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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。
In order to study the displacement analysis of a five-bar RRCCR mechanism in space, the dual quaternion is used to model the closed equations with only four dipoles according to the geometric relationships between the vectors. Expand the closed equation, look for the relation, and decompose the even and odd primary and dual parts. By calculating the symbol, eliminate the two dual angles and derive the unary eight-input-output equation with input angle and output angle, and finally find the remaining variables. Verification by digital examples shows that the number of analytic solutions for the displacement analysis of the five-space RRCCR mechanism is eight.