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.
