  Origami crease patterns are folding paths that transform flat sheets into
spatial objects. Origami patterns with a single degree of freedom (DOF) have
creases that fold simultaneously. More often, several substeps are required to
sequentially fold origami of multiple DOFs, and at each substep some creases
fold and the rest remain fixed. In this study, we combine the loop closure
constraint with Lagrange multiplier method to account for the sequential
folding of rigid origami of multiple DOFs, by controlling the rotation of
different sets of creases during successive substeps. This strategy is also
applicable to model origami-inspired devices, where creases may be equipped
with rotational springs and the folding process involves elastic energy.
Several examples are presented to verify the proposed algorithms in tracing the
sequential folding process as well as searching the equilibrium configurations
of origami with rotational springs.
