Energy-Based Chained Modeling with Improved Beam Constraint Model and analysis of Flexural Pivot

Distributed flexure mechanisms are essential in high-precision engineering, yet the coupling of load-dependency and geometric nonlinearity under high constraints makes traditional equilibrium-based modeling analytically tedious and insufficient accuracy. This paper proposes a generalized Energy-Based Chained Modeling framework based on an Improved Beam Constraint Model (Improved-BCM). By integrating a chained discretization strategy with the principle of minimum potential energy, the framework achieves the decoupling of mechanism-level kinematic constraints from element-level mechanical characteristics. The incorporation of the Improved-BCM, which accounts for rotation stiffening effects, enables a more precise representation of mechanical properties and geometric nonlinearities during large deformations. The method is validated using the Leaf-Type Isosceles-Trapezoidal Flexural Pivot (LITF Pivot). Based on the numerical results and simplified equilibrium relations, the study elucidates the underlying mechanisms of its center shift and stiffness nonlinearity. The results indicate that the proposed method provides higher prediction accuracy for center shift and stiffness compared to existing analytical expressions across a wide range of structural parameters and large rotation angles. This framework offers an efficient, high-fidelity computational approach for the performance prediction of complex compliant mechanisms.