Modelling and simulation of mechanisms with flexible links

When designing the mechanisms that have to carry out all the operations of a machine, most of the times the rigid body design paradigm is followed. The idea behind this work is that introducing flexibility in such systems could have many positive features and even open completely new design possibilities. But, in order to be able to deal with the novelties arising when introducing flexible elements in a system, an adequate way to model their behavior is needed. In this work, a four-bar linkage with flexible coupler link has been studied, in particular having a rigid connection between the coupler and the follower. The first part of the work is dedicated to multibody simulations in the MSC Adams environment, that have the objective of gaining a better understanding of the effects that the introduction of flexible elements has on the motion of the mechanism. Different methods to describe flexible elements are used and different coupler geometries are tested during the simulations, to see how the system behaves in the different configurations. Once the simulation step has provided some basic insight about what the effects of having a flexible coupler in a four-bar mechanism are, the mathematical model of a flexible beam is derived by the use of the port-Hamiltonian formalism applied to the Timoshenko beam equations. Since a continuous flexible body would require an infinite-dimensional state space for its complete description, the system is discretized in a finite number of elements. To complete the beam model, an automatic way to obtain the system matrices is shown which makes it possible to choose the dimension of the discretized system so as to optimally compromise between accuracy of results and computational burden. The proposed mathematical model is finally implemented in Matlab/Simulnik environment and validated on a cantilever beam case study, where simulations results are compared with those obtained via MSC Adams multibody system software.