The advent of parametric design has resulted in a marked increase in the complexity of building. Unfortunately, traditional construction methods make it difficult to meet the needs. Therefore, construction robots have become a pivotal production tool in this context. Since the arm span of a single robot usually does not exceed 3 meters, it is not competent for producing large-scale building components. Accordingly, the extension of the robot,s working range is often achieved by external axes. Nevertheless, the coupling control of external axes and robots and their kinematic solution have become key challenges. The primary technical difficulties include customized construction robots, automatic solutions for 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 effectively solves the above problems, lowers the threshold for architects, and improves production efficiency. The effectiveness of the algorithm and software in this paper is verified through simulation experiments.