Pose Reliability-Oriented Accuracy Synthesis: A Framework With Validation on a Five-Axis Hybrid Kinematic Machining Unit

Abstract

Abstract. This article presents a reliability-oriented accuracy synthesis framework for five-axis hybrid kinematic machining units (HKMUs) that harmonize geometric accuracy, computational efficiency, and manufacturing economy. Current tolerance design methods struggle with the geometric error propagation inherent in parallel-serial HKMUs, which may lead to unreliable pose accuracy. To address this, a trilayer architecture is proposed: (1) a foundational geometric error model employing equivalent joint decomposition and screw theory establishes matrix-form error mappings; (2) a computational layer introduces a dual-criteria pose reliability algorithm (position sphere/orientation cone) accelerated via fourth-moment-maximum-entropy integration, reducing computational load versus Monte Carlo methods; (3) an optimization layer formulates tolerance allocation as a reliability-constrained nonlinear program, solved by a Proportional-Integral-Differential (PID) search algorithm (PSA) to avoid local minima. Validated on a 2PRU&1PRS-2P HKMU (“R”, “U”, “S”, and “P” represent revolute joint, universal joint, spherical joint and actuated prismatic joint, respectively), the framework quantifies the mapping relationships between 9 geometric tolerances and 16 uncompensatable key source errors through the Small Displacement Torsor (SDT) method. Under allowable errors of 0.10 mm (position) and 0.02 deg (orientation), PSA achieves 90% pose reliability—a 203.7% improvement over baseline—while increasing manufacturing costs by only 11.8%. The framework provides a systematic roadmap for designing economically viable, high-reliability HKMUs essential for precision manufacturing.