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This paper presents a fast inverse kinematics (IK) algorithm. In recent years, the robotics computation theory is often applied for detailed and complex multi-body systems. However, the computational complexity of IK is too high to be implemented in large DOF systems. IK of multi-body system is often formulated as nonlinear optimization to minimize the residuals from the references. It usually requires the computation of the gradient vector of the evaluation function. In the method, the computation of the gradient is decomposed into two parts. First, the residuals are considered as external forces and are distributed to each link. Then, the gradient can be computed from static equilibrium by the recursive Newton-Euler algorithm. In addition with the efficient direction search algorithms of nonlinear programing, the computation complexity of IK can be dramatically reduced. The results of numerical evaluation using a large-DOF manipulator and a human musculoskeletal model are shown.