Form generation of rigid origami for approximation of a curved surface based on mechanical property of partially rigid frames

A method is presented for approximating a curved surface by developable rigid origami; polyhedral shape which can be developed to plane without deformation of its facets. Form generation starts from triangulated surface, and an optimization problem solved obtain polyhedron satisfies the geometric conditions developability. The degrees freedom origami mechanism with only triangular facets are often too large engineering application, therefore, it sequentially reduced fixing (removing) some crease lines, along rotate. However, line that not fixed becomes unable rotate in process lines; consequently, cannot plane. To avoid such unfavorable locking situation, selection criteria proposed. They defined based on eigenvalues their derivatives stiffness matrix frame model, numerical model form analysis origami. performance proposed demonstrated through examples surfaces patterns lines.