Heavy changes in pantograph mechanics with slight repositioning of nodes

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.