Dynamic analysis of flexible parallel robots via enhanced co-rotational and rigid finite element formulations

The aim of this paper is to develop formulations for the dynamic analysis of parallel robots considering the links flexibility. These formulations are based on two popular methods which are used frequently in the literature, the Co-rotational and Rigid finite elements. In the first part of this study, the co-rotational elements are incorporated to model the flexible links. Unlike the common co-rotational formulations presented in the literature, the deformation of each element is described directly in its co-rotated frame without the need of expressing any intricate kinematic relations. In the second part, a formulation based on the rigid finite element method is elaborated. The formulation simplifies the form and derivation of kinetic energy of a flexible link, with respect to the co-rotational elements, at the cost of assuming the elements to be rigid. Choosing the Delta parallel robot as a case study, the two aforementioned formulations are implemented and evaluated. The numerical simulations show that, for the same number of nodes, the results differed by 6% in the worst case. However, in terms of computational cost, the rigid finite element formulation always reduces the simulation time by 31%–46%.