本研究尋找出Tricept並聯式機械手臂的正向奇異位置。首先推導出較為簡單的3×3 Jacobian矩陣，並且利用此矩陣尋找此機構的正向奇異位置。針對任何一個活動平台方向，都必定會有至少一個活動平台伸長量，造成機構的正向奇異位置，而這伸長量可由3次多項式方程式解出。本文找出在活動平台工作空間之內，有2個區域的正向奇異位置會出現在無法到達的位置，因此當活動平台在此2個區域內時不必考慮正向奇異位置。

In this research the direct singular positions of the parallel manipulator Tricept are determined. An alternative 3×3 Jacobian matrix, simpler than the existing one, is obtained in this study. For a given moving platform’s orientation, the determinant of the Jacobian matrix may be expressed as a cubic polynomial in moving platform’s extension. Direct singular positions may thus be obtained by solving cubic polynomial equations. For an arbitrarily chosen moving platform’s orientation, there exists at least one moving platform’s extension that causes direct kinematic singularity. It is found that in two regions within the moving platform’s workspace direct kinematic singularities can only occur at positions impossible to reach.

目  錄
中文摘要	I
英文摘要	II
目錄	III
圖目錄	IV
第一章  緒論	1
1.1 文獻回顧與研究動機	1
第二章  機構之特性與運動限制	4
2.1 平台之結構	4
2.2 機構之運動限制	   4
第三章  機構之Jacobian矩陣與工作空間	   5
3.1 Jacobian矩陣之推導	5
3.2 機構之工作空間	    9
第四章  正向奇異位置之推導	  10
4.1 正向奇異位置時的伸長量r	  10
4.2 正向奇異位置	12
第五章  結果與討論 	13
第六章  結論	16
參考文獻    	17
附錄A  Jacobian矩陣	19

圖 目 錄
Figure 1  An illustrative diagram of the hybrid kinematic machine－Tricept	21
Figure 2  An illustrative diagram of Tricept	22
Figure 3  The illustrative diagrams of base and moving platform	23
Figure 4  The revolving angle of U joint	24
Figure 5  The workspace of moving platform	25
Figure 6  Direct singular position for the case  26
Figure 7  Direct singular position for the case  27
Figure 8  Direct singular position for the case  28
Figure 9  Direct singular positions distribution (b=1.5)；roots r1, r2, and r3 [see eqs.(12a)~(12c)] are denoted by x, +, and o respectively	29
Figure 10  Direct singular positions distribution (top view)	30
Figure 11  Direct singular position for the case  31
Figure 12  Direct singular position for the case  32
Figure 13  Direct singular position for the case  33
Figure 14  Direct singular position for the case  34
Figure 15  Direct singular position for the case  35
Figure 16  Direct singular positions distribution (top view)  36
Figure 17  D-H coordinate frames for the passive leg of the Tricept manipulator  37

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