  We present an additive approach for the inverse design of kirigami-based
mechanical metamaterials by focusing on the empty (negative) spaces instead of
the solid tiles. By considering each negative space as a four-bar linkage, we
identify a simple recursive relationship between adjacent linkages, yielding an
efficient method for creating kirigami patterns. This allows us to solve the
kirigami design problem using elementary linear algebra, with compatibility,
reconfigurability and rigid-deployability encoded into an iterative procedure
involving simple matrix multiplications. The resulting linear design strategy
circumvents the solution of a non-convex global optimization problem and allows
us to control the degrees of freedom in the deployment angle field, linkage
offsets and boundary conditions. We demonstrate this by creating a large
variety of rigid-deployable, compact, reconfigurable kirigami patterns. We then
realize our kirigami designs physically using two simple but effective
fabrication strategies with very different materials. Altogether, our additive
approaches present routes for efficient mechanical metamaterial design and
fabrication based on ori/kirigami art forms.
