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This paper presents a novel approach to the modeling and identification of elastic robot joints with hysteresis and backlash. The model captures the dynamic behavior of a rigid robotic manipulator with elastic joints. The model includes electromechanical submodels of the motor and gear from which the relationship between the applied torque and the joint torsion is identified. The friction behavior in both presliding and sliding regimes is captured by generalized Maxwell-slip model. The hysteresis is described by a Preisach operator. The distributed model parameters are identified from experimental data obtained from internal system signals and external angular encoder mounted to the second joint of a 6-DOF industrial robot. The validity of the identified model is confirmed by the agreement of its prediction with independent experimental data not previously used for model identification. The obtained models open an avenue for future advanced high-precision control of robotic manipulator dynamics.