由於撓性機構具有高精度低成本的特點，因此逐漸廣泛的被應用。為了能進行新型撓性機構的設計，本研究提出兩個可以應用於撓性機構設計的拓樸最佳化方法，等體積演進式拓樸最佳化方法(Evolutionary Structural Optimization with Constant Volume，ESOCV)，以及反向型雙向演進式拓樸最佳化方法(Reversed Bi-directional Evolutionary Structural Optimization，RBESO)。ESOCV方法之特點為起始體積與目標體積相等，且運算過程會一直維持於目標體及直到收斂。RBESO方法令設計區間的元素初始密度為極小值，且指定一微小變化量使元素密度每次運算的變化為此微小值。設計區間的體積會依照給定的增加率增加至目標體積，並維持於目標體積直到數值運算收斂。
本文以ESOCV方法以及RBESO方法各進行兩個應變能最小化結構設計與兩個撓性機構輸出端位移最大化設計的範例證明方法之可行性，此兩種方法進行以上設計範例皆能得到與其他方法一樣的結果。兩方法最大的差異為運算時間，經過比較應用ESOCV方法於撓性機構輸出端位移最大化設計可以減少約12%~16%的運算時間，而在應變能最小化設計的計算時間，RBESO方法相較於ESOCV則增加約17%~40%。此兩種方法皆是以改變設計變數初始值來增加收斂速度，而此兩種方法與傳統雙向演進式拓樸最佳化方法比較下，運算速率皆有改善。
本研究亦利用RBESO方法設計自適性撓性夾爪，其自適性使夾爪能利用本身的撓性隨著夾取物體的外型變化而改變，使得單一尺寸設計的系統具備夾取不同外型物體之能力。此夾爪之設計結果經由動態模擬與實驗驗證，結果顯示，夾爪能順應凹、凸兩種不同形狀的物體，且與Petković等人的設計相比，本研究所設計之夾爪幾何利益高約18%。綜合以上所述，本研究所提之RBESO方法成功應用於撓性機構的設計，且此方法於撓性機構設計上具有提高效率的優點。

This research presents two new topology optimization methods for design of compliant mechanisms, Evolutionary Structural Optimization with Constant Volume (ESOCV) and Reversed Bi-directional Evolutionary Structural Optimization (RBESO) methods. Unlike traditional approaches, a multi-level pseudo-density scheme is proposed in this study. The pseudo-density is the design variable in the optimization problem which can be varied (increased or decreased) from a very small value to one with a small increment. In the ESOCV method, one special characteristic of this method is that the volume fraction, which is defined as the calculated volume divided by the full volume, remains the same value throughout the optimization process. In the RBESO method, the pseudo density of each element is initially with a very small value; the calculated volume is linearly increased until the volume fraction constraint is reached, then the calculated volume remains constant until the numerical computation is converged. Four analysis cases are provided as the benchmark examples in this study. The objective functions include the strain energy minimization and output displacement maximization. The results agree well with previous studies.
The proposed RBESO method is used to design an adaptive compliant gripper (ACG) for handling objects with large size and shape variations. Comparing to traditional grippers with rigid links and joints, as well as the general complaint grippers, the ACG has better flexibility to adapt various objects with different sizes and shapes. The dynamic performance and contact behavior of the ACG is analyzed by the nonlinear finite element analysis. The optimal design of the ACG is prototyped by using rubber material. The experimental test shows the results agree well with the numerical model. The geometric advantage of the ACG is better than the current designs. The outcomes of this study provide numerical methods for design and analysis of compliant mechanisms with large deformation and contact nonlinearity, as well as to develop an innovative ACG for industrial automation.
Keywords: Topology optimization, compliant mechanism, gripper.

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