In kinematic calibration of a serial manipulator, to avoid the complex process and determine the relation between measurement coordinates and robot base coordinates when using pose error, a distanceerror model was proposed, which placed its base on the geometric property of joint screw and error compensation scheme of adjoint transform. Comparing with other distanceerror models such as DH model and MDH model, the proposed model can guarantee the geometric constraints on the joint screw to be naturally satisfied. Furthermore, the physical meanings of the kinematic parameters involved in this model were explicit. As a result, it was relatively easy to evaluate the influence of each kinematic parameter on the distance errors. To enhance the robustness of the model, the kinematic parameters redundancy was studied by investigating the null space of the Jacobian matrix. It was found that the number of independent parameters was determined by the measurement method used to measure the distance errors. Specifically, let r be the number of revolute joints, then, the maximum number of the calibrated parameters was 4r-2, and the number became 2r and 3r-1 when measuring the errors by rotating the corresponding joint and taking the initial configuration as the reference, respectively. In order to verify the effectiveness of the proposed model and the correctness of the redundancy analysis, calibration experiments were performed on KUKA youBot with five degrees of freedom. It was found that the result about calibrated parameters obtained from the theoretic analysis was the same as that of experiment. Meanwhile, the mean distance error was decreased by 116 times after calibration than before calibration. Therefore, the kinematic accuracy of the robot can be greatly improved by the proposed distanceerror model.