A folding analysis method for origami based on the frame with kinematic indeterminacy

Abstract The kinematic analysis of the folding process is important in practical engineering applications of the mechanism of origami. This paper proposes an efficient methodology for tracing the folding process of origami in a three-dimensional space. This method directly controls the nodal coordinates in the origami model activated by external force on the vertices. The deforming path is obtained using an algorithm based on the generalized inverse theory. An improved type of origami unit is presented for the computational calculation. The results demonstrate that the computational efficiency is strongly related not only to the number of the unknowns, but also the singular value of the compatibility matrix of the origami model. Furthermore, the validity and versatility of the proposed method are confirmed through numerical examples, including general origami models, origami with gravity, origami with special boundary conditions, and curved-crease origami. The proposed method is validated to be feasible and efficient in analyzing the folding mechanism of origami structures for kinematic design in structural and mechanical applications.

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