Comprehensive SCME: A nonlinear large-deformation modeling approach for planar compliant mechanisms

This work presents a comprehensive energy method based on the smooth curvature model (CoSCME) for modeling the nonlinear large deformations of planar compliant mechanisms, addressing limitations of existing methods. CoSCME accounts for large axial and bending deformations, as well as strain and stress in beams with arbitrary shapes, including straight beams and curved beams. Both axial strain and curvature are fitted using shifted Legendre polynomials, while the corresponding deformations are derived through integration. When modeling initially-curved beams, multiple linear regression is applied to determine the initial generalized coordinates. Additionally, CoSCME adapts to diverse application scenarios, including compresural beams, tensural beams, bistable mechanisms (with straight or initially-curved beams), and general lumped-compliance beams. The modeling of general lumped-compliance beams is achieved by defining moderate geometric parameters in the model and applying coordinate transformations. Various specific configurations of general lumped-compliance beams are then derived. Modeling results are validated through nonlinear finite element analysis conducted in Strand7, demonstrating high consistency. The proposed CoSCME exhibits considerable potential for advancing the design, modeling, and optimization of planar compliant mechanisms.