Conformational control of mechanical networks

Understanding conformational change is crucial for programming and controlling the function of many mechanobiological and mechanical systems such as robots, enzymes and tunable metamaterials. These systems are often modelled as constituent nodes (for example, joints or amino acids) whose motion is restricted by edges (for example, limbs or bonds) to yield functionally useful coordinated motions (for example, walking or allosteric regulation). However, the design of desired functions is made difficult by the complex dependence of these coordinated motions on the connectivity of edges. Here, we develop simple mathematical principles to design mechanical systems that achieve any desired infinitesimal or finite coordinated motion. We specifically study mechanical networks of two- and three-dimensional frames composed of nodes connected by freely rotating rods and springs. We first develop simple principles that govern all networks with an arbitrarily specified motion as the sole zero-energy mode. We then extend these principles to characterize networks that yield multiple specified zero modes, generate pre-stress stability and display branched motions. By coupling individual modules, we design networks with negative Poisson’s ratio and allosteric response. Finally, we extend our framework to networks with arbitrarily specifiable initial and final positions to design energy minima at desired geometric configurations, and create networks demonstrating tristability and cooperativity