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研究生:洪偉恒
研究生(外文):Wei-Heng Hung
論文名稱:並聯式機械臂新保守剛度轉換之研究
論文名稱(外文):New Conservative Stiffness Mapping for Parallel Manipulators
指導教授:黃金沺
指導教授(外文):Chintien Huang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:60
中文關鍵詞:CCT並聯式機械臂剛度轉換
外文關鍵詞:Parallel ManipulatorsCCTStiffness Mapping
相關次數:
  • 被引用被引用:1
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  • 下載下載:116
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摘要
並聯式機械臂為近幾年來熱門的研究課題,主要在於其具有高剛度可以承受較高的負載,適於精確控制的場合。正確計算並聯式機械臂Cartesian空間的剛度為精確控制平台的重要工作,而影響工作平台剛度的主要因素為驅動軸的剛度,如何正確地由驅動軸(關節空間)的剛度求得工作平台(Cartesian空間)的剛度就非常的重要。
著名的剛度轉換公式為Salisbury(1980)所提出,已被使用將近20年,直到Chen和Kao(1998)運用Salisbury的方法於串聯式機械臂剛度控制卻發現能量無法守恆而提出新的保守剛度轉換(CCT,Conservative Congruence Transformation)。
本文以CCT的概念推導並聯式機械臂剛度轉換的一般式,藉由對平面與空間並聯式機械臂的數值模擬,證明所推導的一般式符合保守力場的特性,並說明CCT轉換式中Jacobian矩陣的微分項為機械臂因剛度所造成的幾何改變量,亦即傳統剛度轉換所忽略的。最後,本文提出並聯式機械臂和串聯式機械臂的剛度矩陣具有相同的對稱性質,此性質可作為剛度矩陣正確與否的判斷。
Abstract
Parallel manipulators have been widely used recently, mainly due to their high stiffness structures. Parallel manipulators are suitable for applications requiring high accuracy under heavy loads. The computation of the Cartesian stiffness is essential in the stiffness control of a parallel manipulator. In practice, the compliance of a parallel manipulator is mainly contributed by the actuated joints. Therefore, the stiffness mapping from the joint stiffness to Cartesian stiffness is important.
The widely used formula of stiffness mapping was proposed by Salisbury in 1980. Recently, it was discovered that the work done in joint and Cartesian spaces is not conservative by using Salisbury’s formulation. A conservative congruence transformation (CCT) for serial manipulators has been proposed by Chen and Kao to correct Salisbury’s formulation.
Building upon the concept of CCT for serial manipulators, this thesis derives the formula for the stiffness mapping of parallel manipulators. We show that the proposed formulation obeys the law of conservation of energy by conducting numerical simulation for several planar and spatial parallel manipulators. The new formulation indicates that the change in geometry of a parallel manipulator due to compliance is captured by considering the differentiation of the Jacobian. This thesis also investigates the symmetry properties of parallel and serial manipulators.
目 錄
摘要I
英文摘要II
誌謝III
目錄IV
表目錄VI
圖目錄VII
符號說明IX
第一章緒言1
1.1前言1
1.2文獻回顧2
1.3研究動機與目的2
1.4本文架構3
第二章 並聯式機械臂傳統剛度轉換4
2.1傳統剛度轉換4
2.2Jacobian矩陣6
2.2.1 Conventional Jacobian7
2.2.2 Screw-based Jacobian8
第三章 並聯式機械臂新剛度轉換 18
3.1CCT剛度轉換 18
3.1.1 對關節空間參數微分 18
3.2.2 對Cartesian空間參數微分 19
3.2Jacobian矩陣數值微分 19
3.2.1對關節空間參數微分 20
3.2.2對Cartesian空間參數微分 21
3.3作用力與能量守恆驗證方法 22
第四章 平面與空間並聯式機械臂剛度轉換數值模擬 23
4.1平面並聯式機械臂 23
4.1.1 平面5R並聯式機械臂 23
4.1.2 平面3RPR並聯式機械臂 25
4.1.3 平面3RRR並聯式機械臂 28
4.1.4 平面2RRR1RPR並聯式機械臂 31
4.2空間並聯式機械臂 34
4.2.1空間3-3 SPS並聯式機械臂 34
4.2.2空間6SPS並聯式機械臂 39
第五章 剛度轉換矩陣之討論 45
5.1串並聯式機械臂剛度矩陣對稱性的探討 45
5.2CCT剛度矩陣與Duffy剛度矩陣之比較 49
第六章 結論與未來展望 51
6.1結論 51
6.2未來展望 51
參考文獻 53
附錄A 串聯式機械臂Stanford Arm剛度轉換數值模擬 55
參考文獻[1]Chen, S. F., and Kao. I., 1998, “Simulation of Conservative Properties of Stiffness Matrices in Congruence Transformation,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Canada.[2]Chen, S. F., and Kao. I., 1999, “The Conservative Congruence Transformation of Stiffness Control in Robotic Grasping and Manipulation,” the International Symposium of Robotics Research, Snowbird, USA, pp. 7-14.[3]Dimentberg, F. M., 1965, “The screw calculus and its applications in mechanics,” Technical Report FTD-HT-23-1632-67, US Department of Commerce Translation.[4]Duffy, J., 1996, Statics and Kinematics with Applications to Robotics, Cambridge University Press, Cambridge University Press.[5]Gosselin, C., 1990, “Stiffness Mapping of Parallel Manipulators,” IEEE Trans. Robot. Autom., Vol. 6, pp. 377-382[6]Griffis, M., and Duffy, J., 1993, “Global Stiffness Modeling of a Class of Simple Compliant Couplings,” Mech. Mach. Theory, Vol. 28, No. 2, pp. 207-224[7]Huang, C., Huang, W. H., and Kao, I., 2002, ”New Conservative Stiffness Mapping for the Stewart-Gough Platform,” Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington D. C., May 11-15, 2002.[8]Huang, C. and Kao, I., 2001, “Geometrical Interpretations of the Conservative Congruence Transformation for Serial Manipulators via Screw Theory,” Proceedings of the 10th IFRR International Symposium of Robotics Research, Lorne, Australia, Nov. 9-12, 2001.[9]Kao, I. and Ngo, C., 1999, “Properties of Grasp Stiffness Matrix and Conservative Control Strategy,” the International Journal of Robotics Research, Vol. 18, No. 2, pp. 159-167.[10]Kerr, D. R., 1989, “Analysis, Properties, and Design of a Stewart Platform Transducer,” ASME J. Mech. Transm. Autom. Des., Vol. 111, pp. 25-28.[11]Li, Y., Chen, S. F., and Kao, I., 2002, “Stiffness Control and Transformation for Robotic System with Coordinate and Non-Coordinate Bases,” Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington D. C., May 11-15, 2002.[12]Salisbury, J. K., 1980, “Active Stiffness Control of a Manipulator in Cartesian Coordinates,” Proceeding of the IEEE Conference on Decision and Control, pp. 87-97.[13]Tsai, L. W., 1999, Robot Analysis: the Mechanics of Serial and Parallel Manipulators, John Wiley& Sons, Inc., New York.[14]高子翔,2001,機械臂保守剛性矩陣轉換之模擬,九十年六月,國立成功大學機械工程研究所碩士論文。
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