Modeling Method for Static Large Deflection Problem of Curved Planar Beams in Compliant Mechanisms Based on a Novel Governing Equation

Slender beams serve as typical flexible components to transfer motion, force, and energy in compliant mechanisms (CMs). Therefore, the accurate and efficient kinetostatic modeling for the slender beams are highly needed in the synthesis and analysis of compliant mechanisms. Several impressive and great modeling methods have been completed by the pioneering researchers based on the governing equation of slender beams, which can solve the deflection of the beam while the beam-tip loads are known. However, parts of the beam-tip loads are unknown in some scenarios and the traditional governing equation becomes inefficient in these scenarios. The aim of this paper is to propose a novel modeling method for the compliant mechanism, which can solve the large deflection problem without iterative algorithm. In this research, a novel governing equation of slender beams has been established based on the Castigliano&s principle and simplified by the differential geometry. In the proposed governing equation, the statically force equilibrium equations and geometric constraint equations between different slender beams can be established in the boundary conditions, so the model of compliant mechanisms can be solved directly even if parts of the beam's tip loads and displacements are unknown. The proposed governing equation provides the deformed shapes and cross-sectional loads of the slender beams, which help the designer to check the mechanical interference and strength in the design process. The numerical examples are presented to demonstrate the feasibility of proposed method.