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 當為了進行特定的運動而設計機構時，需要相當了解其運動的範圍。工作範圍是指一個機構其終端可到達的區域。這方面在文獻中受到很大的重視。對工作範圍的分析可依靠對分析法或數值方法。一個工作範圍沒辦法以幾何圖形描述的複雜機構會使用分析法來分析。這方法用於驗證已知工作範圍上每個點的機構運動模型。優化演算法若使用這方法會耗費時間。一個複雜機構3-RRR球面平行機構的工作範圍是以數值分析法來研究他的幾何形狀。對此工作範圍的視覺分析，這是第一次使用不規則勒洛三角形來趨近。其圖像的幾何參數允許的尺寸標記的是可定義的。許多的演算法被寫進程式以確認大量使用不同參數設定的機構相對應的參數值。藉由收集這些資料，可發現一連串的機構設計參數與其工作範圍間的關係性。之後則分析這些模型的準確度。
 As mechanisms are designed to generate a certain motion, it is important to have a good understanding of their range of motion. The workspace is the zone that a mechanism can reach with its end effector. This aspect has been subject to a lot of attention in the literature. Its analysis can rely on analytical or numerical methods. Complex mechanisms which workspace cannot be accurately represented by a geometrical figure will be analyzed using analytical methods. It consists in verifying the mechanism kinematic model for every points of a given workspace. Such a method can be time consuming if used in an optimization algorithm.The workspace of a complex mechanism, the 3-RRR Spherical Parallel Mechanism is analyzed through numerical method to study its geometry. Based on the visual analysis of this workspace, it is first approximated using an Irregular Spherical Reuleux Triangle. The geometrical parameters of this figure allowing its dimensioning are defined. Several algorithms are programmed in order to identify the value of these corresponding parameters for several mechanisms of different design parameters. Using all collected data, a series of relationship are found between the mechanism design parameters and the size of its generated workspace. The accuracy of these models is then evaluated.
 Chinese Abstract iEnglish Abstract iiAcknowledgments iiiTable of Content ivList of Figures vList of Tables viExplanation of Symbols vii1 Introduction 11-1 Spherical Parallel Mechanism 11-2 Workspace Analysis, Representation and Optimization 31-3 Literature Review Analysis and Research objectives 52 Kinematics of the 3-RRR Spherical Parallel Mechanism 82-1 Definition of the Mechanism Architecture and Kinematic 82-2 Kinematic Model of the Mechanism 103 Workspace Modelling of the Spherical Mechanism 123-1 Visualization of the 3-RRR SPM Workspace 123-2 Geometrical Characterization of the SPM Workspace 133-3 Identification Method of the SPM Workspace Parameters 153-3-1 Generation of the SPM Workspace 163-3-2 Identification of the Workspace Vertices 163-3-3 Identification of the Workspace Circumcircle 173-3-4 Identification of the Workspace Edges 174 Numerical Results of the Workspace Parameters 194-1 Preliminary Results and Assumptions 194-2 Identification of the Workspace Vertices 204-3 Identification of the Workspace Edges 234-4 Identification of the Workspace Circumcircle 275 Conclusion 29Reference 30
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