Abstract
This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes.
Highlights
Academic Editor: Gianluca Gatti is paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. e aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest
The availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. e method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation
The flexibility of the links makes the motion planning and control critical and imposes the use of advanced techniques that account for the flexible system dynamics [1,2,3,4,5,6]. erefore, great attention has been paid to dynamic modeling of flexible-link mechanisms (FLMs) to boost the development of effective model-based design or control techniques or to allow for numerical simulations
Summary
The ERLS represents a moving reference from which the elastic displacements are defined. Such an approach allows for a simple formulation and solution of the nonlinear differential equations governing the system motion. Where ui is the vector of the nodal elastic displacements of the ith element expressed with respect to the ERLS, and ri is the vector of the nodal positions of the ith element of the ERLS and it is a function of the ERLS generalized coordinates q, that is, it can be computed through the rigidbody kinematics. The absence of a stable equilibrium would make the mechanism diverge from the initial configuration after the excitations, and the system dynamics would not meet the basic assumption beneath the linearized model.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
