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.
An Analytical Formulation for the Geometrico-Static Problem of Continuum Planar Parallel Robots / Zaccaria F.; Briot S.; Chikhaoui M.T.; Ida E.; Carricato M.. - STAMPA. - 601:(2021), pp. 512-520. [10.1007/978-3-030-58380-4_61]
An Analytical Formulation for the Geometrico-Static Problem of Continuum Planar Parallel Robots
Zaccaria F.;Ida E.;Carricato M.
2021
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.