Forward kinematics, inverse kinematics and their simulations on the pinion bracket mechanism of a heavy ship-lift were discussed in this paper. The passive four-bar linkage was employed to guarantee the relative position of transmission shafts and compensate positioning errors automatically. To solve forward kinematics, non-linear equations and a Simulink model of its simplified structure were built. To solve inverse kinematics, two adaptive neuro-fuzzy inference systems were trained by sample data from forward kinematics. Branch defects were avoided automatically due to continuous constraints of local motion trajectory. Comparisons between the results from nonlinear equations and ANFIS systems for the same case study stimulated by a Gaussian noise shaped horizontal positioning error showed that the passive four-bar linkage was in good agreement with deviations in the margin range of +/-0.0002.