为多自由度柔顺机构设计紧凑硬停结构，防疲劳失效

Compliant mechanisms have significant potential in precision applications due to their ability to guide motion without contact. However, an inherent vulnerability to fatigue and mechanical failure has hindered the translation of compliant mechanisms to real-world applications. This is particularly challenging in service environments where loading is complex and uncertain, and the cost of failure is high. In such cases, mechanical hard stops are critical to prevent yielding and buckling. Conventional hard-stop designs, which rely on stacking single-DOF limits, must be overly restrictive in multi-DOF space to guarantee safety in the presence of unknown loads. In this study, we present a systematic design synthesis method to guarantee overload protection in compliant mechanisms by integrating coupled multi-DOF motion limits within a single pair of compact hard-stop surfaces. Specifically, we introduce a theoretical and practical framework for optimizing the contact surface geometry to maximize the mechanisms multi-DOF working space while still ensuring that the mechanism remains within its elastic regime. We apply this synthesis method to a case study of a caged-hinge mechanism for orthopaedic implants, and provide numerical and experimental validation that the derived design offers reliable protection against fatigue, yielding, and buckling. This work establishes a foundation for precision hard-stop design in compliant systems operating under uncertain loads, which is a crucial step toward enabling the application of compliant mechanisms in real-world systems.