本研究提出一個等力撓性機構拓樸最佳化方法來設計等力輸出撓性機構，等力輸出撓性機構為可在不同的輸入位移條件下，於輸出端維持相同的力量輸出，此特性使得此類型的機構可無需額外配合感測器進行輸出力量的控制。在等力撓性機構拓樸最佳化流程中，為了解決網格相依以及棋盤狀網格之問題，本研究導入密度濾化演算法以及參數化投射方法，且為了滿足等力輸出撓性機構以及夾爪容易產生的幾何非線性問題，採用非線性的有限元素法來進行結構的分析，並以移動漸進線方法來做為設計變數更新的方法。為了加強等力撓性機構設計的穩定性以及拓樸結果的連接性，本研究將原先虛擬輸出位移誤差最小化問題改為本研究提出的考慮真實輸出位移的複合目標函數誤差平方和的最小化問題，並提出適用於密度法之元圖法。藉由本研究提出的等力撓性機構拓樸最佳化流程，本研究成功設計出兩種等力輸出撓性機構以及一種等力輸出撓性夾爪，並以等力輸出撓性夾爪進行試作驗證。本研究並對拓樸過程中產生的低實體密度元素、額外添加的超彈性體元素以及拓樸邊緣的平滑化處理皆有進行詳細的模擬分析與討論，最後使用TPE軟性材料進行3D列印製作，實際的等力輸出撓性夾爪在輸出力量變化穩定之後，於輸入位移為13 mm至33 mm的區間中具有等力效果，其等力值落在41.15 N，而平均絕對誤差則為1.88%。本研究搭配等力輸出撓性夾爪設計並製作出三指等力撓性夾爪模組，將其安裝於四軸機械手臂上進行夾取試驗，基於撓性機構被動式保護被夾取物的特點以及等力機構的等力輸出效果，三指夾爪模組展現出穩定的夾持能力。

This study presents an optimal design procedure to design compliant constant-force mechanisms based on topology optimization. A constant-force mechanism can generate a nearly constant output force over a range of input displacements without the need of additional sensors for output force control. This study uses the density filter scheme to overcome the mesh dependence and checkerboard problems, and makes use of parameterized projection function to reduce the existence of the gray elements. Because of the nonlinear behavior of the compliant constant-force mechanisms, geometrically nonlinear analysis is considered in finite element analysis. The method of moving asymptotes is used to update design variables. To enhance the stability of the optimal design procedure and the connectivity of topological results, a composite objective function and a meta-graph strategy suitable for the SIMP method are proposed. The numerical optimization problem of the composite objective function considering the actual output displacement is to minimize the sum of squares of errors. Through the proposed optimal design procedure, two types of compliant constant-force mechanisms and one type of the compliant constant-force gripper have been presented. The effect of low physical density elements, additional hyperelastic elements, and the smoothing of topological edges are discussed in this study. The prototype of the compliant constant-force gripper is manufactured by 3D printing using thermoplastic elastomer material. The prototype has a constant output force in the input displacement region from 13 to 33 mm, the value of the constant output force is 41.15 N, and the average absolute error is 1.88%. A three-finger constant-force gripper module is developed and installed on a four-axis robotic arm for grasping application. Test results show the presented design is with a stable gripping ability.

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