An Analytical Formulation for the Geometrico-static Problem of Continuum Planar Parallel Robots

Federico Zaccaria , Sébastien Briot (1, 2, 3) , Mohamed Taha Chikhaoui (4, 5) , Edoardo Idá (6) , Marco Carricato (7)

1 LS2N - équipe ARMEN - Autonomie des Robots et Maîtrise des interactions avec l’ENvironnement
2 CNRS - Centre National de la Recherche Scientifique
3 LS2N - Laboratoire des Sciences du Numérique de Nantes
4 TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications Grenoble - UMR 5525
5 TIMC-IMAG-GMCAO - Gestes Médico-chirurgicaux Assistés par Ordinateur
6 DISI - Dipartimento di Scienze dell'Informazione [Bologna]
7 DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]

In this paper, we provide an analytical formulation for the geometrico-static problem of continuum planar parallel robots. This formulation provides to an analytical computation of a set of equations governing the equilibrium configurations. We also introduce a stability criterion of the computed configurations. This formulation is based on the use of Kirchhoff's rod deformation theory and finite-difference approximations. Their combination leads to a quadratic expression of the rod's deformation energy. Equilibrium configurations of a planar parallel robot composed of two hinged flexible rods are computed according to this new formulation and compared with the ones obtained with state-of-the-art approaches. By assessing equilibrium stability with the proposed technique, new unstable configurations are determined.

Domaines: Robotique [cs.RO]

Federico Zaccaria, Sébastien Briot, Mohamed Taha Chikhaoui, Edoardo Idá, Marco Carricato. An Analytical Formulation for the Geometrico-static Problem of Continuum Planar Parallel Robots. 23rd CISM IFToMM Symposium on Robot Design, Dynamics and Control (RoManSy 2020), Sep 2020, Sapporo, Japan. ⟨hal-02849910⟩