Optimal Workpiece Placement in a Five-Leg Parallel Machine Tool Based on Force Manipulability

This article presents a post-design methodology for optimizing workpiece placement withinthe predefined workspace of a five degrees-of-freedom parallel kinematic machine tool(PKMT) with SPR–4SPRR architecture. The objective is to identify workpiece locationsthat improve force-transmission characteristics and reduce actuator effort during machining, without modifying machine geometry or control architecture. The approach combinesanalytical inverse kinematics, screw-theory-based Jacobian formulation, and force-manipulability analysis to evaluate the force-transmission capability of the machine across theworkspace. The workspace is discretized into a dense three-dimensional grid and analyzedfor three representative tool tilt angles (0 deg, 15 deg, and 45 deg). A data-driven thresholdbased on the empirical manipulability distribution is used to retain only well-conditionedconfigurations, and the optimal workpiece position is defined as the manipulabilityweighted centroid of the resulting high-performance region. The method is assessed onan industrial-scale model of the METROM pentapod in MATLAB SIMSCAPE through simulatedmachining trajectories under representative quasi-static cutting loads. Results show thatthe optimized placement reduces mean peak actuator loads across additional simulatedpaths by 7.66% at 0 deg, 1.36% at 15 deg, and 21.22% at 45 deg tilt, with correspondingaverage force reductions of 1.66 N, 0.597 N, and 5.08 N. These findings demonstrate thatworkspace-aware workpiece placement can enhance the mechanical operating conditionsof PKMTs and provide a practical post-deployment strategy for improving machining performance.