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

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 Pade 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.

Automated summary

This paper proposes a more efficient method for solving the boundary value problem of slender beams in CMs, which has higher accuracy and efficiency compared to previous methods. The feasibility of the proposed method has been demonstrated through verification based on the finite element method.