Panel-Pin Model for Kinematic and Equilibrium Analysis of Rigid Origami

In this study, the mathematical model referred to as the panel-pin model is proposed for analyzing the infinitesimal-deformation mechanism and the large-deformation equilibrium path of a rigid origami composed of rigid faces (panels) and subjected to deformation only at its crease lines. The panel-pin model represents a rigid origami as a structure of rigid panels pin-connected at the vertices and has the following advantages: 1) consistent formulation of compatibility equations for any type of the rigid origami structure; 2) systematic computation of vertex displacements, folding angles, and their derivatives; and 3) ease of accounting for gravity acting on the panels. The infinitesimal mechanism of the panel-pin model is studied according to the standard procedure for mechanisms and linkages, and an equilibrium path is traced as the trajectory of equilibrium points obtained by minimizing the total potential energy of the model with a rotational spring along each crease line. The numerical examples with multiple degrees of freedom of the mechanism show that the multiple equilibrium paths can be obtained by assigning the initial imperfection, and this is also confirmed by the physical model.