本研究針對三自由度並聯式機械手臂CaPaMan2及CaPaMan3，尋找其正向位置分析的解析解。解題過程首先是將原機構簡化為等效3RS機構，在此等效機構的座標系之內，利用活動平台上之球窩接頭間的距離為已知長度，可推導出三個多項式方程式，接著利用席維斯透析消去法(Sylvester dialytic elimination method)求得解答。在求得解答後，本研究亦利用圖形法進行逆向位置分析，以驗證正向分析之解答。 In this study analytical results for displacements of 3dof parallel manipulators CaPaMan2 and CaPaMan3 are obtained. The manipulators are firstly simplified into a 3RSmanipulator. Then in the simplified manipulator’s coordinate system three algebraic equations are obtained which constrain the distance between any two spherical joints on the moving platform to be a known value. Analytical solutions are obtained by using the Sylvester dialytic elimination method. Graphical inverse position analysis are also performed to verify the results.