Circular-Hinge Line Element for Finite Element Analysis of Compliant Mechanisms

Abstract

A three-node six degree-of-freedom per-node line element that is sensitive to axial, bending, and torsional loading is introduced to model single-axis right circular hinges of constant width that are utilized in compliant mechanisms. The Timoshenko model is applied for bending because this particular configuration is virtually short, and provisions are taken that the element is shear-locking free. The Saint Venant theory, which includes warping, is utilized to model torsion of the variable rectangular cross-section circular hinge. The principle of minimum total potential energy is employed to formulate the elemental stiffness and mass matrices, as well as the elemental nodal vector. Static force deflection and modal simulation that are performed based on this finite element model produce results that are in agreement with simulation by commercially available finite element software. The three-node line element is also compared to an analytical model in terms of stiffness and the results are again concurring.