本研究以幾何非線性拓樸最佳化方法設計具有路徑跟隨(Path following)功能之路徑產生撓性機構，其目標軌跡路徑不論是直線段或不規則簡單封閉曲線(Simple closed curve)路徑皆適用，且不需參考現有機構設計，並於過程中考慮大變形之幾何非線性問題。由於拓樸最佳化中傳統外加彈簧之虛擬模型會影響輸出位移，不外加彈簧之真實模型卻容易使拓樸最佳化無法產生結果，本研究以結合真實模型與虛擬模型之雙模型設計改善此問題，其中真實模型用於取得不受彈簧影響之真實輸出位移並計算目標函數值，而虛擬模型則用來計算元素靈敏度以穩定最佳化疊代過程。本研究以真實輸出位移與目標軌跡點誤差平方和最小化作為目標函數，並以反向機構和步行機構之軌跡作為範例，驗證本研究之路徑產生撓性機構設計流程分別於直線段和封閉曲線目標軌跡之可行性，其中於直線段軌跡之撓性反向機構範例，單目標軌跡點各案例之誤差皆不超過0.3mm，多目標軌跡點各案例之誤差則不超過0.4mm；而以步行軌跡作為目標輸出路徑之範例，使用至多15個目標軌跡點，其中表現最佳之案例各軌跡點總平均誤差為1.14mm，而步行軌跡中較為重要之直線段誤差僅為0.63mm，符合步行軌跡之直線段特徵。

In this study, a new design procedure for synthesizing path generating compliant mechanisms through geometrically nonlinear topology optimization method is proposed. The target trajectories can be either straight line segments or irregular simple closed curves with one or more presicion points. To design compliant mechanisms with path-following function, traditional spring model in topology optimization is not suitable anymore due to inaccurate output displacements affected by artificial springs. However, only utilizing actual model without the springs can cause numerical instability or poor topology results. Therefore, our proposed procedure combines these two models to prevent this problem while the traditional spring model is used to calculate sensitivities along with stabilizing optimization process. Meanwhile, the actual model is used to obtain actual output displacements and to calculate objective function values as well.
Minimizing an error sum of squares between actual output displacements and target precision points is formulated as objective function for design optimization problem of path generating compliant mechanisms. In this study, compliant inverter mechanisms with straight-line target trajectory are taken as benchmark problems for evaluating effectiveness of propsed method. The results show that error of each case with a single presicion point is less than 0.3mm, and error of each case with multiple presicion points does not exceed 0.4mm. To show the possible practical application of this method, path generating compliant mechanisms with irregular simple closed curve paths using foot locus as a target trajectory are successfully designed within 15 presicion points at most. Results for walking path compliant mechanisms are obtained, and total average error in the best result is 1.14mm while error in straight line region of the walking trajectory is 0.63mm.

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