Full and reduced models for the elastodynamics of fully flexible parallel robots

The elastodynamic analysis of parallel robots still has limitations related to the difficulty of including parts with several input/output nodes. This results in the impossibility of considering fully flexible parallel mechanisms and, therefore, most of the models proposed in the literature only consider flexible legs connected to a rigid moving platform. In this paper, the MSA/CMS-based formulation proposed in Cammarata et al. (2019)[1] is extended to full and reduced models able to describe the elastodynamic of fully flexible parallel robots. In the proposed models, all components can be modeled using different types of finite elements and multiple forces can be applied at multiple input nodes while displacements can be evaluated at several output nodes. Within this MSA/CMS framework, important applications concerning the Cartesian matrices and the direct singularities are investigated. In particular, a novel derivation of the Cartesian stiffness and inertia matrices for parallel robots is provided. The proposed method allows for obtaining consistent Cartesian matrices at different nodes of interest without redefining the transformation matrices typical of the Jacobian-based methods. Finally, the numerical results reveal that the direct singularities of the lower-mobility parallel robots can be also detected using an MSA-based formulation without using any Jacobian analysis.