The accurate dynamic model for industrial robots is required to enhance their efficiency in expanding their range of applications and carrying out complex tasks. In this research, considering the nonlinear friction model of each joint, an identification approach based on swarm intelligence algorithms for nonlinear joint dynamics of a 6-DOF UR5 robot manipulator has been proposed by using a two different excitation trajectory approach for analyzing the accuracy of parameters to be identified. The Coulomb-Viscous friction model, the Stribeck friction model and the centrosymmetric static friction model (CSFM) are chosen to describe the friction effects of the joints. By using five different arbitrary paths and a Fourier reference excitation trajectory, the nonlinear friction model and robot dynamic parameters are identified by using swarm intelligence-based optimization algorithms such as Cuckoo Search (CS), Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), and also the hybrid algorithms called GWO-CS and GWO-PSO. For the purpose of showing the prediction accuracy of the algorithms and comparing the prediction torques of the dynamic model based on the different joint friction models, the verification of parameter estimation is performed. Finally, simulation results are used to illustrate which swarm intelligence algorithms provide better estimation performance and which joint friction models achieve higher torque prediction accuracy.