基于倍矩阵的1P5R串联机械手逆运动学分析

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

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。

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 1 P5 R serial manipulators is proposed. Fourteen kinematic constraint equations for the inverse kinematic analysis are readily obtained by applying the proposed method. A univariate 16 th-degree polynomial equation is derived by the linear elimination and Sylvester resultant elimination from the aforementioned fourteen equations. A numerical example and the corresponding 3 D 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.