Kinematics of 3 D Folding Structures for Nanostructured

The 3D Optical Systems Group at MIT investigates Nanostructured Origami 3D fabrication and assembly. The idea is to assemble complex hybrid (chemical or biological reactors, optical sensing, digital electronic logic, mechanical motion) systems in 3D by using exclusively 2D lithography technology. The 3D shape is obtained by folding the initial 2D membrane in a prescribed way, in a manner reminiscent of the Japanese art of origami (paper-folding). The patterning method (2D nanolithography, nanoimprinting and other techniques) as well as the actuation principle (Lorentz force actuation) which is responsible for initializing the folding process have already been developed and established. The knowledge of the dynamic folding process itself, needed to reach any desired 3D shape from a 2D initial state is to-date unexplored. Hence, the primary objective of this thesis is to determine the motions required to reach the goal (folded state) from a given initial state (unfolded). Hereto general folding operations will be analyzed and a new method to describe its kinematics for any arbitrary structure will be developed. We propose to use origami mathematics in combination with kinematical formulations in the area of robotics and gearing. The most attractive feature of origami is that one can construct a wide variety of complex shapes using a few axioms, simple fixed initial conditions and one mechanical operation, a fold. In a second step, the idea will be pursued to transfer this paper folding concept to a more generally admitted approach which uncouples the paper aspect from the folding operation. Hereby a combination of bodies, which are connected by joints, is used to describe the crease structure. As a result, the crease structure is represented in terms of a closed-loop Multi Body System (MBS) with the property that a change of relative motion at one location induces a change of relative motion elsewhere. To describe this system, a well-known mathematical method, called screw calculus will be applied. Screw calculus is based on Poinsot’s result that an arbitrary rigid body motion can be described in terms of a translation cascaded with a rotation around the translation axis. The “screw” then is a matrix exponential describing the motion. By cascading several screws together one can describe the motion of articulated rigid body systems, such as robotic manipulators and, in our case, origami. The results of the theoretical investigation will be implemented in a design and simulation software tool. The application has features to verify and create folding structures as well as to visualize the folding operation on the basis of the above mentioned kinematics approach.