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The robot kinematic error model may include redundant parameters, which require removal prior to the identification of kinematic parameters to ensure the accuracy and stability of such. Traditionally, the redundant parameters are determined by the numerical analysis. This paper presents an analytical method to determine the identifiable kinematic parameters for serial-robot calibration under various identification conditions. Among various kinematic models of robots, the DH (Denavit-Hartenberg) model is the most commonly used, so the analysis of redundant parameters is based on the DH error model. The correlation between the columns of the Jacobian matrix is analyzed by theoretical methods, resulting in the linear relationship between these columns. The redundant error parameters and the linear independent parameters after removing redundancies from robots with different measurement conditions and different configurations are clearly given. Thus, the redundant parameters can be easily determined based on the values of kinematic parameters, which facilitates the determination of the non-redundant kinematic calibration model. In addition, the physical meanings of redundant parameters are also elaborated, which can reveal the inherent principle of the error parameters’ linear correlation. Finally, the parameter identification simulation experiment shows that the identification results, after removing the redundant parameters, all converge to the true values when the random noise is not considered, which verifies the correctness of the parameter redundancy analysis results. In the case of considering random noise, the non-redundant parameter identification has better convergence than the full parameter identification. This study can provide theoretical and application references for robot kinematic calibration.