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将倍四元数的复指数形式应用于串联机构位置逆解分析中,提出了空间6R(R代表转动副)串联机构位置逆解新算法.基于倍四元数建立了空间6R串联机构位置逆解的数学模型;然后,使用线性消元和Dixon结式消元法,得到了6×6的结式;由于采用未知转角的复指数形式,不需要提取任何公因式,可直接获得该机构位置逆解的一元16次输入输出方程和全部16组封闭解.最后通过数字实例证明了该方法无增根无漏根.算例表明算法简洁,易于程序实现,为串联机构位置逆解分析提供了新的理论基础.
In this paper, a complex quaternion exponential form is applied to the inversed position analysis of tandem mechanism. A new algorithm is proposed for the inverse position reversal of tandem mechanism with space 6R (R stands for rotator pair). Based on the quaternion number, Then, using the linear elimination and the Dixon knot elimination method, a 6 × 6 knot is obtained. Because of adopting the complex exponential form of the unknown corner, no need to extract any common factor, the institution can be directly obtained A set of 16 input and output equations with inverse position and all 16 closed solutions are given.Finally, numerical examples show that this method has no rootless roots and roots.Examples show that the proposed method is simple and easy to implement and provides the inverse solution for tandem mechanism A new theoretical basis.