空间6R串联机器人机构位置逆解新算法

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.

New algorithm for inverse kinematics of 6R serial robot mechanism

The theory of double quaternions and its application in the inverse kinematics of serial mechanisms was introduced. A new algorithm for the inverse kinematics of 6R mechanisms was presented based on the complex exponent form of double quaternions. Based on double quaternions, a mathematical model of 6R mechanisms was created. Then, a 6×6 resultant matrix was obtained directly by using linear elimination and Dixon resultant method, without factoring out or deriving the greatest common divisor, due to the proposed algorithm used the complex exponent form of double quaternions. A 16th degree univariate equation was achieved from the determinant of the matrix and all 16 closed-form solutions were also obtained. The proposed algorithm is comparably easy and simple to program. It was verified by a numerical example that the obtained roots satisfy the original equations. The research result provides a new method for the inverse kinematics of serial mechanisms.