Unified Kinematic and Rigid-Body Dynamic Modeling of an XYZAC Five-Axis Machine Tool via Task-to-Screw-Space Mapping

Aunified analytical framework is developed for an XYZAC five-axis CNC machine tool to establish a physically consistent connection between practical machining-task variables, rigid-body screw motion, and inverse dynamics. The tool-tip/tool-axis task is represented in R3×S2, while the product-of-exponentials formulation is used to establish the forward- and inverse-position kinematics. A topology-constrained two-stage mapping converts the machining-task rate first into the actual six-dimensional rigid-body twist and subsequently into the five generalized axis velocities. A supplementary constrained motion screw and reciprocal screw/wrench duality are employed to construct the corresponding analytical inverse. At the acceleration level, task-space geometric effects and mechanism-configuration effects are explicitly separated, after which the generalized states are coupled with the physical rigid-body chains through Newton–Euler equations and virtual work. A singularity analysis gives σmin=|sinqA| and κ2=1/|sinqA|, quantitatively revealing the degeneration of the orientation mapping as qA→0. Closed-loop kinematic validation yields maximum RMSEs of 3.811000×10−14 mm and 2.657723×10−15 deg and maximum absolute errors below 1.110223×10−13 mm and 1.272222×10−14 deg, while force/torque benchmarking gives maximum RMSEs of 0.0821185 N and 1.39897 N·mm and maximum absolute errors of 0.531176 N and 8.76912 N·mm relative to simulation. The results demonstrate consistent task-to-motion-to-load propagation within the investigated rigid-body regime and provide a unified interface for subsequent elastodynamic and machining-load coupling analyses.