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.
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Notes
- 1.
Gravitational loads were neglected for brevity sake, but they can be introduced into Eq. (5) as nodal external actions \(\mathbf {f}_i\) and \(m_i\).
- 2.
Other types of joints could be considered as well, but we focus on revolute joints for the sake of brevity.
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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: Venture, G., Solis, J., Takeda, Y., Konno, A. (eds) ROMANSY 23 - Robot Design, Dynamics and Control. ROMANSY 2020. CISM International Centre for Mechanical Sciences, vol 601. Springer, Cham. https://doi.org/10.1007/978-3-030-58380-4_61
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DOI: https://doi.org/10.1007/978-3-030-58380-4_61
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