3-CRU平移型並聯式機械手臂之正向奇異位置分析

Direct kinematics singularity analysis of a 3-CRU translational parallel manipulator

陳敏祥(Min‐Hsiang Chen)

指導教授 ： 劉昭華

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2009年)

https://doi.org/10.6846/TKU.2009.01048

摘要

本文對新型式的3-CRU三自由度純平移並聯式機械手臂進行正向奇異位置分析。由速度分析的Jacobian矩陣Jx，將其行列式值表示成活動平台中心點P位置的函數，尋找奇異位置的方法是先假設平台高度 ，再假設工作空間內P點的Y座標，使Jx行列式成為P點X座標的六次方程式，求解方程式並保留在工作空間內之實根。將求出的X、Y及Z座標代回Jx矩陣行列式進行驗證，這方法可求出在工作空間內所有的正向奇異位置。本文繪出奇異位置在工作空間內的分布及數個奇異構形。

關鍵字

3-CRU ； 正向奇異位置 ； 平移並聯式機械手臂

並列摘要

In this thesis we perform direct singularity analysis for the 3-CRU parallel manipulator, which is a three degree-of-freedom manipulator for pure translation. In order to locate direct singular positions, we begin by expressing the determinant of the Jacobian matrix Jx in terms of position of the center P of the moving platform. The Z and the Y coordinates of P may be chosen from the workspace, then the determinant of Jx is now a six order polynomial of X, the x coordinate of P. The direct singular positions corresponding to (Y, Z) are obtained by solving the polynomial equation, and retaining all real roots in the workspace. Direct singular positions so obtained are substituted into the Jacobian matrix Jx to verify results. All direct singular positions may be located by the method described above. In this thesis we show distribution of direct singular positions in the workspace and also several singular configurations.

並列關鍵字

3-CRU ； direct kinematics singular position ； translational parallel manipulator

參考文獻

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