On the Elastodynamics of Parallel Kinematic Machines

Alessandro Cammarata¹; Rosario Sinatra¹

¹ Dipartimento Ingegneria Industriale - Università di Catania

doi:10.20906/CPS/COB-2015-2122

Resumo

The elastodynamics of Parallel Kinematic Machines (PKMs) becomes of outmost importance with the increase in performance. The need to reduce the working time and the energy required to perform an operation requires designers to provide a careful analysis of the distribution of masses and stiffnesses of the parts composing a PKM. Light materials such as aluminum alloys, carbon fibre or titanium are used to reduce the moving masses without weakening the structural integrity of the robot. This article proposes a methodology based on the Matrix Structural Analysis for the study of the elastodynamics of PKMs. The method can be used to combine rigid and flexible parts through different types of joints. In particular, these are implicitly included without resorting to the Lagrange multipliers and can be either rigid or flexible. The flexible bodies must be reduced to two-nodes elastic elements and may be of different nature: Euler or Timoshenko beams, super-elements obtained through FEM, continuous elements. Through a series of examples, the method is applied to the planar PKMs and spatial PKMs with reduced mobility to show the possible applications in terms of natural frequencies and modes determination, structural optimization of the components of a given architecture, comparison of the frequency response of different architectures used for the same purpose.

Palavras-chave: Elastodynamics ; Parallel Kinematic Machines ; Vibrations