Robust design and optimization of a large-stroke compliant constant-torque mechanism under fabrication uncertainties

Compliant constant-torque mechanisms (CCTMs) are capable of delivering a stable output torque across a wide range of input rotational angles. Owing to their compact design and structural simplicity, they offer an attractive alternative to complex active control systems and have gained considerable research attention in recent decades. In many cases, particularly those involving large-stroke applications, CCTMs are fabricated from thin flexure beams using conventional subtractive machining methods, which makes them vulnerable to fabrication-induced variations that may compromise performance. This study presents an integrated design and optimization framework that explicitly accounts for fabrication uncertainties, enhancing the reliability of large-stroke CCTMs. By combining the Chained Beam-Constraint Model, the First-Order Reliability Method, and the Non-dominated Sorting Genetic Algorithm II, a reliability-based design optimization procedure is established. The optimized CCTM demonstrates a constant torque range up to 88°, an average torque deviation within 3%, and a reliability of 99.88%. Theoretical analyses, finite element simulations, and experimental validation confirm the framework's effectiveness in delivering robust and high-performance CCTMs suitable for precision applications.