本文針對兩種3-PUU並聯式平移機械手臂找尋其工作空間內之所有正向奇異位置。 首先從事兩個機構之逆向位置分析，找出各連桿之滑塊在基座上的所有可能位置，且表示成活動平台位置之函數。接著針對所指定之活動平台高度pz找出在這高度之活動平台工作空間，並假設平台中心px位置，將這兩個數值代入Jacobian矩陣Jx之行列式中，此時行列式成為平台中心py的多項式方程式，解出py數值，消去py的虛根且只保留(px,py)在工作空間內的數值。如此不斷修正px數值，即可解出工作空間內之所有正向奇異位置；接著利用所求得的Jacobian矩陣找出行列式為零的特徵向量，此特徵向量即為活動平台在奇異位置時瞬間的速度方向。本文顯示出數個在特定高度時奇異位置的分布及奇異構形。 In this thesis, we deal with two types of 3-PUU translational parallel manipulators, locating their direct singular positions in the workspace. The procedure begins with inverse position analysis of the two manipulators. For each limb of the manipulators, slider positions on the base are determined and expressed in terms of positions (px, py, pz) of a point P on the moving platform. A value of pz is then specified, the workspace for this value of pz can be determined. As px is further specified, the determinant of the Jacobian matrix Jx is expressed as a polynomial function of py, from which the values of py that makes the Jx singular can be obtained. The we retain all the real values of py such that (px, py) lies within the workspace for the specified value of pz. Upon continuously assuming px values, all the direct singular positions (px, py) for the particular value of pz can be determined. At a particular direct singular position, the direction along which the moving platform may move is expressed by the eigenvector of the Jacobian matrix Jx corresponding to the eigenvalue zero. In this thesis we show the distribution of direct singular position for several values of pz, as well as a certain singular configurations.
