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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.