A general acceleration model and a Hessian matrix of the kinematic limbs in the parallel manipulators are established using new skew-symmetric matrixes. First, several extended formulas of the skew-symmetric matrixes are derived and proved. Second, the differentiations of the sub-Jacobian matrixes of the general kinematic limbs are transformed into the multiplication of the general velocity transposition of the parallel manipulator by the sub-Hessian matrixes of the kinematic limbs based on extended formulas of the skew-symmetric matrixes. Third, the formulas for solving the Hessian matrixes and the general accelerations of several typical linear kinematic limbs of the parallel manipulator are derived. Finally, the Hessian matrixes and the accelerations of the kinematic limbs of a 3-DOF RPS + UPU + SPR type parallel manipulator are derived and verified using its simulation mechanism.

使用新的斜对称矩阵，建立了并联机械手的一般加速度模型和运动肢体的Hessian矩阵。首先，推导并证明了偏对称矩阵的几个扩展公式。其次，基于倾斜对称矩阵的扩展公式，将一般运动肢体的亚雅各比亚矩阵的微分转换为平行操纵器的一般速度换位乘以运动肢体的黑塞西亚矩阵。第三，推导了求解Hessian矩阵的公式以及并联机械手的几种典型线性运动肢体的一般加速度。最后，