This paper introduces a systematic approach to identifying a physically feasible set of robot dynamics parameters. The framework consists of four steps: 1) Identification of robot dynamics parameters using least squares combined with a linear friction model. 2) Construction of a weighting matrix based on the least squares identification error, and performing weighted least squares identification combined with the linear friction model. 3) Introduction of a nonlinear friction model to fit joint friction. 4) Optimization of the remaining robot dynamics parameters to adhere to physical feasibility constraints. Various combinations of identification methods with linear or nonlinear friction models are analyzed experimentally, using a 6-DoF industrial robot and a 7-DoF collaborative robot, respectively, to demonstrate the effectiveness of the proposed recognition framework. Experimental results affirm that the proposed method provides accurate estimates of the robot joint torques while maintaining the physical feasibility of the dynamics.