The paper presents a methodology to rapidly solve the inverse kinematics of anthropomorphic hands, which is particularized for a mechanical hand considering 27 degrees of freedom. Given the contact points and normal directions on an object surface, the proposed algorithm nds the joint values and the wrist position and orientation that make the ngertips satisfy the contact constraints. The approach combines an iterative algorithm with an o - line analysis that allows signi cant reductions of the execution time. The approach has been implemented and the paper includes application examples. The e ectiveness and fast execution of the algorithm is demonstrated with statistical results.