自行車後變速器系統之理論研究與最佳化設計

Abstract

自行車的後變速器主要功能在於導引鏈條至所選擇的後齒片以完成換檔的 動作。因此如何設計一個良好的後變速器可以精確而且迅速的進行換檔動 作乃成為設計者最大的挑戰。在本論文中，基於一些基本的假設，導出後 變速器的理論數學模式，此模式將一個實際上為六連桿的機構簡化為等效 四連桿機構，再利用幾何關係及靜力分析求出未知的狀態變數值。為驗證 此數學模式的正確性，本論文同時發展一實驗設備用來量測導鏈導輪中心 在各檔位之空間位置。經由量測值及理論值的比對後發現兩者相當吻合， 因而成功的驗證理論數學模式之正確性。最後，再利用此數學模式作為分 析工具以進行後變速器的最佳化設計，並利用敏感度分析方法將系統參數 加以適當的分類使得最佳化設計更有效率。本論文所發展的最佳設計程序 可運用於發展一般常見的後變速器。 The rear derailleur on a multi-speed bicycle guides the running chain rapidly and precisely to a selected freewheel sprocket position without disengagement from the freewheel assembly. The refore, the design of the rear derailleurs is a most important target for designers. In this study, a mathematical model for the rear derailleurs is developed based on some basic assumptions. It involves modeling a typical rear derailleur as an equivalent four-bar linkage from an original six-bar physical model. Unknown state variables in the model are determined by using geometrical and static analyses. An experiment facility is furnished to verify the validation of the developed model. Good agreement is achieved by comparing the spatial positions of the guide pulley center measured in the experiment and calculated based on the mathematical model at various speed ratios. Thus performance of the rear derailleur can be predicted further based on its corresponding simulated model. Finally, an efficient optimum design procedure for the rear derailleurs is presented. It makes the upper/ lower bounds of design variables easier to determine. This reduces the trial-and-error efforts during iterative searching for optimum solutions. It is worth emphasizing that the design procedure proposed herein is applicable to most known types of rear derailleurs.