This paper presents a generic error model, which is based on the product of exponentials (POEs) formula, for serial-robot calibration. The identifiability of parameters in this error model was analyzed. The analysis shows the following: 1) Errors in all joint twists are identifiable. 2) The joint zero-position errors and the initial transformation errors cannot be identified when they are involved in the same error model. With either or neither of them, three practicable error models were obtained. The joint zero-position errors are identifiable when the following condition is satisfied: Coordinates of joint twists are linearly independent. 3) The maximum number of identifiable parameters is 6n + 6 for an n-degree-of-freedom (DOF) generic serial robot. Simulation results show the following: 1) The maximum number of identifiable parameters is 6r + 3t + 6, where r is the number of revolute joints, and t is the number of prismatic joints. 2) All the kinematic parameters of the selective compliant assembly robot arm (SCARA) robot and programmable universal machine for assembly (PUMA) 560 robots were identified by using the three error models, respectively. The error model based on the POE formula can be a complete, minimal, and continuous kinematic model for serial-robot calibration.