The Optimal Dimensional Synthesis of Four-Bar Linkage for Open Path Generation

[[abstract]]本研究主要目的是利用路徑創成原理，合成吻合指定開迴路耦點曲線段的連桿尺寸。作法係將所指定之需求曲線段任意補一連續曲線段，使產生一完整之耦點曲線，再利用路徑創成法則，配合基因演算法合成最佳四連桿尺寸。以需求曲線與非需求曲線的比例、不同的總合成路徑點數、及不同的基因代數為參數進行分析。因本研究指定之欲求曲線段可為任何連續的曲線，與其組合成完整耦點曲線的非欲求曲線也可為任意曲線段，且依本研究的創成法，可將需求曲線段之點座標輸入後，直接合成連桿尺寸，在使用上更具方便性及主導性。研究結果顯示欲求曲線段與非欲求曲線段之點分配比例越高誤差越小，原則上4:1即可；欲求曲線段之點分佈取越密集即點數越多，欲求曲線會與創成曲線有較吻合的趨勢；另外基因演算法之演算代數方面，約在600代即可收斂得到很好之結果。[[abstract]]The purpose of the study is to apply the method of path generation to synthesize the optimal dimension of Four-Bar Linkage for open path. The procedure is to fill up the desired curve with a random curve, and then obtains a complete coupler curve. After that, combined with the genetic algorithm, the method of path generation is applied to get the optimal size of four-bar linkage where the desired and undesired curve could be any continuing arbitrary curve. The ratios of considering point between the desired curve and the undesired curve, total number of giving points of forming the full coupler curve, and the number of generation of genetic algorithm are selected as the parameters to analyze the results. The method used in the study could just input the coordinate of points of coupler curve, and then the dimensions of the four-bar linkage could be synthesized directly. It would be more convenient and dominant. The results show that the higher the ratio of point distribution of the desired curve, the smaller the differences, and the ratio of 4:1 would be better enough. If the point distribution of the desired curve could be more concentrated, the desired curve and the generated one would be highly matched. In addition, 600 generations for the genetic algorithm would be enough for giving a converged synthesis