Port-Based Modeling and Simulation of Mechanical Systems With Rigid and Flexible Links

In this paper, a systematic procedure for the defi- nition of the dynamical model in port-Hamiltonian form of me- chanical systems is presented as the result of the power-conserving interconnection of a set of basic components (rigid bodies, flexible links, and kinematic pairs). Since rigid bodies and flexible links are described within the port-Hamiltonian formalism, their inter- connection is possible once a proper relation between the power- conjugated port variables is deduced. These relations are the anal- ogous of the Kirchhoff laws of circuit theory. From the analysis of a set of oriented graphs that describe the topology of the mecha- nism, an automatic procedure for deriving the dynamical model of a mechanical system is illustrated. The final model is a mixed port- Hamiltonian system, because of the presence of a finite-dimensional subsystem (modeling the rigid bodies) and an infinite-dimensional one (describing the flexible links). Besides facilitating the deduction of the dynamical equations, it is shown how the intrinsic modularity of this approach also simplifies the simulation phase.