The aim of extrinsic parameter calibration is to build the relationship between vision coordinate system and extrinsic standard coordinate system. The substitutable target sphere for vision-measurement is designed to cooperate the vision-measurement and instrument measurement. The vision-measurement target sphere and the equipment-measurement target sphere replace each other to get the coordinate of common points in both vision coordinate and standard coordinate. And the extrinsic parameters are solved by optimizing the target function with the coordinate of common points in both systems using non-linear optimization method. The design of substitutable vision-measurement target sphere consists of target, light source and sphere shell to satisfy the substitutability with equipment-measurement target sphere and the availability of center of sphere. The propagation of error during the calibration is presented. The accuracy of calibration is promoted through simulation and verified by experiment. The result shows that the accuracy reaches 0.036 mm, which shows that the proposed method can realize public point data acquisition directly, flexibly and high-accuracyly.