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A straightforward inverse kinematic algorithm for multilink flexible robots is proposed to improve the control performance. The inclusion of a dynamic constraint maximizes the performance of feedback controllers in high-speed applications. To obtain a numerically feasible solution, the singular perturbation approach is employed, which decomposes the inverse kinematics into an averaged part (slow part) and a parasitic part (fast part). The solution of the averaged part is considered the desired inverse kinematics, while the parasitic part is intentionally removed. The parameter expansion is carried out to obtain the solution sequentially. The implicit expansion method, which is a refined version of the expansion method, reduces computing time considerably. The formula in discrete time offers efficiency in computer applications. In addition, a requirement on differentiability of the desired task trajectory is derived.