本研究目的是尋找3PPSR六自由度並聯式機械手臂之正向奇異位置。此機構的運動可以分解為以下兩部份1.整個機構的剛體位移，機構形狀並未改變。2.旋轉接頭旋轉，造成機構形狀改變。本文分別探討這兩種運動形態下的正向奇異位置。針對機構形狀會改變的運動，我們以機構運動倒置的方法，推導出旋轉接頭旋轉角度與球窩接頭間距離的關係式，再將這些距離對時間微分後可得到3×3 Jacobian矩陣，若矩陣行列式值為零即會發生正向奇異位置。針對整個機構剛體位移的運動，我們發現正向奇異位置發生在三個球窩接頭位在同一直線上的情況。本研究使用上述條件找出3PPSR並聯式機械手臂正向奇異位置在工作空間的分佈，並發現此機構在工作空間內任何區域皆有正向奇異位置。 The purpose of this study is to locate direct singular positions of the 3PPSR 6dof parallel manipulator. The motion of this manipulator can be categorized into the following two types: 1. rigid body displacement without changing its configuration, and 2. rotation of at least one revolute joint-causing a change in configuration. Direct kinematic singularities for these two types of motion are discussed. For the first type of motion, we found that direct kinematic singularity occurs when all three spherical joints lie along a straight line. As for the second type of motion, namely motion with a configuration change, we may obtain the 3×3 Jacobian matrix by kinematic inversion. Direct singular positions for the second type of motion may be determined by solving a quartic polynomial equation. The technique discussed above helps us to determine the distribution of direct singular positions in the manipulators workspace.
