With the rise of parametric design, the complexity of building components continues to increase. Traditional construction methods are difficult to meet the needs. Construction robots have become an important production tool in this context. Since the arm span of a single robot usually does not exceed 3 meters, it is not competent for the production of large-scale building components. Therefore, the extension of the robot"s working range is often achieved by external axes. However, the coupling control of external axes and robots and their kinematic solution have become key challenges. The main technical difficulties include: customized construction robots, automatic solution of external axes, fixed axis joints, and specific motion mode control. This paper proposes solutions to these difficulties, introduces the relevant basic concepts and algorithms in detail, and encapsulates these robotics principles and algorithm processes into the Grasshopper plug-in commonly used by architects to form the FURobot software platform. This platform not only effectively solves the above problems, but also reduces the threshold for architects to use and improves production efficiency. The effectiveness of the algorithm and software in this paper is verified through simulation experiments.