[Modifications importantes de la mécanique du pantographe avec léger repositionnement des nœuds]
Pantographic unit cells are well-known and used both for deployable structures and metamaterials design. It is surely less known that with minor changes, moving the nodes in the reference configuration or using angulated elements, this unit cells can be used to build curved shapes in the strain-free configuration. Curved pantographs are employable in several technical applications. One interesting application is related with robot arms. The peculiar characteristic of pantographic structures, linear or curved, is the existence of a floppy mode, i.e. a zero energy mode, which ensures the existence of a branch of the equilibrium path without strain in all its parts. This characteristic provides the deployability of the pantographic structures and several exotic mechanical behaviours in metamaterials based on the same pattern. We discuss some results obtained by a mechanical digital twin capable of: (i) verifying the deployability, i.e. the existence of a floppy mode when it is not prevented by constraints, of the considered scheme checking for the whole equilibrium path the absence of strain on all the springs modelling the problem; (ii) providing some information, useful for a preliminary structural design, about the mechanical behaviour of a simple structural scheme in the hypothesis of large displacements when the floppy mode is prevented by a large enough number of constraints.
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Les cellules unitaires pantographiques sont bien connues et utilisées à la fois pour les structures déployables et la conception de métamatériaux. Il est certainement moins connu qu’avec des modifications mineures, en déplaçant les nœuds dans la configuration de référence ou en utilisant des éléments angulaires, ces cellules unitaires peuvent être utilisées pour construire des formes courbes dans une configuration sans contrainte. Les pantographes courbes peuvent être utilisés dans plusieurs applications techniques. Une application intéressante concerne les bras robotiques. La caractéristique particulière des structures pantographiques, linéaires ou courbes, est l’existence d’un mode floppy, c’est-à-dire un mode à énergie nulle, qui garantit l’existence d’une branche du chemin d’équilibre sans contrainte dans toutes ses parties. Cette caractéristique permet le déploiement des structures pantographiques et plusieurs comportements mécaniques exotiques dans les métamatériaux basés sur le même modèle. Nous discutons certains résultats obtenus par un jumeau numérique mécanique capable de : (i) vérifier la déployabilité, c’est-à-dire l’existence d’un mode floppy lorsqu’il n’est pas empêché par des contraintes, du schéma considéré en vérifiant pour l’ensemble du chemin d’équilibre l’absence de contrainte sur tous les ressorts modélisant le problème ; (ii) fournir des informations utiles pour une conception structurelle préliminaire sur le comportement mécanique d’un schéma structurel simple dans l’hypothèse de grands déplacements lorsque le mode floppy est empêché par un nombre suffisant de contraintes.
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Mots-clés : Mécanique des pantographes courbes, analyse des grands déplacements, modèle à éléments discrets, structures déployables
Emilio Turco 1
CC-BY 4.0
@article{CRMECA_2026__354_G1_183_0,
author = {Emilio Turco},
title = {Heavy changes in pantograph mechanics with slight repositioning of nodes},
journal = {Comptes Rendus. M\'ecanique},
pages = {183--201},
year = {2026},
publisher = {Acad\'emie des sciences, Paris},
volume = {354},
doi = {10.5802/crmeca.352},
language = {en},
}
Emilio Turco. Heavy changes in pantograph mechanics with slight repositioning of nodes. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 183-201. doi: 10.5802/crmeca.352
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