本研究的主要目的為發展一套設計方法，配合貝茲曲線來設計撓性機構的形狀。相較於以微小的連續元素或直桿元素的拓樸設計方法，利用曲線元素來建構撓性機構能大量改善撓性機構形狀的平滑度，並進一步減少應力集中的現象。由於有容易描述與數字化的特性，在本論文中，我們採用貝茲曲線來做為建構撓性機構的元素。本文中撓性機構變形是利用漸進的線性化方法來分析。由於將分析問題線性化，因此此分析方法能提供穩定、快速且準確的數值計算。在本論文中所提出的設計方法是使用二個步驟，分別完成撓性機構拓樸與形狀的設計。在第一步驟使用少量的直桿來建構撓性機構，在第二步驟改變桿件形狀來達成設計目標。此設計方法的關鍵是利用最佳化方法得到較好的桿件形狀來改善利用大量桿件的設計方式。因此設計流程就能簡單的建構並快速的得到結果。在將設計問題分解成二個步驟並以少量桿件設計機構的情況下，本設計方法能簡單的建構設計流程並快速的得到結果。也利用三個數值上的例子來比較確認其可行性。最後也以設計並製造一雙穩態撓性機構來證明本設計方法能應用在實際設計上。期望本設計方法未來能有效幫助設計者來設計實際的撓性機構。

A method using Bezier curves to design the shape of compliant mechanisms is presented in this thesis. Compared to continuum-element or frame-element based topology design methods, the use of curved beam elements can improve the shape smoothness of compliant mechanisms. Furthermore, the stress concentration can also be reduced. We apply Bezier curves to construct the shape of compliant mechanisms due to their simple expression and ease of manipulating shapes. The analyses of compliant mechanisms are based on an incremental linearization approach. This approach provides stable, rapid, yet accurate numerical computation since the deformation problem is linearized. The presented design method applies two steps to design the topology and shape of compliant mechanisms, respectively. The first step uses a few straight beams to construct the topology of a compliant mechanism and the second step accomplishes the object by determining the optimal shapes of beams. Key to the success of this method is that it improves the optimal results by finding better beam shapes rather than using more beam elements. Thus the design process can be simply constructed and optimal results rapidly obtained. Three numerical examples are illustrated and compared for validation. Finally, we design and manufacture a bi-stable compliant mechanism to show that the design method can be applied to real design problems. We expect the two-step design method based on Bezier curves can efficiently assist the design of practical compliant mechanisms.

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