Repetitive skeletal structures controlled with bracing elements

Abstract

Bar and joint frameworks provide useful models to the structure of building, metals, glasses, crystal states materials, nano-materials, and some biological systems. Using the symmetry and the periodicity of the structures, their rigidity is a problem of long-standing interest in kinematics, statics, and optimization. We considered the skeletal of a wide class of 3-dimensional tiling with the special assumption that the original polygonal faces are allowed to deform in a way that faces remaining central symmetrical and not necessarily planar. Some vectors that represent the parallel edges with the bracing elements as auxiliary framework characterize the mobility of this framework. A new theorem provides a necessary and sufficient condition for the rigidity of the tiling framework applying face diagonals as bracing elements. This result implies an efficient algorithm for the rigidity of the braced tiling structure. Based on simple elements, we construct new mechanisms which move as the skeleton tiling structure with the planar and the central symmetrical assumption. In the applications we regard the bracing elements as actuators; we provide a method controlling the motion of braced reconfigurable meta-materials and the rhombic type origami.