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

Abstract

This paper presents a post-design methodology for optimizing workpiece placement within the predefined workspace of a five-degree-of-freedom parallel kinematic machine tool (PKMT) with SPR–4SPRR architecture. The objective is to identify workpiece locations that improve force-transmission characteristics and reduce actuator effort during machining, without modifying machine geometry or control architecture. The approach combines analytical inverse kinematics, screw-theory-based Jacobian formulation, and force manipulability analysis to evaluate the force transmission capability of the machine across the workspace. The workspace is discretized into a dense three-dimensional grid and analysed for three representative tool tilt angles (0°, 15°, 45°). A data-driven threshold based on the empirical manipulability distribution is used to retain only well-conditioned configurations, and the optimal workpiece position is defined as the manipulability-weighted centroid of the resulting high-performance region. The method is assessed on an industrial-scale model of the METROM pentapod in MATLAB Simscape through simulated machining trajectories under representative quasi-static cutting loads. Results show that the optimized placement reduces mean peak actuator loads across additional simulated paths by 7.66% at 0°, 1.36% at 15°, and 21.22% at 45° tilt, with corresponding average force reductions of 1.66 N, 0.597 N, and 5.08 N. These findings demonstrate that workspace-aware workpiece placement can enhance the mechanical operating conditions of PKMTs and provide a practical post-deployment strategy for improving machining performance.