為了降低機構高速運轉時產生之搖撼力及搖撼力矩，常應用添加圓盤配重的方式，作為四連桿機構之平衡設計。為進一步改善之，更有前人加入變轉速輸入的概念為之。但因輸入轉速函數需具微分連續性，故需加入限制式而得之。而本研究之主要目的為引入具無窮多階微分連續的傅立葉級數，表示輸入變轉速函數，讓微分連續性問題能直接滿足。

　　文中，採用傅立葉級數表示輸入桿之運動特性，且運用向量迴路法及運動係數法，建立其它桿件之運動分析模式。再應用牛頓法建立添加圓盤配重後各桿接頭力、驅動扭矩、驅動功率、搖撼力及搖撼力矩之分析模式。並以此為基礎分別以添加平衡配重、輸入變轉速及同時考慮平衡配重與輸入變轉速等三種方式，進行最佳平衡設計，並各以實例設計分析顯示與比較其結果。

　　本文採用傅立葉函數表示輸入轉速函數，能自動滿足輸入運動曲線皆為微分連續的要求，可簡化其最佳化設計問題，並可將此概念運用到其它變轉速輸入機構的設計。

　Adding disk counterweights has been applied to reduce the shaking force and shaking moment of high speed mechanisms. For further reduction, some researchers tried to optimize the trajectories of the input speed instead of using a constant one. However in order to maintain the continuity of the input motion at the instant of the end of one cycle and the beginning of the next one, they used equality constraints, which often make the optimization more difficult. In order to improve it, Fourier series, which is continuous and so its differentiations are, is proposed for the determination of the trajectories of the input speed.

　Except using Fourier series to express the input motion, the vector loop approach and kinematic coefficients are applied to develop the model of kinematic analysis. Newton’s 2nd Law is used to build the model of kinetostatic analysis, such that the bearing forces, driving torque, driving power, shaking force and shaking moment of the four bar linkage can be determined.

　Based on the derived models, three strategies of the optimal balancing design of the four-bar linkage are used; they are adding disk counterweights, using variable input speed, and with the integration of both two. Examples are given, and the results of all the balancing designs are compared and discussed.

　It is found that by using Fourier series, the continuity of the input function can be satisfied automatically, consequently, the optimization can be greatly simplified. The design methodology proposed in this thesis can also be applied to design the trajectories of the input speed of other mechanisms for other purposes.

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