Design of Pantograph Lattices

A pantograph mechanism is a four bar linkage which is traditionally used as a mechanical aid for reproducing drawings and sculptures at different scales. We characterize a class of linkage-based lattice surface structures inspired by the pantograph mechanism which transform between a deployed three dimensional geometry and a folded one dimensional state. The deployed geometry is generated through choice of the length of legs of each pantograph mechanism which must also satisfy a local constraint we name “flat-shearabilithy” which ensures compatibility with the folded state.

We derive an additive algorithm for the construction of such flat-sharable structures and demonstrate that it can design lattices which map to any quad-meshed surface including geometries with single and double curvature. We build a set of desktop-scale models using plastic sheeting and rivets to demonstrate our algorithm and a possible construction methodology for macro-scale architectures.

In addition, we note that pantograph lattices may be used as a platform for physical computing: as an example we construct a lattice of bistable nodes which can be reset using the collapsing mechanism.