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Origami-inspired structures and material systems have been used in many engineering applications because of their unique kinematic and mechanical properties induced by folding. However, accurately modeling and analyzing origami folding and the associated mechanical properties are challenging, especially when large deformation and dynamic responses need to be considered. In this paper, we formulate a high-fidelity model — based on the iso-parametric Absolute Nodal Coordinate Formulation (ANCF) — for simulating the dynamic folding behaviors of origami involving large deformation. The centerpiece of this new model is the characterization of crease deformation. To this end, we model the crease using rotational spring at the nodes. The corresponding folding angle is calculated based on the local surface normal vectors. Compared to the currently popular analytical methods for analyzing origami, such as the rigid-facet and equivalent bar-hinge approach, this new model is more accurate in that it can describe the large crease and facet deformation without imposing many assumptions. Meanwhile, the ANCF based origami model can be more efficient computationally compared to the traditional finite element simulations. Therefore, this new model can lay down the foundation for high-fidelity origami analysis and design that involves mechanics and dynamics. 

Recently, multi-stable origami structures and material systems have shown promising potentials to achieve multi-functionality. Especially, origami folding is fundamentally a three-dimensional mechanism, which imparts unique capabilities not seen in the more traditional multi-stable systems. This paper proposes and analytically examines a multi-stable origami cellular structure that can exhibit asymmetric energy barriers and a mechanical diode behavior in compression. Such a structure consists of many stacked Miura-ori sheets of different folding stiffness and accordion-shaped connecting sheets, and it can be divided into unit cells that features two different stable equilibria. To understand the desired diode behavior, this study focuses on two adjacent unit cells and examines how folding can create a kinematic constraint onto the deformation of these two cells. Via estimating the elastic potential energy landscape of this dual cell system. we find that the folding-induced kinematic constraint can significantly increase the potential energy barrier for compressing the dual-cell structure from a certain stable state to another, however, the same constraint would not increase the energy barrier of the opposite extension switch. As a result, one needs to apply a large force to compress the origami cellular structure but only a small force to stretch it, hence a mechanical diode behavior. Results of this study can open new possibilities for achieving structural motion rectifying, wave propagation control, and embedded mechanical computation. 

This research investigates the feasibility of utilizing origami folding techniques to create an optimized jumping mechanism. As a theoretical example, we study the dynamic characteristics of a jumping mechanism consisting of two masses connected by a Tachi-Miura Polyhedron (TMP) origami structure with nonlinear stiffness characteristics. We show how the desired “strain-softening” effects of the TMP structure can lead to design of jumping mechanisms with optimized performance. The kinematics of TMP origami structure is reviewed and a modified model of its reaction-force displacement curve is presented. We derive the equations of motion of the jumping process and use their numerical solutions extensively for design optimization. Through this process we are able to obtain optimum geometrical configurations for two different objectives: The maximum time spent in the air and the maximum clearance off the ground. Results of this study can lead to emergence of a new generation of more efficient jumping mechanisms with optimized performance in the future.