Nowadays, integrated joint modules are increasingly adopted in manipulators for their advantages of high integration, miniaturization and high repeatability positioning accuracy. The problem of generally low absolute positioning accuracy (namely angle measurement accuracy) must be solved before they can be introduced into the self-driven articulated arm coordinate measuring machine which is under study in our laboratory. In this study, the sources of joint module’s angle error were analyzed and the error model based on harmonic analysis was established. Two integrated joint modules were calibrated on the self-designed calibration platform and the model parameters were deduced, respectively. The angle error was then compensated in the experiments and the results demonstrated that the angle error of the joint modules was reduced by 82.03% on average. The established angle error model can be effectively applied into the self-driven articulated arm coordinated measuring machine.