Tiled Plates with One Degree of Freedom

We investigate a design concept for thin tiled plates having exactly one degree of freedom. A tiled plate is realized as a tessellation composed by rigid tiles hinged to each other along the sides. The plate can deform in just one way, that is, into a predetermined surface. The family of tilings we consider, the monohedral hexagonal one, with either convex or concave tiles, is rich enough to include many noteworthy tessellations. Corresponding plates can approximate surfaces with positive, negative, and null Gaussian curvature, and may exhibit an auxetic behavior. The proposed architecture is highly scalable and easily manufacturable, and it can find applications not only for civil and aerospace engineering purposes, but also for biomechanical scaffolds, energy harvesters, and wearable devices.