空间五杆RRCCR机构的位移分析

Displacement analysis of the spatial five-link RRCCR mechanism

为了对空间五杆RRCCR机构的位移分析进行研究,采用对偶四元数进行建模,根据矢量间的几何关系推导出只含有4个对偶角的封闭方程。展开封闭方程,寻找关系式,分解对偶数的初级部和对偶部,通过符号计算,消去两个对偶角,导出含有输入角和输出角的一元八次输入输出方程,最后求出其余变量。通过数字实例进行验证,表明了空间五杆RRCCR机构位移分析的解析解个数是8个。

To study the displacement analysis of the spatial five-link RRCCR mechanism,adopt dual quatemion algorithm to set up mathematic model.According to the geometric relation of vectors,we derive the close-form equation contained 4 dual-angles.Expand the close-form equation,find relationship,decompose the primary part and dual part,reduced 2 dual-angles to derive an 8th degree input-output polynomial equation with a single unknown by symbolic computation.At last,other middle variables are solved.Numerical example confirms that the numbers of analytical solutions for five-link RRCCR mechanism are 8.