A new algorithm for the position inverse solution of the introduced general 6R robot was introduced. It is the homogeneous transformation matrix that translated to the double quaternions form, and on this basis, the series 6R robot kinematics equation with double quaternions form was established. And five variables were eliminated by the elimination of linear and two-time applications lexicographic Groebner base, a 16th degree equation contained a variable has been obtained. This method did not have any roots, it is a new algorithm that solves and presents the space of arbitrary size 6R robot modeling. Groebner base which used computer algebra system rational calculation was requested, and the current solution is not yet a high speed, it needs further improvement.
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倪振松,廖启征,魏世民,李瑞华,乔曙光.基于倍四元数和Groebner基的6R机械手的位置反解[J].农业机械学报,2009,40(2):190-194. Qeneral 6R Robot Inverse Solution Based on Double Quaternion and Groebner Base[J]. Transactions of the Chinese Society for Agricultural Machinery,2009,40(2):190-194.