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This paper deals with the solution of the inverse kinematic problem for kinematically redundant robots. After summarizing the most widespread methods currently used, a new algorithm is proposed which finds the solution with a constrained optimization, using a parameterized form of the kinematic equation's space. Along with the derivation of the new algorithm, extension possibilities (e.g., singularity handling) are also described. Further comparison then shows the relation between gradient projection and optimization methods through a special case. Finally, application examples are presented for an eight-degrees-of-freedom arm and a mobile manipulator.