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.

翻译：我们提出了一种基于剪纸的力学超材料逆向设计的加法方法，通过关注空白（负空间）而非实体单元。将每个负空间视为四杆机构后，我们发现相邻机构间存在简单的递归关系，从而建立了生成剪纸图案的高效方法。该方法通过基础线性代数解决剪纸设计问题，将兼容性、可重构性与刚性可展开性编码为包含简单矩阵乘法的迭代过程。这种线性设计策略避免了求解非凸全局优化问题，并使我们能够控制展开角度场、机构偏移量及边界条件中的自由度。我们通过生成大量刚性可展开、紧凑、可重构的剪纸图案验证了该方法，并采用两种简单有效的制造策略（使用截然不同的材料）实现了剪纸设计的物理成型。综上所述，我们的加法方法为基于折纸/剪纸艺术形式的力学超材料高效设计与制造提供了可行途径。