Hard-Stop Synthesis for Multi-Degrees-of-Freedom Compliant Mechanisms

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, fatigue, and buckling. Conventional hard-stop designs, which rely on stacking single-degree-of-freedom (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 mechanism's multi-DOF working space while still ensuring that internal stresses remain below prescribed safety thresholds. 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.