精密定位在精密機械領域中扮演重要角色，其定位技術的優劣會直接影響到產品製造的品質與檢測的精密程度，其中位移定位平台用於精密儀器中試片位置的微調或是主動減振，角度定位平台常用於在雷射加工系統中的光學反射鏡，透過定位平台改變反射鏡角度決定雷射光束的加工路徑，然而純粹旋轉之定位平台無法補償雷射加工過程中，聚焦透鏡溫昇而改變焦距的問題，因此，需要加入一個平移軸向的定位來補償雷射焦距。而過去研究多以撓性機構設計定位平台，為了因應其非等向剛性的需求形狀往往較為複雜，一旦性能需求更改常就要重新設計撓性結構，為了改善撓性機構的問題，過去有學者引入橡膠軸承進行定位平台的設計，而橡膠軸承的非等向剛性設計來自於橡膠的幾何形狀比例，以簡單的形狀即可設計出與撓性結構相當的非等向剛性，加之橡膠的剪切剛性會隨著壓縮預力而改變，用以設計精密定位平台能夠藉由調整壓縮預力的方式來改變平台的動態特性，但是目前尚未能完整描述橡膠軸承在扭矩與彎矩負荷下的剛性及其剪切剛性隨壓縮預力的變化特性。鑒於此問題，本論文透過模擬與實驗的方式建立一套橡膠軸承設計精密機械之參考，成功預測橡膠受到彎矩與扭矩時的剛性表現，並以此為基礎，設計一個以音圈馬達驅動的新型三軸橡膠軸承定位平台，具備一個平移與兩個旋轉自由度，且以最少致動器驅動定位平台，並設計PID控制器與抑制耦合補償器，在Y軸、θX軸與θZ軸分別達到頻寬80Hz、62Hz與54Hz，定位精度84nm、5.4μrad與1.9μrad。本研究建立一套設計精密機械之橡膠軸承剛性參考，透過準確的剛性分析能夠在機械結構設計階段較精準地預測系統的動態特性，本研究也以此為基礎設計實現一個三軸橡膠軸承精密定位平台，並設計抑制耦合補償器來減少多軸定位平台無可避免的耦合效應的影響。

Positioning stage plays an important role in precision metrology and manufacturing systems. One key application is the fast steering mirrors, which mainly comprised of a rotational positioning stage and they have been widely used in laser manufacturing related applications. In this thesis, a novel 3-DoF translational and rotational positioning stage is designed and realized. It consists of two rotational DoF for guiding the laser path in manufacturing and one translational DoF for compensating the focusing error caused by lens curvature variation due to temperature changes. This stage utilizes elastomeric bearing for providing anisotropic stiffness and has the advantages of size miniaturization and structurally simple design. The stage is driven by three voice coil motors and the resulted displacements are measured by three capacitive displacement sensors. In order to establish the system dynamics, the rubber stiffness is also characterized in different loading manners by both simulation and experiment using a biaxial material testing system and a high strain compression testing system. The characterized hyperelastic behavior is then modelled via Arruda-Boyce model, for subsequent finite element simulation. Based on these stiffness characterization and additional vibrational analyses, a 3-DOF stage dynamics model is developed and is validated using the FE simulations. The models of three positioning axes and coupling effect are established by kinematics and system identification using both including step and swept sine responses. The PID controllers are designed based on loop transmission shaping method and simulated by MATLAB/Simulink. Furthermore, in order to suppress the coupling effect, different compensators are also added in control system. The controllers are implemented in NI cRIO with LabVIEW FPGA program for positioning control experiments. By the step and sinusoidal tracking control experiment, the achieved positioning precision are 84nm, 5.4μrad and 1.9μrad and bandwidths are 80Hz, 62Hz and 54Hz in Y-, θX- and θZ-axis, respectively. The strokes can be up to ±159μm and ±5mrad in translational and rotational axis, respectively. In summary, this research successfully develops a tri-axial positioning stage and realize PID controller with decoupled compensators to eliminate the coupled effect. Compared to two DoF fast steering mirror, the translational DoF in this stage can compensate the focusing error in laser manufacturing. On the other hand, this stage is designed based on elatomeric bearing characterization, and the results of material testing and finite element analysis can be taken as reference for mechanical desing in the future.

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