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。

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.

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