Indices for Stiffness and Singularity Evaluation for Designing 5R Parallel Manipulators

Rogério Sales Goncalves1, Joao Carlos Mendes Carvalho1, Giuseppe Carbone*, 2, Marco Ceccarelli*, 2
1 School of Mechanical Engineering, Federal University of Uberlândia, Uberlândia, Brasil
2 LARM, DiMSAT, University of Cassino, Cassino, Italy

© 2010 Gonçalves et al

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the LARM, DiMSAT, University of Cassino, Cassino, Italy; Tel: +39-0776-2993663; Fax: +39-0776-2993989; E-mails:,


Parallel manipulators have various advantages over serial robots but they have a few drawbacks mainly referring to stiffness and singularities. Close to or in singular configurations the structure can not resist an external wrench applied to the mobile platform, therefore it may have uncontrolled movements. The study of the stiffness becomes of primary importance to design multibody robotic systems in order to properly choose materials, component geometry, shape and size, and the interaction of each component with others. This paper addresses the problem of a numerical evaluation of the structure stiffness by using the Matrix Structural Analysis when considering both links and joint stiffness, and by analyzing the singularity through stiffness performance indices. In order to prove the feasibility of the methodology for design purposes, the case for 5R parallel manipulator is formulated by comparing several stiffness performance indices.

Keywords: Parallel robots, stiffness matrix, matrix structural analysis, singularity, stiffness performance indice.