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系統識別號 U0026-2206201416152800
論文名稱(中文) 應用電子試算表於平面連桿機構合成與步行機構分析
論文名稱(英文) Synthesis of Planar Linkages and Analysis of Walking Mechanisms Using Spreadsheet Software
校院名稱 成功大學
系所名稱(中) 機械工程學系
系所名稱(英) Department of Mechanical Engineering
學年度 102
學期 2
出版年 103
研究生(中文) 嚴幼軒
研究生(英文) You-Hsuan Yen
學號 N16014530
學位類別 碩士
語文別 中文
論文頁數 87頁
口試委員 指導教授-黃金沺
口試委員-陳家豪
口試委員-許來興
中文關鍵字 電子試算表  平面機構合成  步行機構 
英文關鍵字 Spreadsheet  Synthesis of Planar Linkages  Walking Mechanisms 
學科別分類
中文摘要 本論文以Microsoft Excel電子試算表進行平面連桿機構合成與步行機構分析,並將研究與使用者介面結合,建立相關的動畫模擬。此軟體不但可應用於機構合成與分析方面,也適用於課程教學之目的,軟體中的參數可自行設定與變更並立即觀察設計與修改結果,再藉由動畫模擬的視覺輔助來提升使用者的理解。
在平面連桿機構合成方面,利用幾何法對三個導引位置問題求解,合成時主要計算資料為極心、映射極心、圓周點與圓心點、滑動接頭選取及其滑行線與角度,模擬則需要計算輸入桿轉動時,合成機構所對應之相對位置。在多連桿步行機構分析方面,探討現今常見的連桿步行機構,其中又以六連桿以上機構為主,因為連桿數目愈多,愈能使步行機構滿足所需的運動要求,佔有較多的優勢。本論文利用向量迴路分析進行程式計算及模擬。
本論文在Excel環境下可合成之機構包含四連桿機構、曲柄滑塊機構、雙滑塊機構及倒置曲柄滑塊機構;完成分析之機構包含Chebyshev四連桿步行機構、Klann六連桿步行機構、Jansen八連桿步行機構及王式、邱式、洪式與沈式八連桿步行機構。對於文中所討論的案例皆附上其對應的試算表檔案,使用者可以自由調整參數數值並觀察此參數對機構的影響,利用已設計好的檔案進行結果分析,其附加之圖表及模擬動畫會隨著參數改變而同步變化,有助於驗證計算結果的正確性。
由本論文可以證明確實能夠以電子試算表設計出具備良好使用者介面的分析軟體,且此軟體可做為未來建立更完整機構設計與分析的資料庫。藉由電子試算表具有進行問題分析之潛能,能夠作為一個強大的運算分析工具應用於其他工程相關領域。
英文摘要 SUMMARY

This thesis presents the use of Microsoft Excel spreadsheet programs in the synthesis of planar linkages and analysis of walking mechanisms. Such programs can be used for design, as well as teaching purposes. These programs contain parameters for the user to specify and provide animations as visual aids. In the synthesis of planar linkages, we use graphical methods in solving three-position problems. We calculate poles in order to find slider joints. Then, we compute the dimensions of linkages and build animation models with graphical user interface. In the analysis of walking mechanisms, this thesis focuses on commonly used walking mechanisms, which mostly contain more than six links. We use the vector loop method to calculate and simulate these walking mechanisms. Three kinds of slider linkages are synthesized, and seven types of walking mechanisms are analyzed systematically in this thesis. In these cases, the user can freely modify the parameters and view animated plots that synchronize with the change of data in order to verify the results. This thesis shows that spreadsheet programs have the potential to serve as powerful tools in more engineering applications due to its user-friendly interface. The studied cases given in this thesis can serve as a base for developing more sophisticated programs for complicated planar mechanisms.

Keywords: Spreadsheet, Synthesis of Planar Linkages, Walking Mechanisms

INTRODUCTION

The development of numerical computing software has enhanced the analysis ability, efficiency, and reliability in engineering applications. Common software analysis tools, such as Mathworks Matlab, ANSYS, and Mathematica, offer useful toolboxes and packages that help users perform data analysis without the need of lower-level programming. However, the prices for such software can be quite costly.

Spreadsheet is a type of computer application program that features the storage and analysis of data in a tabular form, i.e., in the form of cells. It is frequently used in data storage and sorting, often related to business administration and financial work. However, spreadsheet is not limited to simple data storage; its computing features can be applied in engineering applications too. Spreadsheet has numerical computing, matrix operations, programming, graphics, and animation capabilities. The main characteristic of spreadsheet is that we can observe design results and modify parameters immediately. This thesis uses the spreadsheet program for engineering applications, and our focus is on the synthesis of planar linkages and analysis of walking mechanisms.

MATERIALS AND METHODS

In the synthesis of planar linkages, we use graphical methods in three-position problems. The synthesis of binary links is divided into two parts, cranks and sliders. For synthesizing cranks, we choose one point as the circle point in position 1. We then obtain the corresponding circle points in positions 2 and 3 after coordinate transformations. The center of the three circle points is the fixed joint of a crank. For synthesizing sliders, we calculate poles, image poles, and the circle and image circle of the pole triangle. We then select slider joints and find their sliding lines. Combining these two parts, we can synthesize slider crank, double-slider, and inverted slider crank linkages. We use the vector loop method to calculate the positions of linkages when the input parameters vary and to construct animation of linkages.

