关键词: 6R机器人, 迪克逊结式, 对偶四元数, 逆运动学分析

Abstract: Complex exponential form of dual four elements is introduced into the inverse kinematics analysis of serial mechanisms. A new algorithm is proposed for the inverse solution of space 6R serial mechanism. The mathematical model is established for the space 6R serial mechanism by adopting complex exponential form and dual four elements. A 6×6 matrix is obtained from the Dixon resultant constructed with the obtained four position constraint equations. By deleting the interrelated rows of the matrix and taking the determinant, a 16th degree polynomial equation in a single unknown is derived. Through calculation, a 16th degree equation containing a variable is properly derived from the resultant and a maximum of 16 group’s conclusions. The root and no means seamless root are proved through a case research. This proposed algorithm can automatically eliminate the institutional structure of the parameters change in the elimination process or trajectory planning process caused by some singular position equation relevance, so it can avoid the emergence of seam root.

Key words: 6R robot, Dixon resultant, Dual quaternion, Inverse kinematics analysis