摘要
为了对空间五杆RCRCR机构的位移分析进行研究,采用对偶数矩阵进行数学建模,建立封闭方程.首先引入3×3酉交矩阵和欧拉公式,使部分对偶矩阵对角化;然后寻找关系式,分解对偶数的初级部和对偶部,通过符号计算,导出一元四次输入输出方程;最后求出其余变量.数字实例验证结果表明,空间五杆RCRCR机构的位移分析的解析解的个数是4,方法是正确的.
To study the displacement mechanism of the spatial five-link RCRCR,dual-number matrices are adopt to set up mathematic model and close-form equation.Firstly,3 × 3 unitary matrix and Euler formula are introduced to make some dual-number matrices diagonalizable,then,to find relationships,the primary part and dual part are decomposed to derive a 4th 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 RCRCR mechanism are 4.
出处
《北京邮电大学学报》
EI
CAS
CSCD
北大核心
2013年第3期108-112,共5页
Journal of Beijing University of Posts and Telecommunications
基金
山东省自然科学基金项目(ZR2010EL022)
关键词
RCRCR机构
位移分析
对偶矩阵
酉交矩阵
欧拉公式
RCRCR mechanism
displacement analysis
dual-number matrices
unitary matrix
Euler formula
