基于倍矩阵的1P5R串联机械手逆运动学分析

将倍矩阵引入到串联机械手运动学分析的建模中，结合四维旋转矩阵，提出了一种空间1P5R串联机械手逆运动学分析的新方法。基于倍矩阵和四维旋转矩阵对空间1P5R串联机械手进行运动学建模，直接得到14个逆运动学约束方程；将14个方程通过线性消元和Sylvester结式消元，得到只含1个关节变量的一元16次方程。通过数字实例求解和SolidWorks软件仿真验证了所提方法的正确性。所提方法最大的优势在于可直接获得14个逆运动学约束方程，不需要进行矢量运算或者投影等，为空间其他串联机械手的逆运动学建模提供了一种新思路。

The Inverse Kinematic Analysis of Spatial 1P5R Serial Manipulators Based on The Double Matrix

Introducing the double-matrix into the kinematic analysis of serial manipulators, and combined with the four-dimensional rotation matrix, a novel method for the inverse kinematic analysis of spatial 1P5R serial manipulators is proposed. Fourteen kinematic constraint equations for the inverse kinematic analysis are readily obtained by applying the proposed method. A univariate 16th-degree polynomial equation is derived by the linear elimination and Sylvester resultant elimination from the aforementioned fourteen equations. A numerical example and the corresponding 3D configuration based on SolidWorks are provided to verify the correctness. A signficant advantage of the proposed method lies in that 14 inverse kinematic constraint equations can be readily obtained without vector operation and projection operation, and it also provides a new insight for the modeling to the inverse kinematic analysis of other serial manipulators.