Role of Connectivity in the Conformational Control of Maxwell Frames

Understanding conformational changes is crucial for programming and controlling the function of many mechanical systems such as allosteric enzymes, auxetics, and tunable metamaterials. Of particular interest is the relationship between the network setup (connection topology and geometry) and specific observed motions under controlling perturbations. Here we study this relationship in mechanical networks of 2-D and 3-D Maxwell frames composed of point masses connected by rigid rods with zero bending modulus about the masses. We first develop some basic principles that yield a simplified and intuitive understanding of how complex network connectivity gives rise to specific zero modes. Using these principles, we then construct networks with desirable properties such as modularity, tunable Poisson ratio, and multiple modes of conformation.