze the acceleration of planar linkages. This analysis method contains four main steps. The first step is to find the velocity poles for the velocity analysis of linkages using the auxiliary point method for velocity. Next, the changing velocities of poles are determined by using a virtual linkage constructed from the auxiliary lines for finding velocity poles. Then, the Hartmann construction is applied to find the centers of path curvature of coupler points. Thus, the original linkage can be considered as several instantaneously equivalent four-bar linkages. Finally, using the acceleration analysis technique for the equivalent four-bar linkages, the acceleration analysis of the original complex linkages can be successfully accomplished.
    The key step of the procedures is to find the pole changing velocity. However, the pole changing velocities of linkages having kinematic indeterminacies can’t be obtained with the existing method. Thus, this article presents an improved way to find the pole changing velocities through the changing velocities of auxiliary points and tips of their orthogonal velocities, which can be obtained from the motion constrains between virtual links.
    Three planar linkages without four-bar loops, i.e., the two-degree-of-freedom five-bar linkage, the double butterfly eight-bar linkage, and a three-degree-of-freedom eight-bar linkage, are analyzed using the proposed method. The results are verified by a commercial software.

    摘要........................................ I Abstract.................................... II 誌謝........................................ III 目錄........................................ IV 圖目錄...................................... VII 表目錄...................................... X 第一章 前言................................. 1 1-1 研究動機................................ 1 1-2 文獻回顧................................ 3 1-3 研究目的與方法.......................... 5 1-4 論文架構................................ 6 第二章 基礎理論............................. 9 2-1 Burmester-Mehmke 定理及其延伸........... 9 2-2 速度輔助點法............................ 11 2-3 極心改換速度與幾何作圖法................ 13 2-4 Hartmann 定理及構圖法................... 15 2-5 四連桿組加速度極心之幾何作圖法.......... 16 第三章 雙自由度五連桿組之速度與加速度分析... 18 3-1 速度分析................................ 18 3-2 極心改換速度分析........................ 20 3-2-1 極心P25的改換速度與輸入桿之關係....... 20 3-2-2 極心P24的改換速度..................... 25 3-2-3 極心P14的改換速度..................... 27 3-3 耦桿接頭C0瞬時路徑曲率中心分析.......... 27 3-4 加速度分析.............................. 29 3-5 數值實例................................ 31 3-6 討論.................................... 33 3-6-1 輸入桿角速度相同...................... 33 3-6-2 C0與輸入桿之關係...................... 33 第四章 雙蝴蝶八連桿組之速度與加速度分析..... 36 4-1 速度分析................................ 36 4-2 極心改換速度分析........................ 37 4-2-1 點M及N的改換速度...................... 40 4-2-2 點M_及N_的改換速度.................... 42 4-2-3 點F_的改換速度........................ 46 4-2-4 極心P13與P17之改換速度................ 46 4-3 耦桿接頭D、E、F瞬時路徑曲率中心分析..... 50 4-4 加速度分析.............................. 52 4-5 數值實例................................ 57 4-6 討論.................................... 58 4-6-1 指定雙接頭桿為輸入桿.................. 58 4-6-2 指定雙接頭桿為固定桿.................. 61 第五章 三自由度八連桿組之速度與加速度分析... 64 5-1 速度分析................................ 65 5-2 極心改換速度分析........................ 66 5-2-1 點A_、B_、C_的改換速度................ 67 5-2-2 點M及N的改換速度...................... 70 5-2-3 點M_及N_的改換速度.................... 73 5-2-4 極心P18之改換速度UP18................. 73 5-3 耦桿點瞬時路徑曲率中心分析.............. 77 5-4 加速度分析.............................. 77 5-5 數值實例................................ 79 5-6 討論.................................... 79 第六章 結論與建議........................... 85 6-1 結論.................................... 85 6-2 建議.................................... 86 參考文獻.................................... 87 自述........................................ 92 著作權聲明.................................. 93

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