In the analysis of walking mechanisms, this thesis focuses on commonly used walking mechanisms, which mostly contain more than six links. The more links a walking mechanism contains, the more requirements are needed for the movement of the walking mechanism. For a complex multi-link walking mechanism, we divide it into various loops and analyze them using the vector loop method. Although each loop is calculated separately, the parameters of different loops may be dependent on one another. Once the analysis of a walking mechanism is finished, we simulate these walking mechanisms by constructing animation with graphical user interfaces.

RESULTS AND DISCUSSION

Four-bar and three types of slider linkages are synthesized in this thesis. Slider crank and double-slider linkages are synthesized using the theory about three homologous points through a line. The solution is a circle passing P12, P13 , and P231, and it is the so-called circle of sliders. Inverted slider crank linkages is synthesized using the theory about three homologous lines through a point. The solution is on the circle passing P12, P13 , and P23.

Seven walking mechanisms are analyzed in this thesis Chebyshev, Klann, Jansen, Wang, Chiu, Shen, and Hung walking mechanisms. The more links a walking mechanism contains, the more requirements are needed for the movement of the walking mechanism. As a result, the geometry of complex multi-link walking mechanisms must be carefully chosen, and the adjustable ranges of parameters are relatively small. Small changes in link lengths may result in impractical walking mechanisms. Therefore, the most important advantage of using spreadsheet software is that we can observe the locus of a walking path and modify parameters immediately.

CONCLUSION

This thesis provides spreadsheet files that simulate the studied linkages, and the spreadsheet files allow the user to modify the parameters freely. Using such files, the analysis of linkages can be performed, and animated plots that synchronize with the change of data can help in verifying the motions of linkages. It is demonstrated that spreadsheet programs can be used to develop programs with user-friendly interface in the application of mechanism synthesis and analysis. This thesis also shows that spreadsheet programs have the potential to serve as a powerful tool in more engineering applications. The studied cases given in this thesis can serve as a base for developing more sophisticated programs for complicated planar mechanisms.
論文目次 目錄
摘要 I
Abstract II
誌謝 V
表目錄 IX
圖目錄 X
符號表 XIV
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 研究動機 4
1-4 本文架構 4
第二章 基本理論 6
2-1 向量迴路法 6
2-2 平面剛體位移 8
2-3 極心 9
2-4 極心三角形 11
2-5 映射極心 12
2-6 三相關點在一直線上 14
2-7 三相關線通過一定點 15
第三章 Excel環境下的機構設計功能簡介 16
3-1 Microsoft Excel簡介 16
3-2 案例說明:Mercedes Benz Mono Wiper 17
3-2-1 向量迴路分析 18
3-2-2 Excel使用介面說明及應用 21
第四章 使用Excel進行平面四連桿滑塊機構合成 27
4-1 剛體經過三個有限分離位置之極心關係 27
4-2 曲柄機構合成方法 29
4-2-1 選取圓周點計算圓心點 29
4-2-2 四連桿機構模擬方法 31
4-3 曲柄滑塊機構與雙滑塊機構合成方法 35
4-3-1 滑動接頭的選取 36
4-3-2 曲柄滑塊機構模擬方法 37
4-3-2 雙滑塊機構模擬方法 41
4-4 倒置曲柄滑塊機構合成方法 45
4-4-1 滑動接頭的選取 45
4-4-2 倒置曲柄滑塊機構模擬方法 46
4-5 討論 50
第五章 使用Excel進行平面多連桿步行機構分析 51
5-1 四連桿步行機構 52
5-1-1 Chebyshev Walking Mechanism 52
5-2 六連桿步行機構 55
5-2-1 Klann linkage 55
5-3 八連桿步行機構 62
5-3-1 Jansen Linkage 62
5-3-2 王式步行機構 68
5-3-3 邱式步行機構 73
5-3-4 洪式步行機構 74
5-3-5 沈式步行機構 76
5-4 討論 81
第六章 結論與未來方向 82
6-1 結論 82
6-2 未來方向 83
參考文獻 85
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2. Söylemez, E., Mechanisms, 4th Edition, Middle East Technical University, 2009.
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6. Mechanism by Tchebyshev, Plantigrade machine, http://tcheb.ru/
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http://cyberneticzoo.com/walking-machines/1850-chebyshev-walking-platform-russian/
8. Wikipedia—Klann linkage,
http://en.wikipedia.org/wiki/Klann_linkage#History
9. Wikipedia—Theo Jansen,
http://en.wikipedia.org/wiki/Theo_Jansen
10. C&S Creation, Theo Jansen (in Chinese), Special issue, C&S Creation, Taipei, Taiwan, R.O.C., 2011.(圓方創意,泰奧陽森,特刊,園方創意,台灣台北市,2011。)
11. 邱正平,波浪型步態機器馬之設計,國立成功大學機械工程學系碩士論文,1996。
12. 沈煥文,八連桿型機器馬之機構設計,國立成功大學機械工程學系碩士論文,1999。
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14. Kiper G., Huang C., and Söylemez E., “Numerical Analysis of Planar Cam Follower Mechanisms,” The 2nd IFToMM Asian Conference on Mechanism and Machine Science, Tokyo, Japan, 2012.
15. 陳建宏,應用電子試算表進行齒輪嚙合分析,國立成功大學機械工程學系碩士論文,2013。
16. Mechanical Design Handbook, Hoekens Straight-line Mechanism,
http://mechanical-design-handbook.blogspot.tw/2011/02/hoekens-straight-line-mechanism.html
17. Walk Like a Man—Kinetic Sculptures by Theo Jansen,
http://artstormer.com/2011/01/31/walk-like-a-man-kinetic-sculptures-by-theo-jansen/
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