Extending Timoshenko Beam Theory for Large Deflections in Compliant Mechanisms

Abstract Compliant mechanisms (CMs) have presented its inherently advantageous properties due to the fact that CMs utilize elastic deformation of elementary flexible members transfer motion, force, and energy. Previously, classic Euler–Bernoulli beam theory is most used in terms modeling large deflections CMs. However, it has some assumptions may decrease accuracy, such as ignoring shear strain axial cross sections. In this article, take into account strains, we adopt Timoshenko along with modifications consider elongation. To simplify complexity proposed governing boundary value problem (BVP), transform BVP an explicit formulation use weighted residual methods numerically approximate solution. We first focus on single-beam deflection a straight initially curved (ICB) using theory, solid mechanics analyze contributions influences strains deflections. Then, prove feasibility strategy via mechanism synthesis for bi-stable ICB-based parallelogram mechanism. Finally, deduction mathematical model numerical results are provided brief analysis mechanical performances studied