Kinematics and Dynamics of Nanostructured Origami

Two-dimensional (2D) nanofabrication processes such as lithography are the primary tools for building functional nanostructures. The third spatial dimension enables completely new devices to be realized, such as photonic crystals with arbitrary defect structures and materials with negative index of refraction [1]. Presently, available methods for threedimensional (3D) nanopatterning tend to be either cost inefficient or limited to periodic structures. The Nanostructured Origami method fabricates 3D devices by first patterning nanostructures (electronic, optical, mechanical, etc) onto a 2D substrate and subsequently folding segments along predefined creases until the final design is obtained [2]. This approach allows almost arbitrary 3D nanostructured systems to be fabricated using exclusively 2D nanopatterning tools. In this paper, we present two approaches to the kinematic and dynamic modeling of folding origami structures. The first approach deals with the kinematics of unfolding single-vertex origami. This work is based on research conducted in the origami mathematics community, which is making rapid progress in understanding the geometry of origami and folding in general [3]. First, a unit positive “charge” is assigned to the creases of the structure in its folded state. Thus, each configuration of the structure as it unfolds can be assigned a value of electrostatic (Coulomb) energy. Because of repulsion between the positive charges, the structure will unfold if allowed to decrease its energy. If the energy minimization can be carried out all the way to the completely unfolded state, we are simultaneously guaranteed of the absence of collisions for the determined path. The second method deals with dynamic modeling of folding multi-segment (accordion style) origamis. The actuation method for folding the segments uses a thin, stressed metal layer that is deposited as a hinge on a relatively stress free structural layer. Through the use of robotics routines, the hinges are modeled as revolute joints, and the system dynamics are calculated.