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This contribution proposes a mathematical model for an amplification mechanism (scissors mechanism) intended to be used as an actuating platform in the setup of a driving simulator. The main goal is reproducing different types of road profiles. For this purpose, hydraulic actuation has been chosen by means of high forces and powers that need to be developed. An optimization method is presented (GA and hybrid functions) for the geometrical parameters of the mechanism and the effectiveness of the method is validated by the simulation results in MATLAB/Simulink.