  Rigid origami is a branch of origami with great potential in engineering
applications to deal with rigid-panel folding. One of the challenges is to
compactly fold the polyhedra made from rigid facets with a single degree of
freedom. In this paper, we present a new method to design origami cubes with
three fundamental characteristics, rigid foldability, flat foldability and one
degree of freedom (DOF). A total of four cases of crease patterns that enable
origami cubes with distinct folding performances have been proposed with all
possible layouts of the diagonal creases on the square facets of origami cubes.
Moreover, based on the kinematic equivalence between the rigid origami and the
spherical linkages, the corresponding spherical linkage loops are introduced
and analysed to reveal the motion properties of the origami cubes. The newly
found method can be readily utilized to design deployable structures for
various engineering applications including cube-shaped cartons, small
satellites, containers, etc.
