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.
Zaccaria F., Briot S., Chikhaoui M.T., Ida E., Carricato M. (2021). An Analytical Formulation for the Geometrico-Static Problem of Continuum Planar Parallel Robots. Cham : Springer [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.
