彈性桿件與接頭間隙對於並聯式機器手臂之撓性運動分析

Effect of Link Flexibility and Joint Clearance on Elastic Motion of Parallel Robot

顏銘賢(Ming-Hsien Yen)

指導教授 ： 楊智媖

國立中正大學/工學院/機械工程學系/碩士(2014年)

摘要

本研究目的為針對Delta機械手臂之桿件撓曲變形及接頭間隙特性，進行系統靜態撓曲變形與振動模態分析。於靜態負載撓曲變形分析部分，利用結構矩陣分析方法，將結構桿件簡化為雙節點樑元素(2-node beam element)，進而建立各桿件之剛性矩陣，由於結構中之接頭存在組裝間隙，於結構承受負載時，接頭之連接點會產生偏移量，且結構運動受限於接頭之自由度，因此可藉由建立考慮接頭間隙偏移量之結構運動限制條件，將結構中各桿件之剛性矩陣進行整合，以求得整機之負載剛性矩陣，由於系統剛性將隨著機械手臂姿態改變，因此將理論推導撰寫為MATLAB程式，進行模擬機械手臂於不同姿態下之負載變形特性，並經由有限元素軟體(ABAQUS)驗證理論推導之正確性。
於系統振動模態分析部分，探討機械手臂於靜力平衡姿態下之系統自由振動特性，藉由將結構桿件簡化為多段雙節點樑元素，推導系統之動能與位能，並引用Lagrange方程式建立系統之動態方程式，由於系統節點變形量之自由度並不是完全獨立的，因此利用結構運動限制條件與靜力平衡分析，推導具拘束限制之系統動態方程式，同時進行此系統之振動模態分析，並將理論推導撰寫為模態分析程式，討論機械手臂於不同姿態下，系統剛性與自然頻率之關係，最後藉由對照有限元素軟體與模擬程式所計算之自然頻率與振動模態結果，驗證本研究提出理論分析方法之準確性。

關鍵字

負載剛性 ； 接頭間隙 ； 彈性桿件 ； 並聯式機械手臂 ； 振動分析

並列摘要

The study is devoted in the effects of the link flexibility and joint clearance on the loading deflection and vibration of a parallel robot. For the loading deflection, links are considered as two-node beam elements and the structure matrix is adopted to establish the stiffness matrix of links. The nodal deflection would be derived based on the stiffness matrix. However, some of the nodal deflections are dependent accordance with the constrain by the joints and the rigid body. Therefore, the effects of the joint clearance are formulated using an explicit mathematical model which is the function of the applied force and clearance amount, and the constrain equations of nodal deflections on the rigid link are formulated based on the geometry. The equivalent stiffness and the loading deflection of the moved platform are derived based on the links stiffness and constrain equations of joints and links. In addition, we can find that the equivalent stiffness of the moved platform is not constant in the workspace of the parallel robot, and it is dependent on the posture of the robot. Finally, we program the loading deflection analysis by MATLAB, and the correction is confirmed by comparing the analysis results with those simulated via ABAQUS.
For the vibration analysis, we derive the potential and dynamic energy based on the analysis model component of beam elements. The Lagrange function is applied to find the mass and stiffness matrix of the parallel robot. However, the nodal vibration are constrained by the structure of the parallel robot. We apply the transform matrix and constrain equations to decouple the independent and dependent terms, and we establish the dynamic equation of the delta robot. Therefore, the nature frequencies and vibration modes are defined by solved the eigenvalues and eigenvectors. We also confirmed the correction by comparing the result with those analysis applying ABAQUS. In addition, the nature frequencies are dependent with the position in the workspace, and the difference is also shown in results. Finally, the analysis program is programmed with Graphical User Interface (GUI) to provide convenience to users.

並列關鍵字

Stiffness ； Link flexibility ； Parallel manipulator ； Vibration analysis

參考文獻

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