Solutions to large beam-deflection problems by Taylor series and Padé approximant for compliant mechanisms

Abstract

Compliant Mechanisms (CMs) serve as a promising alternative for transferring motion, force and energy compared to rigid mechanisms. The mentioned desired function is achieved by making the most of the elastic deflection of all built-in flexible members in CMs, such as slender straight beams and slender initially curved beams (ICBs). Therefore, accurately characterizing the deformation of these slender beams plays a considerable role in modeling CMs. As is well-known in the field of CMs, static planar large deflection of slender beams can be modeled via Euler Bernoulli beam theory, and it is essentially a boundary value problem (BVP). In this paper, we propose to use Taylor series method and Padé approximant to solve this BVP in a more efficient manner compared to the previous work. Its accuracy and efficiency have been compared with weighted residual method and also verified by solid-mechanics-based Finite Element Method (FEM) respectively. The feasibility of the proposed method has also been proved in terms of synthesizing CMs where three representative cases are studied.