Formulation of a New Index for the Evaluation of Mechanism Workspace

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蔡逸文(Christopher Reinaldo) 查詢紙本館藏

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機械工程學系

論文名稱

(Formulation of a New Index for the Evaluation of Mechanism Workspace)

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摘要(中)

機構的工作空間被定義為其末端受動器所可以到達的區域。當一種新型機器人機構問世時，對其可達到的工作空間通常也會包含在其理論分析中。一些研究提出了專門用於評估機構性能的指標，如條件數或傳輸指數，它們都重點專注於工作空間內的性能。工作空間本身對於具有超過3自由度（DoF）的機構來說很難去表示。而本研究主要集中探討在工作空間本身及其演變方式。
因此，一種新的工作空間演變指數（WEI）由此而被規範出來。該指數可以表示線性工作空間在角度工作空間中的演變，反之亦然。WEI由兩種方法決定：基於平均值的指數及基於範數的指數。基於平均值的指數表示透過從某個坐標移動的方式，來判斷機構將平均獲得或是失去工作空間。基於範數的指數將顯示在某個坐標處，其工作空間的變化。在此文章中，將對於三自由度（DoF）平面機構，3-RRR和3-RPR進行更進一步地探討，並使用WEI以及WEI和條件數的組合方式來進行比較。而後會進行更深入的研究，對三自由度空間機構進行了深入探討：3-RPS 和 3-PSP 機構，以及六自由度空間機構：3-PRP-3-RPS 和 3-RPS-3-PRP。

摘要(英)

The workspace of a mechanism is defined as the region in which its end effector can reach. When a novel robotic mechanism is reported, the study on the workspace it can reach is included in its theoretical analysis. Several studies proposed indexes to evaluate the performance of a mechanism with indexes such as the condition number or transmission index, both of them focused on the performance of the mechanism within its workspace. The workspace itself is difficult to represent for mechanism with more than 3 DoF. This present study mainly focuses on the workspace itself on how it evolves.
A new Workspace Evolution Index (WEI) is formulated. This index can indicate either how the linear workspace evolves in the angular workspace or vice versa. The WEI is determined by two methods: the mean-based index and the norm-based index. The mean-based index indicates that by moving from a certain coordinate a mechanism will indicate average gain or lose workspace. The norm-based index will show the variation of the workspace at a certain coordinate. In this study the WEI will be used to evaluate parallel mechanisms: three degrees of freedom (DoF) planar mechanisms, 3-RRR and 3-RPR which are investigated and its results are compared using the WEI, and combinations of WEI and condition number, three DoF spatial mechanisms: 3-RPS and 3-PSP mechanism, and the six-DoF spatial mechanisms: 3-PRP-3-RPS and 3-RPS-3-PRP.

關鍵字(中)

★ 並聯機構；平面機構；三腳架機構；工作空間

關鍵字(英)

★ Parallel mechanism；planar mechanism；spatial mechanism；Workspace

論文目次

摘要 i
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 Mechanism Workspace Analysis 1
1-2 Workspace Problems and Objective of the Study 3
2 Workspace Evolution Index 8
2-1 Index Formulation 8
2-1-1 Workspace Evolution Index 8
2-1-2 Workspace Conditions 10
2-2 Index Analysis and Illustration 13
2-2-1 Planar Mechanisms Comparison 13
2-2-2 Application and Result 16
3 Application to Tripod Spatial Mechanisms 27
3-1 3-DoF Spatial Mechanism Comparison 27
3-2 Analysis and Results 30
4 Application to 6-DoF Hybrid Mechanisms 35
4-1 Kinematic analysis of the Hybrid Six-DoF Mechanisms 35
4-2 Workspace Analysis of Hybrid Mechanisms 37
5 Conclusion 40
Reference 42

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指導教授

伊泰龍(Terence Essomba)

審核日期

2024-1-29

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