公差設計為機械設計與製造中之重要環節，常被用來衡量品質和成本之間的取捨。以本研究使用之並聯式機械手臂為例，每提升0.01mm終端定位精度，平均就可能增加28%的總成本，故準確訂定公差精度可以提升產品品質且節省生產成本。近年來，機械手臂已在各項產業中廣泛的被使用，尤其在機械製造領域，機械手臂常被用於置物、取物、焊接、噴漆、銑床、鑽床、組裝等製程，而其精度便成為產品加工時必須考量的重要因素，有鑒於此，本研究針對機械手臂之長度與節點之公差進行設計，並考量精度與成本之最佳化綜合指標。
本研究的主要目標為在給定產品精度下，模擬零件生產製造及機械手臂之運作，並利用吾人撰寫之基因演算法程式求得最佳公差設定，首先運用蒙地卡羅方法模擬製造機械手臂零件的真實情況，並將機械手臂視為一個多體系統並進行分析，代入機械手臂的運動方程式模擬機械手臂真實運動，得到在運動範圍內各個點的精度誤差。若符合精度要求，將其公差代入經濟成本方程式(economic cost function)和質量損失方程式(quality loss function)，將兩者相加得到綜合成本(comprehensive cost)。達基因演算法之終止條件後，最低成本者就為模擬得到的最佳公差設計數值。
本文中使用了六種模型，即Fortini’s 離合器、四連桿模型、六聯桿模型、SCARA機器手臂、關節式機器手臂及並聯式機器手臂模型作為範例，實際運用本文所呈之研究方法進行分析、模擬，以得出數據與分析結果後並與文獻及常用之傳統公差設計法作比較，視其結果能否顯示本文所用之研究方法相較於其他研究方法的便利之處。
為了得到機械系統中各個零件之最佳公差精度設定，本文透過Fortini’s 離合器、四連桿模型、六連桿模型、SCARA機器手臂、關節式機器手臂及並聯式機器手臂模型使用基因演算法，找出最佳的公差精度設定。從基因演算法模擬實例得到的結果可以歸納為以下三點結論，基因演算法應用於公差設計可以滿足產品生產與品質服務的設計要求，能滿足生產製造、精度與品質服務之最低成本設計，可以套用到不同型態的產品上，從靜態的離合器系統到三維動態的機械手臂，程式可應用的範圍廣泛，可以供業界於自動化設計流程上使用，且優於傳統所使用的WCM(worst-case model)和RSS(root sum squared) model。

Tolerance allocation is a significant process in mechanical design for real production. It indeed plays as a critical bridge for linking system performance, design requirements, product quality as well as manufacturing cost. In other words, allocating proper tolerance for each involving system components can achieve both the quality and economic requirements for various industrial production systems. Since the allocation of tolerances requires lots of operating data ranging from product manufacturing to analysis, the improvement on computing technology, the process of design, manufacturing, and production processes can be better systematically optimized via a newly developed computing CPT (cost-precision-time) approach presented in this thesis.

In order to obtain best tolerance allocation of each component in a mechanical system, six kinds of model including fortini’s clutch model, four-bar linkage model, six-bar linkage model, SCARA robot, articulated robot and delta robot model are employed, to compute and optimize for best tolerance allocation all possible combinations in the working range by Monte Carlo, genetic algorithm and experimental approaches. The results of simulation show that the aforementioned methods can be applied to design for static, dynamic and various robotic arms systems for 3D motion. In addition, the results obtained by tolerance optimal CPT method are accurate as compared to other methods. This indicates that the CPT tolerance method can be used for the tolerance allocation for various products. Moreover, as applied in the manufacturing of real-world productions, the need for tolerance allocation problem can be adopted to help design of better machines and robotic systems.

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