Collapsible scissored surfaces

We introduce an additive approach for the design of a class of transformable structures based on two-bar linkages ("scissor mechanisms") joined at vertices to form a two-dimensional mesh which we call a pantograph lattice. Our approach shows how these lattices unfold from a one-dimensional collapsed state to two-dimensional surfaces of single and double curvature. We provide an algorithm for growing pantograph structures that allows us to explore the full space of possible mechanisms, and we use it to computationally design and physically assemble a series of examples of varying complexity. We finally demonstrate a streamlined method for automated fabrication of pantograph lattices using multimaterial 3D printing.