一平动两转动3-UPU并联机构奇异性分析
Singularity Analysis of a 3-UPU Parallel Manipulator with One Translation and Two Rotations

应用线几何工具和旋量理论分析了一平动两转动3-UPU并联机构的奇异形位。根据动平台的静力学平衡条件，推导出机构的6×6 Jacobian矩阵，该Jacobian矩阵也可看作6个线矢量的集合，基于这些线矢量的线性相关性，可识别出机构的奇异形位。引入线性丛逼近算法（LCAA）定义和分析了机构的结构和约束奇异形位，这两种奇异形位均和机构得到多余的自由度相关，文中统称为并联奇异；LCAA算法可得到用旋量坐标表示的最近线性丛的轴线和节距，当并联机构处于或接近奇异形位运动时，该线性丛的轴线和节距提供了机构自运动的额外信息。给出了3-UPU并联机构奇异性分析的实例。
This paper deals with singularity analysis of 3-UPU parallel manipulator (PM) with one translation and two rotations utilizing the line geometry tool and screw theory. Firstly, the static equilibrium condition of the moving platform is derived to obtain the full 6×6 matrix, which is set of governing lines of the manipulator. Based on linear dependency of these lines, the singular configurations of the manipulator can be identified. Secondly, architecture and constraint singularities associated with gain of DOFs (parallel singularity) are defined and analyzed using linear complex approximation algorithm (LCAA), which is employed to obtain the closest linear complex, presented by its screw coordinates, to the set of governing lines. The linear complex axis and pitch provide additional information of the manipulator's self-motion when in or closed to a singular configuration. Finally, various singularities of an example 3-UPU manipulator are presented and analyzed using the proposed methods