Insight into numerical solutions of static large deflection of general planar beams for Compliant Mechanisms

Abstract

Compliant Mechanisms (CMs) have been a hot research spot in recent years due to their distinguished mechanism concept from conventional rigid-body mechanisms: CMs can transfer motion, force, and energy only through the deflection of flexible components. Therefore, the accurate and efficient kinetostatic modeling for these elementary flexible components plays a rather important role regarding conducting synthesis of a studied compliant mechanism. In this paper, we have reviewed the commonly-used beam modeling methods in CMs, most of which are essentially dedicated to handling geometrically nonlinear Euler–Bernoulli beam theory. Mathematically speaking, this beam model is essentially a boundary value problem (BVP) of an ordinary differential equation (ODE). We then introduced certain commonly used numerical methods for BVPs to solve the problem where straight beams and circular initially curved beams (ICBs) are studied as two example cases. We have also demonstrated the detailed derivation of these methods and the numerical results along with the corresponding insights on them as well. Besides, we have modeled 2 representative revolute mechanisms (straight-beam-based cross-axis compliant revolute joint and circular-beam-based compliant revolute joint) to prove the feasibility of synthesizing CMs using these numerical methods. Error analysis is presented thereafter, which also confirms the effectiveness of these numerical methods.