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.
CITATION STYLE
Zaccaria, F., Briot, S., Chikhaoui, M. T., Idà, E., & Carricato, M. (2021). An Analytical Formulation for the Geometrico-Static Problem of Continuum Planar Parallel Robots. In CISM International Centre for Mechanical Sciences, Courses and Lectures (Vol. 601, pp. 512–520). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-58380-4_61
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