New algorithm for inverse kinematics of 6R serial robot mechanism
Huang Xiguang1, Liao Qizheng2*
1. School of Mechanical and Electrical Engineering, North China University of Technology, Beijing 100041, China;
2. School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China
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.