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研究生:黃尉愷
研究生(外文):Wei-Kai Huang
論文名稱(外文):Workspace Characterization of a 3-RRR Spherical Parallel Mechanism
指導教授:伊泰龍
指導教授(外文):Térence Essomba
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文出版年:2020
畢業學年度:108
語文別:英文
論文頁數:41
中文關鍵詞:球面平行機構遠端運動中心工作範圍
外文關鍵詞:Spherical Parallel MechanismRemote Center of MotionWorkspace
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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 i
English Abstract ii
Acknowledgments iii
Table of Content iv
List of Figures v
List of Tables vi
Explanation of Symbols vii
1 Introduction 1
1-1 Spherical Parallel Mechanism 1
1-2 Workspace Analysis, Representation and Optimization 3
1-3 Literature Review Analysis and Research objectives 5
2 Kinematics of the 3-RRR Spherical Parallel Mechanism 8
2-1 Definition of the Mechanism Architecture and Kinematic 8
2-2 Kinematic Model of the Mechanism 10
3 Workspace Modelling of the Spherical Mechanism 12
3-1 Visualization of the 3-RRR SPM Workspace 12
3-2 Geometrical Characterization of the SPM Workspace 13
3-3 Identification Method of the SPM Workspace Parameters 15
3-3-1 Generation of the SPM Workspace 16
3-3-2 Identification of the Workspace Vertices 16
3-3-3 Identification of the Workspace Circumcircle 17
3-3-4 Identification of the Workspace Edges 17
4 Numerical Results of the Workspace Parameters 19
4-1 Preliminary Results and Assumptions 19
4-2 Identification of the Workspace Vertices 20
4-3 Identification of the Workspace Edges 23
4-4 Identification of the Workspace Circumcircle 27
5 Conclusion 29
Reference 30
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