Comparison of flexibility models for the multibody simulation of compliant mechanisms

This paper presents a comparison among different flexibility models of elastic elements to be implemented in multibody simulations of compliant mechanisms. In addition to finite-element analysis and a pseudo-rigid body model, a novel matrix-based approach, called the Displaced Compliance Matrix Method, is proposed as a further flexibility model to take into account geometric nonlinearities. According to the proposed formulation, the representation of the elastic elements is obtained by resorting to the ellipse of elasticity theory, which guarantees the definition of the compliance matrices in diagonal form. The ellipse of elasticity is also implemented to predict the linear response of the compliant mechanism. Multibody simulations are performed on compliant systems with open-loop and closed-loop kinematic chains, subject to different load conditions. Beams with uniform cross-section and initially curved axis are considered as flexible elements. For each flexibility model, accuracies of displacements and rotations, and computational time, are evaluated and compared. The numerical results have been also compared to the data obtained through a set of experimental tests.