## 1 Introduction  
Modern machining centers ensure a level of accuracy, versatility and productivity that traditional manual machines could not reach. The complexity of these apparatuses makes necessary the development of working process simulations that consider the structural dynamics and the vibrations generated during machining. Finite-element methods provide a well-known way to forecast the static and dynamic behavior of flexible bodies; however, this technique cannot be applied if the mechatronic design of a system must be carried out. In those cases, in fact, it is most relevant to consider in the same simulation environment the rigid body motion of the components moved by the actuators and the vibrations induced by motion and external loads. This result is typically obtained into multibody modeling environment. In addition, the effects of moving constraints are quite difficult to be implemented when not impossible. Two main approaches are used for modeling flexible bodies: lumped parameters methods and finite-element analysis. [PERSON] presents an overview of the various models used for studying flexible multibody mechanical systems [1]. A more recent work by [PERSON] [2] offers an overview of common approaches to models flexible body and suggests a method to prepare the required data. [PERSON] and [PERSON] [3] modeled a constrained rigid-flexible robot arm as a set of nonlinear hybrid ordinary-partial differential equations and an algebraic constraint equation and investigated the effects of axial force on bending vibrations. [PERSON] [4] used, instead, spatial algebra for representing multibody flexible system, implementing the flexible nature of the bodies using Lagrangian equation. [PERSON] et al. [5] proposed an approach for modeling flexible element in Modelica language to create an assembly of thin flexible beam. [PERSON] and [PERSON] [6] proposed a new algorithm for solving equations of motion of flexible multibody system. This algorithm was based on a tree topology articulated system made up of an arbitrary number of flexible and rigid bodies connected together. The positioning accuracy of high-speed machine tools is determined by the bandwidth of servo controllers, which is limited by the structural vibrations that are transmitted to the control loop. Some studies focused on controlling the position of the part of interest and/or the vibrations that can arise. For example, in [7] active damping is introduced, while in [8] the coupling on the host linkage surface-bonded Lead Zirconate Titanate (PZT) patches (which demonstrate to damp the vibrations) is used. Other methods contemplated the introduction of position control loops in the system as a partial feedback linearization control [9], a delayed position feedback signal [10], a passive velocity feedback and strain feedback approaches [11]. [PERSON] et al. [12], modeled non-proportional damped systems with typical software tools of the mechatronic simulation (as Simulink and Matlab). [PERSON] et al. [13] investigated the complex interaction among structural dynamics, motion control and friction forces. In [14], the possibility of implementing a control system in finite-element commercial codes, introducing differential equations for the control, is investigated. In [15], different configurations of a machine tool were investigated for estimating the influence of the four axes configuration parameters on the first three degrees of freedom without considering the machine during its motion. In [16], the problem of identifying the value of the stiffness of the constraints was addressed by comparing simulation and experimental results. [PERSON] et al. [17] presented a complete scenario, coupling finite-element method and control using multipoint dynamics to solve the problem of moving constraints. A different approach was used in [18], where simple flexible multibody systems were built in Simscape Multibody environment to obtain a visual result of the simulations.