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

This paper presents a reliability-oriented accuracy synthesis framework for five-axis hybrid kinematic machining units (HKMUs) that harmonizes geometric accuracy, computational efficiency, and manufacturing economy. Current tolerance design methods struggle with the geometric error propagation inherent in parallel-serial HKMUs, may leading to unreliable pose accuracy. To address this, a tri-layer 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 PID Search Algorithm (PSA) to avoid local minima. Validated on a 2PRU&1PRS-2P HKMU, the framework quantifies the mapping relationships between 9 geometric tolerances and 16 uncompensatable key source errors through the Small Displacement Torsor method. Under allowable errors of 0.10 mm (position) and 0.02°(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.