Groebner base is an important concept and a powerful tool for solving the problems in nonlinear
polynomial algebraic systems. In this paper, an algebraic method based on Groebner bases is applied to the
synthesis of a spatial 5S-S parallel robot mechanism for the first time. The symbolic triangular Groebner
bases,i. e., the analytic solution of the problem of a rigid body with six given precise points, are
obtained.